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What is a Hypothesis – Types, Examples and Writing Guide

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Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

• Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
• Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
• Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
• Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
• Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
• Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

• Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
• Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
• Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
• Education : “Implementing a new teaching method will result in higher student achievement scores.”
• Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
• Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
• Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

• In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
• In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
• I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
• Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
• Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

• Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
• Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
• Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
• Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
• Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
• Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

• Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
• May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
• May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
• Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
• Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
• May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

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• Knowledge Base

Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

• State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a  or H 1 ).
• Collect data in a way designed to test the hypothesis.
• Perform an appropriate statistical test .
• Decide whether to reject or fail to reject your null hypothesis.
• Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

• H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

• an estimate of the difference in average height between the two groups.
• a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

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The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

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• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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Statistics Made Easy

Introduction to Hypothesis Testing

A statistical hypothesis is an assumption about a population parameter .

For example, we may assume that the mean height of a male in the U.S. is 70 inches.

The assumption about the height is the statistical hypothesis and the true mean height of a male in the U.S. is the population parameter .

A hypothesis test is a formal statistical test we use to reject or fail to reject a statistical hypothesis.

The Two Types of Statistical Hypotheses

To test whether a statistical hypothesis about a population parameter is true, we obtain a random sample from the population and perform a hypothesis test on the sample data.

There are two types of statistical hypotheses:

The null hypothesis , denoted as H 0 , is the hypothesis that the sample data occurs purely from chance.

The alternative hypothesis , denoted as H 1 or H a , is the hypothesis that the sample data is influenced by some non-random cause.

Hypothesis Tests

A hypothesis test consists of five steps:

1. State the hypotheses. 

State the null and alternative hypotheses. These two hypotheses need to be mutually exclusive, so if one is true then the other must be false.

2. Determine a significance level to use for the hypothesis.

Decide on a significance level. Common choices are .01, .05, and .1. 

3. Find the test statistic.

Find the test statistic and the corresponding p-value. Often we are analyzing a population mean or proportion and the general formula to find the test statistic is: (sample statistic – population parameter) / (standard deviation of statistic)

4. Reject or fail to reject the null hypothesis.

Using the test statistic or the p-value, determine if you can reject or fail to reject the null hypothesis based on the significance level.

The p-value  tells us the strength of evidence in support of a null hypothesis. If the p-value is less than the significance level, we reject the null hypothesis.

5. Interpret the results. 

Interpret the results of the hypothesis test in the context of the question being asked. 

The Two Types of Decision Errors

There are two types of decision errors that one can make when doing a hypothesis test:

Type I error: You reject the null hypothesis when it is actually true. The probability of committing a Type I error is equal to the significance level, often called  alpha , and denoted as α.

Type II error: You fail to reject the null hypothesis when it is actually false. The probability of committing a Type II error is called the Power of the test or  Beta , denoted as β.

One-Tailed and Two-Tailed Tests

A statistical hypothesis can be one-tailed or two-tailed.

A one-tailed hypothesis involves making a “greater than” or “less than ” statement.

For example, suppose we assume the mean height of a male in the U.S. is greater than or equal to 70 inches. The null hypothesis would be H0: µ ≥ 70 inches and the alternative hypothesis would be Ha: µ < 70 inches.

A two-tailed hypothesis involves making an “equal to” or “not equal to” statement.

For example, suppose we assume the mean height of a male in the U.S. is equal to 70 inches. The null hypothesis would be H0: µ = 70 inches and the alternative hypothesis would be Ha: µ ≠ 70 inches.

Note: The “equal” sign is always included in the null hypothesis, whether it is =, ≥, or ≤.

Related:   What is a Directional Hypothesis?

Types of Hypothesis Tests

There are many different types of hypothesis tests you can perform depending on the type of data you’re working with and the goal of your analysis.

The following tutorials provide an explanation of the most common types of hypothesis tests:

Introduction to the One Sample t-test Introduction to the Two Sample t-test Introduction to the Paired Samples t-test Introduction to the One Proportion Z-Test Introduction to the Two Proportion Z-Test

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• Knowledge Base
• Methodology
• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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How to Write a Great Hypothesis

Hypothesis Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk,  "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis, operational definitions, types of hypotheses, hypotheses examples.

• Collecting Data

Frequently Asked Questions

A hypothesis is a tentative statement about the relationship between two or more  variables. It is a specific, testable prediction about what you expect to happen in a study.

One hypothesis example would be a study designed to look at the relationship between sleep deprivation and test performance might have a hypothesis that states: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. It is only at this point that researchers begin to develop a testable hypothesis. Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore a number of factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk wisdom that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis.   In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in a number of different ways. One of the basic principles of any type of scientific research is that the results must be replicable.   By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. How would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

In order to measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming other people. In this situation, the researcher might utilize a simulated task to measure aggressiveness.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests that there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type of hypothesis suggests a relationship between three or more variables, such as two independent variables and a dependent variable.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative sample of the population and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• Complex hypothesis: "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "Children who receive a new reading intervention will have scores different than students who do not receive the intervention."
• "There will be no difference in scores on a memory recall task between children and adults."

Examples of an alternative hypothesis:

• "Children who receive a new reading intervention will perform better than students who did not receive the intervention."
• "Adults will perform better on a memory task than children." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when it would be impossible or difficult to  conduct an experiment . These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a correlational study can then be used to look at how the variables are related. This type of research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

A Word From Verywell

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Some examples of how to write a hypothesis include:

• "Staying up late will lead to worse test performance the next day."
• "People who consume one apple each day will visit the doctor fewer times each year."
• "Breaking study sessions up into three 20-minute sessions will lead to better test results than a single 60-minute study session."

The four parts of a hypothesis are:

• The research question
• The independent variable (IV)
• The dependent variable (DV)
• The proposed relationship between the IV and DV

Castillo M. The scientific method: a need for something better? . AJNR Am J Neuroradiol. 2013;34(9):1669-71. doi:10.3174/ajnr.A3401

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Table of Contents

In today’s data-driven world , decisions are based on data all the time. Hypothesis plays a crucial role in that process, whether it may be making business decisions, in the health sector, academia, or in quality improvement. Without hypothesis & hypothesis tests, you risk drawing the wrong conclusions and making bad decisions. In this tutorial, you will look at Hypothesis Testing in Statistics.

What Is Hypothesis Testing in Statistics?

Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.

Let's discuss few examples of statistical hypothesis from real-life - 

• A teacher assumes that 60% of his college's students come from lower-middle-class families.
• A doctor believes that 3D (Diet, Dose, and Discipline) is 90% effective for diabetic patients.

Now that you know about hypothesis testing, look at the two types of hypothesis testing in statistics.

Hypothesis Testing Formula

Z = ( x̅ – μ0 ) / (σ /√n)

• Here, x̅ is the sample mean,
• μ0 is the population mean,
• σ is the standard deviation,
• n is the sample size.

How Hypothesis Testing Works?

An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.

The null hypothesis is typically an equality hypothesis between population parameters; for example, a null hypothesis may claim that the population means return equals zero. The alternate hypothesis is essentially the inverse of the null hypothesis (e.g., the population means the return is not equal to zero). As a result, they are mutually exclusive, and only one can be correct. One of the two possibilities, however, will always be correct.

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Null Hypothesis and Alternate Hypothesis

The Null Hypothesis is the assumption that the event will not occur. A null hypothesis has no bearing on the study's outcome unless it is rejected.

H0 is the symbol for it, and it is pronounced H-naught.

The Alternate Hypothesis is the logical opposite of the null hypothesis. The acceptance of the alternative hypothesis follows the rejection of the null hypothesis. H1 is the symbol for it.

Let's understand this with an example.

A sanitizer manufacturer claims that its product kills 95 percent of germs on average. 

To put this company's claim to the test, create a null and alternate hypothesis.

H0 (Null Hypothesis): Average = 95%.

Alternative Hypothesis (H1): The average is less than 95%.

Another straightforward example to understand this concept is determining whether or not a coin is fair and balanced. The null hypothesis states that the probability of a show of heads is equal to the likelihood of a show of tails. In contrast, the alternate theory states that the probability of a show of heads and tails would be very different.

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Hypothesis Testing Calculation With Examples

Let's consider a hypothesis test for the average height of women in the United States. Suppose our null hypothesis is that the average height is 5'4". We gather a sample of 100 women and determine that their average height is 5'5". The standard deviation of population is 2.

To calculate the z-score, we would use the following formula:

z = ( x̅ – μ0 ) / (σ /√n)

z = (5'5" - 5'4") / (2" / √100)

z = 0.5 / (0.045)

 We will reject the null hypothesis as the z-score of 11.11 is very large and conclude that there is evidence to suggest that the average height of women in the US is greater than 5'4".

Steps of Hypothesis Testing

Step 1: specify your null and alternate hypotheses.

It is critical to rephrase your original research hypothesis (the prediction that you wish to study) as a null (Ho) and alternative (Ha) hypothesis so that you can test it quantitatively. Your first hypothesis, which predicts a link between variables, is generally your alternate hypothesis. The null hypothesis predicts no link between the variables of interest.

Step 2: Gather Data

For a statistical test to be legitimate, sampling and data collection must be done in a way that is meant to test your hypothesis. You cannot draw statistical conclusions about the population you are interested in if your data is not representative.

Step 3: Conduct a Statistical Test

Other statistical tests are available, but they all compare within-group variance (how to spread out the data inside a category) against between-group variance (how different the categories are from one another). If the between-group variation is big enough that there is little or no overlap between groups, your statistical test will display a low p-value to represent this. This suggests that the disparities between these groups are unlikely to have occurred by accident. Alternatively, if there is a large within-group variance and a low between-group variance, your statistical test will show a high p-value. Any difference you find across groups is most likely attributable to chance. The variety of variables and the level of measurement of your obtained data will influence your statistical test selection.

Step 4: Determine Rejection Of Your Null Hypothesis

Your statistical test results must determine whether your null hypothesis should be rejected or not. In most circumstances, you will base your judgment on the p-value provided by the statistical test. In most circumstances, your preset level of significance for rejecting the null hypothesis will be 0.05 - that is, when there is less than a 5% likelihood that these data would be seen if the null hypothesis were true. In other circumstances, researchers use a lower level of significance, such as 0.01 (1%). This reduces the possibility of wrongly rejecting the null hypothesis.

Step 5: Present Your Results 

The findings of hypothesis testing will be discussed in the results and discussion portions of your research paper, dissertation, or thesis. You should include a concise overview of the data and a summary of the findings of your statistical test in the results section. You can talk about whether your results confirmed your initial hypothesis or not in the conversation. Rejecting or failing to reject the null hypothesis is a formal term used in hypothesis testing. This is likely a must for your statistics assignments.

Types of Hypothesis Testing

To determine whether a discovery or relationship is statistically significant, hypothesis testing uses a z-test. It usually checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more, can a z-test be applied.

A statistical test called a t-test is employed to compare the means of two groups. To determine whether two groups differ or if a procedure or treatment affects the population of interest, it is frequently used in hypothesis testing.

Chi-Square 

You utilize a Chi-square test for hypothesis testing concerning whether your data is as predicted. To determine if the expected and observed results are well-fitted, the Chi-square test analyzes the differences between categorical variables from a random sample. The test's fundamental premise is that the observed values in your data should be compared to the predicted values that would be present if the null hypothesis were true.

Hypothesis Testing and Confidence Intervals

Both confidence intervals and hypothesis tests are inferential techniques that depend on approximating the sample distribution. Data from a sample is used to estimate a population parameter using confidence intervals. Data from a sample is used in hypothesis testing to examine a given hypothesis. We must have a postulated parameter to conduct hypothesis testing.

Bootstrap distributions and randomization distributions are created using comparable simulation techniques. The observed sample statistic is the focal point of a bootstrap distribution, whereas the null hypothesis value is the focal point of a randomization distribution.

A variety of feasible population parameter estimates are included in confidence ranges. In this lesson, we created just two-tailed confidence intervals. There is a direct connection between these two-tail confidence intervals and these two-tail hypothesis tests. The results of a two-tailed hypothesis test and two-tailed confidence intervals typically provide the same results. In other words, a hypothesis test at the 0.05 level will virtually always fail to reject the null hypothesis if the 95% confidence interval contains the predicted value. A hypothesis test at the 0.05 level will nearly certainly reject the null hypothesis if the 95% confidence interval does not include the hypothesized parameter.

Simple and Composite Hypothesis Testing

Depending on the population distribution, you can classify the statistical hypothesis into two types.

Simple Hypothesis: A simple hypothesis specifies an exact value for the parameter.

Composite Hypothesis: A composite hypothesis specifies a range of values.

A company is claiming that their average sales for this quarter are 1000 units. This is an example of a simple hypothesis.

Suppose the company claims that the sales are in the range of 900 to 1000 units. Then this is a case of a composite hypothesis.

One-Tailed and Two-Tailed Hypothesis Testing

The One-Tailed test, also called a directional test, considers a critical region of data that would result in the null hypothesis being rejected if the test sample falls into it, inevitably meaning the acceptance of the alternate hypothesis.

In a one-tailed test, the critical distribution area is one-sided, meaning the test sample is either greater or lesser than a specific value.

In two tails, the test sample is checked to be greater or less than a range of values in a Two-Tailed test, implying that the critical distribution area is two-sided.

If the sample falls within this range, the alternate hypothesis will be accepted, and the null hypothesis will be rejected.

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Right Tailed Hypothesis Testing

If the larger than (>) sign appears in your hypothesis statement, you are using a right-tailed test, also known as an upper test. Or, to put it another way, the disparity is to the right. For instance, you can contrast the battery life before and after a change in production. Your hypothesis statements can be the following if you want to know if the battery life is longer than the original (let's say 90 hours):

• The null hypothesis is (H0 <= 90) or less change.
• A possibility is that battery life has risen (H1) > 90.

The crucial point in this situation is that the alternate hypothesis (H1), not the null hypothesis, decides whether you get a right-tailed test.

Left Tailed Hypothesis Testing

Alternative hypotheses that assert the true value of a parameter is lower than the null hypothesis are tested with a left-tailed test; they are indicated by the asterisk "<".

Suppose H0: mean = 50 and H1: mean not equal to 50

According to the H1, the mean can be greater than or less than 50. This is an example of a Two-tailed test.

In a similar manner, if H0: mean >=50, then H1: mean <50

Here the mean is less than 50. It is called a One-tailed test.

Type 1 and Type 2 Error

A hypothesis test can result in two types of errors.

Type 1 Error: A Type-I error occurs when sample results reject the null hypothesis despite being true.

Type 2 Error: A Type-II error occurs when the null hypothesis is not rejected when it is false, unlike a Type-I error.

Suppose a teacher evaluates the examination paper to decide whether a student passes or fails.

H0: Student has passed

H1: Student has failed

Type I error will be the teacher failing the student [rejects H0] although the student scored the passing marks [H0 was true]. 

Type II error will be the case where the teacher passes the student [do not reject H0] although the student did not score the passing marks [H1 is true].

Level of Significance

The alpha value is a criterion for determining whether a test statistic is statistically significant. In a statistical test, Alpha represents an acceptable probability of a Type I error. Because alpha is a probability, it can be anywhere between 0 and 1. In practice, the most commonly used alpha values are 0.01, 0.05, and 0.1, which represent a 1%, 5%, and 10% chance of a Type I error, respectively (i.e. rejecting the null hypothesis when it is in fact correct).

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A p-value is a metric that expresses the likelihood that an observed difference could have occurred by chance. As the p-value decreases the statistical significance of the observed difference increases. If the p-value is too low, you reject the null hypothesis.

Here you have taken an example in which you are trying to test whether the new advertising campaign has increased the product's sales. The p-value is the likelihood that the null hypothesis, which states that there is no change in the sales due to the new advertising campaign, is true. If the p-value is .30, then there is a 30% chance that there is no increase or decrease in the product's sales.  If the p-value is 0.03, then there is a 3% probability that there is no increase or decrease in the sales value due to the new advertising campaign. As you can see, the lower the p-value, the chances of the alternate hypothesis being true increases, which means that the new advertising campaign causes an increase or decrease in sales.

Why is Hypothesis Testing Important in Research Methodology?

Hypothesis testing is crucial in research methodology for several reasons:

• Provides evidence-based conclusions: It allows researchers to make objective conclusions based on empirical data, providing evidence to support or refute their research hypotheses.
• Supports decision-making: It helps make informed decisions, such as accepting or rejecting a new treatment, implementing policy changes, or adopting new practices.
• Adds rigor and validity: It adds scientific rigor to research using statistical methods to analyze data, ensuring that conclusions are based on sound statistical evidence.
• Contributes to the advancement of knowledge: By testing hypotheses, researchers contribute to the growth of knowledge in their respective fields by confirming existing theories or discovering new patterns and relationships.

Limitations of Hypothesis Testing

Hypothesis testing has some limitations that researchers should be aware of:

• It cannot prove or establish the truth: Hypothesis testing provides evidence to support or reject a hypothesis, but it cannot confirm the absolute truth of the research question.
• Results are sample-specific: Hypothesis testing is based on analyzing a sample from a population, and the conclusions drawn are specific to that particular sample.
• Possible errors: During hypothesis testing, there is a chance of committing type I error (rejecting a true null hypothesis) or type II error (failing to reject a false null hypothesis).
• Assumptions and requirements: Different tests have specific assumptions and requirements that must be met to accurately interpret results.

After reading this tutorial, you would have a much better understanding of hypothesis testing, one of the most important concepts in the field of Data Science . The majority of hypotheses are based on speculation about observed behavior, natural phenomena, or established theories.

If you are interested in statistics of data science and skills needed for such a career, you ought to explore Simplilearn’s Post Graduate Program in Data Science.

If you have any questions regarding this ‘Hypothesis Testing In Statistics’ tutorial, do share them in the comment section. Our subject matter expert will respond to your queries. Happy learning!

1. What is hypothesis testing in statistics with example?

Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population. It involves formulating two competing hypotheses, the null hypothesis (H0) and the alternative hypothesis (Ha), and then collecting data to assess the evidence. An example: testing if a new drug improves patient recovery (Ha) compared to the standard treatment (H0) based on collected patient data.

2. What is hypothesis testing and its types?

Hypothesis testing is a statistical method used to make inferences about a population based on sample data. It involves formulating two hypotheses: the null hypothesis (H0), which represents the default assumption, and the alternative hypothesis (Ha), which contradicts H0. The goal is to assess the evidence and determine whether there is enough statistical significance to reject the null hypothesis in favor of the alternative hypothesis.

Types of hypothesis testing:

• One-sample test: Used to compare a sample to a known value or a hypothesized value.
• Two-sample test: Compares two independent samples to assess if there is a significant difference between their means or distributions.
• Paired-sample test: Compares two related samples, such as pre-test and post-test data, to evaluate changes within the same subjects over time or under different conditions.
• Chi-square test: Used to analyze categorical data and determine if there is a significant association between variables.
• ANOVA (Analysis of Variance): Compares means across multiple groups to check if there is a significant difference between them.

3. What are the steps of hypothesis testing?

The steps of hypothesis testing are as follows:

• Formulate the hypotheses: State the null hypothesis (H0) and the alternative hypothesis (Ha) based on the research question.
• Set the significance level: Determine the acceptable level of error (alpha) for making a decision.
• Collect and analyze data: Gather and process the sample data.
• Compute test statistic: Calculate the appropriate statistical test to assess the evidence.
• Make a decision: Compare the test statistic with critical values or p-values and determine whether to reject H0 in favor of Ha or not.
• Draw conclusions: Interpret the results and communicate the findings in the context of the research question.

4. What are the 2 types of hypothesis testing?

• One-tailed (or one-sided) test: Tests for the significance of an effect in only one direction, either positive or negative.
• Two-tailed (or two-sided) test: Tests for the significance of an effect in both directions, allowing for the possibility of a positive or negative effect.

The choice between one-tailed and two-tailed tests depends on the specific research question and the directionality of the expected effect.

5. What are the 3 major types of hypothesis?

The three major types of hypotheses are:

• Null Hypothesis (H0): Represents the default assumption, stating that there is no significant effect or relationship in the data.
• Alternative Hypothesis (Ha): Contradicts the null hypothesis and proposes a specific effect or relationship that researchers want to investigate.
• Nondirectional Hypothesis: An alternative hypothesis that doesn't specify the direction of the effect, leaving it open for both positive and negative possibilities.

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About the author.

Avijeet is a Senior Research Analyst at Simplilearn. Passionate about Data Analytics, Machine Learning, and Deep Learning, Avijeet is also interested in politics, cricket, and football.

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• Fundamental Analysis

Hypothesis to Be Tested: Definition and 4 Steps for Testing with Example

What Is Hypothesis Testing?

Hypothesis testing, sometimes called significance testing, is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.

Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Such data may come from a larger population, or from a data-generating process. The word "population" will be used for both of these cases in the following descriptions.

Key Takeaways

• Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.
• The test provides evidence concerning the plausibility of the hypothesis, given the data.
• Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed.
• The four steps of hypothesis testing include stating the hypotheses, formulating an analysis plan, analyzing the sample data, and analyzing the result.

How Hypothesis Testing Works

In hypothesis testing, an  analyst  tests a statistical sample, with the goal of providing evidence on the plausibility of the null hypothesis.

Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed. All analysts use a random population sample to test two different hypotheses: the null hypothesis and the alternative hypothesis.

The null hypothesis is usually a hypothesis of equality between population parameters; e.g., a null hypothesis may state that the population mean return is equal to zero. The alternative hypothesis is effectively the opposite of a null hypothesis (e.g., the population mean return is not equal to zero). Thus, they are mutually exclusive , and only one can be true. However, one of the two hypotheses will always be true.

The null hypothesis is a statement about a population parameter, such as the population mean, that is assumed to be true.

4 Steps of Hypothesis Testing

All hypotheses are tested using a four-step process:

• The first step is for the analyst to state the hypotheses.
• The second step is to formulate an analysis plan, which outlines how the data will be evaluated.
• The third step is to carry out the plan and analyze the sample data.
• The final step is to analyze the results and either reject the null hypothesis, or state that the null hypothesis is plausible, given the data.

Real-World Example of Hypothesis Testing

If, for example, a person wants to test that a penny has exactly a 50% chance of landing on heads, the null hypothesis would be that 50% is correct, and the alternative hypothesis would be that 50% is not correct.

Mathematically, the null hypothesis would be represented as Ho: P = 0.5. The alternative hypothesis would be denoted as "Ha" and be identical to the null hypothesis, except with the equal sign struck-through, meaning that it does not equal 50%.

A random sample of 100 coin flips is taken, and the null hypothesis is then tested. If it is found that the 100 coin flips were distributed as 40 heads and 60 tails, the analyst would assume that a penny does not have a 50% chance of landing on heads and would reject the null hypothesis and accept the alternative hypothesis.

If, on the other hand, there were 48 heads and 52 tails, then it is plausible that the coin could be fair and still produce such a result. In cases such as this where the null hypothesis is "accepted," the analyst states that the difference between the expected results (50 heads and 50 tails) and the observed results (48 heads and 52 tails) is "explainable by chance alone."

Some staticians attribute the first hypothesis tests to satirical writer John Arbuthnot in 1710, who studied male and female births in England after observing that in nearly every year, male births exceeded female births by a slight proportion. Arbuthnot calculated that the probability of this happening by chance was small, and therefore it was due to “divine providence.”

What is Hypothesis Testing?

Hypothesis testing refers to a process used by analysts to assess the plausibility of a hypothesis by using sample data. In hypothesis testing, statisticians formulate two hypotheses: the null hypothesis and the alternative hypothesis. A null hypothesis determines there is no difference between two groups or conditions, while the alternative hypothesis determines that there is a difference. Researchers evaluate the statistical significance of the test based on the probability that the null hypothesis is true.

What are the Four Key Steps Involved in Hypothesis Testing?

Hypothesis testing begins with an analyst stating two hypotheses, with only one that can be right. The analyst then formulates an analysis plan, which outlines how the data will be evaluated. Next, they move to the testing phase and analyze the sample data. Finally, the analyst analyzes the results and either rejects the null hypothesis or states that the null hypothesis is plausible, given the data.

What are the Benefits of Hypothesis Testing?

Hypothesis testing helps assess the accuracy of new ideas or theories by testing them against data. This allows researchers to determine whether the evidence supports their hypothesis, helping to avoid false claims and conclusions. Hypothesis testing also provides a framework for decision-making based on data rather than personal opinions or biases. By relying on statistical analysis, hypothesis testing helps to reduce the effects of chance and confounding variables, providing a robust framework for making informed conclusions.

What are the Limitations of Hypothesis Testing?

Hypothesis testing relies exclusively on data and doesn’t provide a comprehensive understanding of the subject being studied. Additionally, the accuracy of the results depends on the quality of the available data and the statistical methods used. Inaccurate data or inappropriate hypothesis formulation may lead to incorrect conclusions or failed tests. Hypothesis testing can also lead to errors, such as analysts either accepting or rejecting a null hypothesis when they shouldn’t have. These errors may result in false conclusions or missed opportunities to identify significant patterns or relationships in the data.

The Bottom Line

Hypothesis testing refers to a statistical process that helps researchers and/or analysts determine the reliability of a study. By using a well-formulated hypothesis and set of statistical tests, individuals or businesses can make inferences about the population that they are studying and draw conclusions based on the data presented. There are different types of hypothesis testing, each with their own set of rules and procedures. However, all hypothesis testing methods have the same four step process, which includes stating the hypotheses, formulating an analysis plan, analyzing the sample data, and analyzing the result. Hypothesis testing plays a vital part of the scientific process, helping to test assumptions and make better data-based decisions.

Sage. " Introduction to Hypothesis Testing. " Page 4.

Elder Research. " Who Invented the Null Hypothesis? "

Formplus. " Hypothesis Testing: Definition, Uses, Limitations and Examples. "

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Hypothesis Testing in Data Science [Types, Process, Example]

Home Blog Data Science Hypothesis Testing in Data Science [Types, Process, Example]

In day-to-day life, we come across a lot of data lot of variety of content. Sometimes the information is too much that we get confused about whether the information provided is correct or not. At that moment, we get introduced to a word called “Hypothesis testing” which helps in determining the proofs and pieces of evidence for some belief or information.  

What is Hypothesis Testing?

Hypothesis testing is an integral part of statistical inference. It is used to decide whether the given sample data from the population parameter satisfies the given hypothetical condition. So, it will predict and decide using several factors whether the predictions satisfy the conditions or not. In simpler terms, trying to prove whether the facts or statements are true or not.   

For example, if you predict that students who sit on the last bench are poorer and weaker than students sitting on 1st bench, then this is a hypothetical statement that needs to be clarified using different experiments. Another example we can see is implementing new business strategies to evaluate whether they will work for the business or not. All these things are very necessary when you work with data as a data scientist.  If you are interested in learning about data science, visit this amazing  Data Science full course   to learn data science.    

How is Hypothesis Testing Used in Data Science?

It is important to know how and where we can use hypothesis testing techniques in the field of data science. Data scientists predict a lot of things in their day-to-day work, and to check the probability of whether that finding is certain or not, we use hypothesis testing. The main goal of hypothesis testing is to gauge how well the predictions perform based on the sample data provided by the population. If you are interested to know more about the applications of the data, then refer to this  D ata  Scien ce course in India  which will give you more insights into application-based things. When data scientists work on model building using various machine learning algorithms, they need to have faith in their models and the forecasting of models. They then provide the sample data to the model for training purposes so that it can provide us with the significance of statistical data that will represent the entire population.  

Where and When to Use Hypothesis Test?

Hypothesis testing is widely used when we need to compare our results based on predictions. So, it will compare before and after results. For example, someone claimed that students writing exams from blue pen always get above 90%; now this statement proves it correct, and experiments need to be done. So, the data will be collected based on the student's input, and then the test will be done on the final result later after various experiments and observations on students' marks vs pen used, final conclusions will be made which will determine the results. Now hypothesis testing will be done to compare the 1st and the 2nd result, to see the difference and closeness of both outputs. This is how hypothesis testing is done.  

How Does Hypothesis Testing Work in Data Science?

In the whole data science life cycle, hypothesis testing is done in various stages, starting from the initial part, the 1st stage where the EDA, data pre-processing, and manipulation are done. In this stage, we will do our initial hypothesis testing to visualize the outcome in later stages. The next test will be done after we have built our model, once the model is ready and hypothesis testing is done, we will compare the results of the initial testing and the 2nd one to compare the results and significance of the results and to confirm the insights generated from the 1st cycle match with the 2nd one or not. This will help us know how the model responds to the sample training data. As we saw above, hypothesis testing is always needed when we are planning to contrast more than 2 groups. While checking on the results, it is important to check on the flexibility of the results for the sample and the population. Later, we can judge on the disagreement of the results are appropriate or vague. This is all we can do using hypothesis testing.   

Different Types of Hypothesis Testing

Hypothesis testing can be seen in several types. In total, we have 5 types of hypothesis testing. They are described below:

1. Alternative Hypothesis

The alternative hypothesis explains and defines the relationship between two variables. It simply indicates a positive relationship between two variables which means they do have a statistical bond. It indicates that the sample observed is going to influence or affect the outcome. An alternative hypothesis is described using H a  or H 1 . Ha indicates an alternative hypothesis and H 1  explains the possibility of influenced outcome which is 1. For example, children who study from the beginning of the class have fewer chances to fail. An alternate hypothesis will be accepted once the statistical predictions become significant. The alternative hypothesis can be further divided into 3 parts.   

• Left-tailed: Left tailed hypothesis can be expected when the sample value is less than the true value.   
• Right-tailed: Right-tailed hypothesis can be expected when the true value is greater than the outcome/predicted value.    
• Two-tailed: Two-tailed hypothesis is defined when the true value is not equal to the sample value or the output.   

2. Null Hypothesis

The null hypothesis simply states that there is no relation between statistical variables. If the facts presented at the start do not match with the outcomes, then we can say, the testing is null hypothesis testing. The null hypothesis is represented as H 0 . For example, children who study from the beginning of the class have no fewer chances to fail. There are types of Null Hypothesis described below:   

Simple Hypothesis:  It helps in denoting and indicating the distribution of the population.   

Composite Hypothesis:  It does not denote the population distribution   

Exact Hypothesis:  In the exact hypothesis, the value of the hypothesis is the same as the sample distribution. Example- μ= 10   

Inexact Hypothesis:  Here, the hypothesis values are not equal to the sample. It will denote a particular range of values.   

3. Non-directional Hypothesis 

The non-directional hypothesis is a tow-tailed hypothesis that indicates the true value does not equal the predicted value. In simpler terms, there is no direction between the 2 variables. For an example of a non-directional hypothesis, girls and boys have different methodologies to solve a problem. Here the example explains that the thinking methodologies of a girl and a boy is different, they don’t think alike.    

4. Directional Hypothesis

In the Directional hypothesis, there is a direct relationship between two variables. Here any of the variables influence the other.   

5. Statistical Hypothesis

Statistical hypothesis helps in understanding the nature and character of the population. It is a great method to decide whether the values and the data we have with us satisfy the given hypothesis or not. It helps us in making different probabilistic and certain statements to predict the outcome of the population... We have several types of tests which are the T-test, Z-test, and Anova tests.  

Methods of Hypothesis Testing

1. frequentist hypothesis testing.

Frequentist hypotheses mostly work with the approach of making predictions and assumptions based on the current data which is real-time data. All the facts are based on current data. The most famous kind of frequentist approach is null hypothesis testing.    

2. Bayesian Hypothesis Testing

Bayesian testing is a modern and latest way of hypothesis testing. It is known to be the test that works with past data to predict the future possibilities of the hypothesis. In Bayesian, it refers to the prior distribution or prior probability samples for the observed data. In the medical Industry, we observe that Doctors deal with patients’ diseases using past historical records. So, with this kind of record, it is helpful for them to understand and predict the current and upcoming health conditions of the patient.

Importance of Hypothesis Testing in Data Science

Most of the time, people assume that data science is all about applying machine learning algorithms and getting results, that is true but in addition to the fact that to work in the data science field, one needs to be well versed with statistics as most of the background work in Data science is done through statistics. When we deal with data for pre-processing, manipulating, and analyzing, statistics play. Specifically speaking Hypothesis testing helps in making confident decisions, predicting the correct outcomes, and finding insightful conclusions regarding the population. Hypothesis testing helps us resolve tough things easily. To get more familiar with Hypothesis testing and other prediction models attend the superb useful  KnowledgeHut Data Science full course  which will give you more domain knowledge and will assist you in working with industry-related projects.          

Basic Steps in Hypothesis Testing [Workflow]

1. null and alternative hypothesis.

After we have done our initial research about the predictions that we want to find out if true, it is important to mention whether the hypothesis done is a null hypothesis(H0) or an alternative hypothesis (Ha). Once we understand the type of hypothesis, it will be easy for us to do mathematical research on it. A null hypothesis will usually indicate the no-relationship between the variables whereas an alternative hypothesis describes the relationship between 2 variables.    

• H0 – Girls, on average, are not strong as boys   
• Ha - Girls, on average are stronger than boys   

2. Data Collection

To prove our statistical test validity, it is essential and critical to check the data and proceed with sampling them to get the correct hypothesis results. If the target data is not prepared and ready, it will become difficult to make the predictions or the statistical inference on the population that we are planning to make. It is important to prepare efficient data, so that hypothesis findings can be easy to predict.   

3. Selection of an appropriate test statistic

To perform various analyses on the data, we need to choose a statistical test. There are various types of statistical tests available. Based on the wide spread of the data that is variance within the group or how different the data category is from one another that is variance without a group, we can proceed with our further research study.   

4. Selection of the appropriate significant level

Once we get the result and outcome of the statistical test, we have to then proceed further to decide whether the reject or accept the null hypothesis. The significance level is indicated by alpha (α). It describes the probability of rejecting or accepting the null hypothesis. Example- Suppose the value of the significance level which is alpha is 0.05. Now, this value indicates the difference from the null hypothesis. 

5. Calculation of the test statistics and the p-value

P value is simply the probability value and expected determined outcome which is at least as extreme and close as observed results of a hypothetical test. It helps in evaluating and verifying hypotheses against the sample data. This happens while assuming the null hypothesis is true. The lower the value of P, the higher and better will be the results of the significant value which is alpha (α). For example, if the P-value is 0.05 or even less than this, then it will be considered statistically significant. The main thing is these values are predicted based on the calculations done by deviating the values between the observed one and referenced one. The greater the difference between values, the lower the p-value will be.

6. Findings of the test

After knowing the P-value and statistical significance, we can determine our results and take the appropriate decision of whether to accept or reject the null hypothesis based on the facts and statistics presented to us.

How to Calculate Hypothesis Testing?

Hypothesis testing can be done using various statistical tests. One is Z-test. The formula for Z-test is given below:  

            Z = ( x̅  – μ 0 )  / (σ /√n)    

In the above equation, x̅ is the sample mean   

• μ0 is the population mean   
• σ is the standard deviation    
• n is the sample size   

Now depending on the Z-test result, the examination will be processed further. The result is either going to be a null hypothesis or it is going to be an alternative hypothesis. That can be measured through below formula-   

• H0: μ=μ0   
• Ha: μ≠μ0   
• Here,   
• H0 = null hypothesis   
• Ha = alternate hypothesis   

In this way, we calculate the hypothesis testing and can apply it to real-world scenarios.

Real-World Examples of Hypothesis Testing

Hypothesis testing has a wide variety of use cases that proves to be beneficial for various industries.    

1. Healthcare

In the healthcare industry, all the research and experiments which are done to predict the success of any medicine or drug are done successfully with the help of Hypothesis testing.   

2. Education sector

Hypothesis testing assists in experimenting with different teaching techniques to deal with the understanding capability of different students.   

3. Mental Health

Hypothesis testing helps in indicating the factors that may cause some serious mental health issues.   

4. Manufacturing

Testing whether the new change in the process of manufacturing helped in the improvement of the process as well as in the quantity or not.  In the same way, there are many other use cases that we get to see in different sectors for hypothesis testing. 

Error Terms in Hypothesis Testing

1. type-i error.

Type I error occurs during the process of hypothesis testing when the null hypothesis is rejected even though it is accurate. This kind of error is also known as False positive because even though the statement is positive or correct but results are given as false. For example, an innocent person still goes to jail because he is considered to be guilty.   

2. Type-II error

Type II error occurs during the process of hypothesis testing when the null hypothesis is not rejected even though it is inaccurate. This Kind of error is also called a False-negative which means even though the statements are false and inaccurate, it still says it is correct and doesn’t reject it. For example, a person is guilty, but in court, he has been proven innocent where he is guilty, so this is a Type II error.   

3. Level of Significance

The level of significance is majorly used to measure the confidence with which a null hypothesis can be rejected. It is the value with which one can reject the null hypothesis which is H0. The level of significance gauges whether the hypothesis testing is significant or not.   

P-value stands for probability value, which tells us the probability or likelihood to find the set of observations when the null hypothesis is true using statistical tests. The main purpose is to check the significance of the statistical statement.   

5. High P-Values

A higher P-value indicates that the testing is not statistically significant. For example, a P value greater than 0.05 is considered to be having higher P value. A higher P-value also means that our evidence and proofs are not strong enough to influence the population.

In hypothesis testing, each step is responsible for getting the outcomes and the results, whether it is the selection of statistical tests or working on data, each step contributes towards the better consequences of the hypothesis testing. It is always a recommendable step when planning for predicting the outcomes and trying to experiment with the sample; hypothesis testing is a useful concept to apply.   

Frequently Asked Questions (FAQs)

We can test a hypothesis by selecting a correct hypothetical test and, based on those getting results.   

Many statistical tests are used for hypothetical testing which includes Z-test, T-test, etc. 

Hypothesis helps us in doing various experiments and working on a specific research topic to predict the results.   

The null and alternative hypothesis, data collection, selecting a statistical test, selecting significance value, calculating p-value, check your findings.    

In simple words, parametric tests are purely based on assumptions whereas non-parametric tests are based on data that is collected and acquired from a sample.   

Gauri Guglani

Gauri Guglani works as a Data Analyst at Deloitte Consulting. She has done her major in Information Technology and holds great interest in the field of data science. She owns her technical skills as well as managerial skills and also is great at communicating. Since her undergraduate, Gauri has developed a profound interest in writing content and sharing her knowledge through the manual means of blog/article writing. She loves writing on topics affiliated with Statistics, Python Libraries, Machine Learning, Natural Language processes, and many more.

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The data-hypothesis relationship

Teppo felin.

1 Saïd Business School, University of Oxford, Oxford, UK

Jan Koenderink

2 Department of Physics, Delft University of Technology, Delft, The Netherlands

3 Department of Experimental Psychology, University of Leuven, Leuven, Belgium

Joachim I. Krueger

4 Department of Cognitive, Linguistic and Psychological Sciences, Brown University, Providence, USA

Denis Noble

5 Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, UK

George F.R. Ellis

6 Department of Mathematics, University of Cape Town, Cape Town, South Africa

Every conscious cognitive process will show itself to be steeped in theories; full of hypotheses. Rupert Riedl [ 1 ]

In a provocative editorial, Yanai and Lercher (henceforth Y&L) claim that “a hypothesis is a liability” [ 2 ]. They contend that having a hypothesis is costly because it causes scientists to miss hidden data and interesting phenomena. Y&L advocate “hypothesis-free” data exploration, which they argue can yield significant scientific discoveries.

We disagree. While we concur that a bad hypothesis is a liability, there is no such thing as hypothesis-free data exploration. Observation and data are always hypothesis- or theory-laden. Data is meaningless without some form of hypothesis or theory. Any exploration of data, however informal, is necessarily guided by some form of expectations. Even informal hunches or conjectures are types of proto-hypothesis. Furthermore, seemingly hypothesis-free statistical tools and computational techniques also contain latent hypotheses and theories about what is important—what might be interesting, worth measuring or paying attention to. Thus, while Y&L argue that a “hypothesis is a liability,” we argue that hypothesis-free observation is not possible (nor desirable) and that hypotheses in fact are the primary engine of scientific creativity and discovery.

The hidden gorilla

To illustrate their point about how a hypothesis is a liability, Y&L present their own version of the famous gorilla experiment [ 3 ]. In their experiment, subjects receive some made-up data featuring three variables: the BMI of individuals, the number of steps taken on a particular day, and their gender. One experimental group received three hypotheses to consider, while the other was “hypothesis-free.” Subjects in this latter group were simply asked to address the question “what do you conclude from the dataset?”

The “catch” of Y&L’s experiment was that a visual plot of the data showed a waving gorilla. And the key finding was that subjects in the hypothesis-free group were five times more likely to see the gorilla, compared with subjects in the hypothesis-focused group. Y&L concluded from this that hypotheses blind us to hidden patterns and insights in the data. Perhaps ironically, Y&L come to this conclusion based on their own hypothesis about the dangers of hypotheses.

But how exactly does missing the gorilla generalize to Y&L’s point about a hypothesis being a liability in scientific discovery? They argue that missing the gorilla is a problem, even though it is hard to see how finding an irrelevant gorilla mimics making a scientific insight. Now, we understand the gorilla is used as a metaphor for missing surprising or hidden things in science. But a meteorologist missing a cloud that looks like a gorilla is roughly equivalent to what Y&L are doing. A gorilla-shaped cloud has no scientific interest to the meteorologist, just as the gorilla-shaped data is irrelevant to Y&L’s context (the health data with three variables: BMI, steps taken and gender). Furthermore, the gorilla example does not generalize to scientific discovery because a gorilla is something that is universally recognized, while scientific discovery is essentially about finding new data, establishing new facts and relationships. New insights and scientific discoveries do not somehow “pop out” like the gorilla does once one plots the raw data. Hypotheses are needed. Thus, there is a mismatch between the experiment and what Y&L are claiming, on a number of levels.

Y&L import some of these problems from the original gorilla study [ 4 ]. The most serious concern is that various versions of the gorilla study can be seen as a form of attentional misdirection, similar to what is practiced by magicians. Experimental tasks are artificially constructed and designed to prove a specific hypothesis: that people are blind and miss large objects in their visual scenes. Experimenters first hide something in the visual scene, then distract their subjects with other tasks (whether counting basketball passes or asking them to analyze specific hypotheses), and then, voilà, reveal to them what they have missed. The problem is that—whether in science or in everyday life—an indefinite number of things remain undetected when we interact with data or visual scenes. It is not obvious what an apple falling means, without the right question, hypothesis, or theory. Visual scenes and data teem with possibilities, uses and meanings. Of course, the excitement generated by these studies comes from the fact that something so large and surprising—like a gorilla—goes undetected, even though it should be plainly obvious.

But there are deeper issues here. Reductionist forms of science assume that cues and data (somehow) jump out and tell us why they are relevant and important, based on the characteristics of the data itself (the physical properties of the world). In vision science, this assumption is based on research in psychophysics (and inverse optics and ideal observer theory) that focuses on salience as a function of cue or stimulus characteristics. From this perspective, cues and stimuli become data, information, and evidence due to their inherent nature [ 5 ].

To illustrate the problem with this, consider two stimulus or cue characteristics that are important to various versions of the gorilla study—and central to psychophysics and the cognitive sciences more generally—namely “size” and “surprisingness” [ 6 ]. The idea in psychophysics is that these characteristics should make cues salient. For example, researchers embedded an image of a gorilla in the CT scan images of patients’ lungs. They then asked expert radiologists to look for nodules as part of lung-cancer screening. Eighty-three percent of the radiologists missed the gorilla embedded in the image, despite the fact that the gorilla was 48 times the size of the nodules they were looking for [ 7 ].

But if radiologists or experimental subjects were asked to, say, “look for something unusual” or to “see if you can find the animal,” they would presumably find the gorilla. Thus, visual awareness or recognition has little to do with size or surprisingness. It has more to do with the question posed by the experimenter or the expectations of experimental subjects. In fact, experimental subjects themselves might suspect that the study actually is not about counting basketball passes or about analyzing health data or finding cancerous nodules in lungs. If subjects think that they are being tricked by experimenters—as is often the case—they might ignore the distracting tasks and priming questions and look for and find the gorilla. Note, again, that the a priori hypothesis of experimenters themselves is that people are blind, and so the experiments themselves are designed to prove this point. Alert subjects might suspect that they are being purposefully distracted and thus try to guess what they are meant to look for and find it.

The key point here is that the “transformation” of raw cues or data to information and evidence is not a straightforward process. It requires some form of hypothesis. Cues and data do not automatically tell us what they mean, whether or why they are relevant, or for which hypothesis they might provide evidence. Size is relevant in some situations, but not in others. Cues and data only become information and evidence in response to the questions and queries that we are asking.

Fishing expeditions require a net

One alternative to having a hypothesis, Y&L argue, is hypothesis- free exploration of data or what they call fishing expeditions. Of course, the idea of engaging in a fishing expedition—as Y&L recognize—has highly negative connotations, suggesting haphazard, unscientific, and perhaps even unethical practices. But they make a valid point: more exploratory and imaginative practices are important in science.

But fishing expeditions are hardly hypothesis-free. That is, fishing expeditions—to extend Y&L’s metaphor—require a net or some type of device for catching fish. Data and insights (just like fish) do not jump out and declare their relevance, meaning, or importance. As put by physical chemist Michael Polanyi, “things are not labelled ‘evidence’ in nature” [ 8 ]. The relevant data needs to be identified and lured in some fashion. Even the most exploratory process in science features choices and assumptions about what will count as data and evidence and what should be measured (and how). Any look at data—however preliminary it might be— necessarily represents some form of proto-hypothesis: a latent expectation, question, or even guess about what might be lurking, about what might potentially be interesting or relevant and how it might be caught.

In short, there’s no systematic way to extract and identify anything hidden without at least some rough idea of what one is looking for. The tools and devices scientists use are the net, sieve, or filter for capturing relevance and meaning. These nets come in vastly different materials and textures, sizes, types of weights, and anchors. Choices also need to be made about where to cast these nets. There are various ways to use and deploy them (trolling, longline, and so forth). Each choice implies a hypothesis. The choice of fishing net implies a hypothesis about what one is looking for and about what one might expect to catch and see as relevant [ 9 ].

Now, it might seem like we are stretching the definition of a hypothesis by including expectations, conjectures, and even the statistical and computational tools that are used to generate insights. But we think it is important to recognize that any tool—whether cognitive, computational, or statistical—functions like a net, as it already embodies implicit hypotheses about what matters and what does not. Perhaps these are not full-fledged, formal hypotheses in the sense that Y&L discuss. But they certainly are proto-hypotheses that direct awareness and attention toward what should be measured and what counts as data and evidence. A hypothesis is some form of expectation or question about what one is looking for and about what one expects to find. The identification and collection of data necessarily is of the same form, as one cannot collect all data about what is going on in the world at a specific time: flu patterns in China, weather patterns in the Pacific, sunspot cycles, the state of the New York stock exchange, earthquakes in Tahiti, and so on. Science is about making decisions about what subset of all this “stuff” should be focused on and included in the analysis.

Y&L specifically emphasize correlations and the generation of various statistical patterns as a way to make hypothesis-free discoveries in data. Correlations are one form of “net” for looking at data. But correlations are ubiquitous and their strength tells us little [ 10 ]. One needs a hypothesis to arbitrate between which correlation might be worth investigating and which not. The genome-wide associational studies have pointed this out. With the exception of the usual outliers (rare genetic diseases), the association levels are relatively small. More data may offer more stable statistical estimates, but it will not achieve the identification of causality required for a physiological explanation. On the contrary, the extremely low association data can be hiding substantial causality or perhaps more complex or interconnected, omnigenic factors are at play in the genome [ 11 ]. A causal hypothesis, tested rigorously with quantitative modeling, can reveal the potential pathways for understanding genetic variation, epigenetic factors, and disease or traits [ 12 ].

Science: bottom-up versus top-down

Y&L argue that scientific discoveries are “undiscoverable without data.” While this is correct in principle, Y&L mis-specify the data-hypothesis relationship by privileging the role the data to the detriment of hypothesis and theory. They ignore the temporal primacy of theory and hypothesis. A hypothesis tells us what data to look for. Data emerges and becomes evidence in response to a hypothesis. In physics, for example, the existence of gravitational waves had long been hypothesized. The hypothesis guided scientists to look for this data. This specifically led to the invention and construction of exquisitely sensitive devices to detect and measure gravitational radiation (e.g., LIGO and VIRGO observations). Eventually, in 2015, gravitational waves were discovered. The data emerged because of the conceptualization, design, and construction of relevant devices for measurement. The data was manifest due to the hypothesis rather than the other way around. And the data analysis itself is theory-based [ 13 ]: it depends on templates of waves expected from the gravitational coalescence of black holes or neutron stars.

Einstein aptly captured the relationship between hypotheses and data when noting that “whether you can observe a thing or not depends on the theory which you use. It is the theory which decides what can be observed.” Einstein’s point might be illustrated by the so-called DIKW hierarchy (Fig.  1 ) [ 14 ]. Currently popular data-first approaches assume that scientific understanding is built from the bottom-up. But to the contrary, many of the greatest insights have come “top-down,” where scientists start with theories and hypotheses that guide them to identify the right data and evidence. One of the most profound ways this happens is when scientists query fundamental assumptions that are taken for granted, such as that species are fixed for all time, or that simultaneity is independent of the state of motion. This questioning of axiomatic assumptions drives the creation of transformational theories (the theory of evolution, special relativity) and the subsequent collection of associated data that tests such profound reshaping of the foundations.

The DIKW “hierarchy” is often seen as “bottom-up.” But, as we argue, top-down mechanisms play a critical role in discovering data, relevance, and meaning

There certainly are significant reciprocal influences between these “levels” of the hierarchy. But Y&L’s central argument that a “hypothesis is a liability” simply does not recognize the profound, top-down influence played by hypotheses and theories in science, and how these enable the identification and generation of data.

Our concern is that starting at the bottom—as suggested by Y&L’s notion of hypothesis-free exploration of data—will inadvertently lead to an overly descriptive science: what Ernest Rutherford called “stamp collecting.” Charles Darwin anticipated this problem when he wrote to a friend:

It made me laugh to read of [Edwin Lankester’s] advice or rather regret that I had not published facts alone . How profoundly ignorant he must be of the very soul of observation. About 30 years ago there was much talk that Geologists ought only to observe and not theorise ; and I well remember someone saying, that at this rate a man might as well go into a gravel-pit and count the pebbles and describe their colours. How odd it is that everyone should not see that all observation must be for or against some view , if it is to be of any service [ 15 ].

Acknowledgements

TF, DN and GFRE  gratefully acknowledge University of Oxford's Foundations of Value and Values-initiative for providing a forum to discuss these types of interdisciplinary issues.

Authors’ contributions

TF wrote the initial draft of the manuscript. JK, JIK, DN and GFRE added many ideas, examples and further edits to subsequent iterations of the article. The authors read and approved the final manuscript.

Competing interests

The authors declare that they have no competing interests.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

What is Hypothesis Testing in Statistics? Types and Examples

By Varun Saharawat | January 6, 2024

Hypothesis testing in statistics involves testing an assumption about a population parameter using sample data. Learners can download Hypothesis Testing PDF to get instant access to all information!

What exactly is hypothesis testing, and how does it work in statistics? Can I find practical examples and understand the different types from this blog?

Hypothesis Testing : Ever wonder how researchers determine if a new medicine actually works or if a new marketing campaign effectively drives sales? They use hypothesis testing! It is at the core of how scientific studies, business experiments and surveys determine if their results are statistically significant or just due to chance.

Hypothesis testing allows us to make evidence-based decisions by quantifying uncertainty and providing a structured process to make data-driven conclusions rather than guessing. In this post, we will discuss hypothesis testing types, examples, and processes!

Table of Contents

Hypothesis Testing

Hypothesis testing is a statistical method used to evaluate the validity of a hypothesis using sample data. It involves assessing whether observed data provide enough evidence to reject a specific hypothesis about a population parameter. 

Hypothesis Testing in Data Science

Hypothesis testing in data science is a statistical method used to evaluate two mutually exclusive population statements based on sample data. The primary goal is to determine which statement is more supported by the observed data.

Hypothesis testing assists in supporting the certainty of findings in research and data science projects. This statistical inference aids in making decisions about population parameters using sample data. For those who are looking to deepen their knowledge in data science and expand their skillset, we highly recommend checking out Master Generative AI: Data Science Course by Physics Wallah .

Also Read: What is Encapsulation Explain in Details

What is the Hypothesis Testing Procedure in Data Science?

The hypothesis testing procedure in data science involves a structured approach to evaluating hypotheses using statistical methods. Here’s a step-by-step breakdown of the typical procedure:

1) State the Hypotheses:

• Null Hypothesis (H0): This is the default assumption or a statement of no effect or difference. It represents what you aim to test against.
• Alternative Hypothesis (Ha): This is the opposite of the null hypothesis and represents what you want to prove.

2) Choose a Significance Level (α):

• Decide on a threshold (commonly 0.05) beyond which you will reject the null hypothesis. This is your significance level.

3) Select the Appropriate Test:

• Depending on your data type (e.g., continuous, categorical) and the nature of your research question, choose the appropriate statistical test (e.g., t-test, chi-square test, ANOVA, etc.).

4) Collect Data:

• Gather data from your sample or population, ensuring that it’s representative and sufficiently large (or as per your experimental design).

5)Compute the Test Statistic:

• Using your data and the chosen statistical test, compute the test statistic that summarizes the evidence against the null hypothesis.

6) Determine the Critical Value or P-value:

• Based on your significance level and the test statistic’s distribution, determine the critical value from a statistical table or compute the p-value.

7) Make a Decision:

• If the p-value is less than α: Reject the null hypothesis.
• If the p-value is greater than or equal to α: Fail to reject the null hypothesis.

8) Draw Conclusions:

• Based on your decision, draw conclusions about your research question or hypothesis. Remember, failing to reject the null hypothesis doesn’t prove it true; it merely suggests that you don’t have sufficient evidence to reject it.

9) Report Findings:

• Document your findings, including the test statistic, p-value, conclusion, and any other relevant details. Ensure clarity so that others can understand and potentially replicate your analysis.

Also Read: Binary Search Algorithm

How Hypothesis Testing Works?

Hypothesis testing is a fundamental concept in statistics that aids analysts in making informed decisions based on sample data about a larger population. The process involves setting up two contrasting hypotheses, the null hypothesis and the alternative hypothesis, and then using statistical methods to determine which hypothesis provides a more plausible explanation for the observed data.

The Core Principles:

• The Null Hypothesis (H0): This serves as the default assumption or status quo. Typically, it posits that there is no effect or no difference, often represented by an equality statement regarding population parameters. For instance, it might state that a new drug’s effect is no different from a placebo.
• The Alternative Hypothesis (H1 or Ha): This is the counter assumption or what researchers aim to prove. It’s the opposite of the null hypothesis, indicating that there is an effect, a change, or a difference in the population parameters. Using the drug example, the alternative hypothesis would suggest that the new drug has a different effect than the placebo.

Testing the Hypotheses:

Once these hypotheses are established, analysts gather data from a sample and conduct statistical tests. The objective is to determine whether the observed results are statistically significant enough to reject the null hypothesis in favor of the alternative.

Examples to Clarify the Concept:

• Null Hypothesis (H0): The sanitizer’s average efficacy is 95%.
• By conducting tests, if evidence suggests that the sanitizer’s efficacy is significantly less than 95%, we reject the null hypothesis.
• Null Hypothesis (H0): The coin is fair, meaning the probability of heads and tails is equal.
• Through experimental trials, if results consistently show a skewed outcome, indicating a significantly different probability for heads and tails, the null hypothesis might be rejected.

What are the 3 types of Hypothesis Test?

Hypothesis testing is a cornerstone in statistical analysis, providing a framework to evaluate the validity of assumptions or claims made about a population based on sample data. Within this framework, several specific tests are utilized based on the nature of the data and the question at hand. Here’s a closer look at the three fundamental types of hypothesis tests:

The z-test is a statistical method primarily employed when comparing means from two datasets, particularly when the population standard deviation is known. Its main objective is to ascertain if the means are statistically equivalent. 

A crucial prerequisite for the z-test is that the sample size should be relatively large, typically 30 data points or more. This test aids researchers and analysts in determining the significance of a relationship or discovery, especially in scenarios where the data’s characteristics align with the assumptions of the z-test.

The t-test is a versatile statistical tool used extensively in research and various fields to compare means between two groups. It’s particularly valuable when the population standard deviation is unknown or when dealing with smaller sample sizes. 

By evaluating the means of two groups, the t-test helps ascertain if a particular treatment, intervention, or variable significantly impacts the population under study. Its flexibility and robustness make it a go-to method in scenarios ranging from medical research to business analytics.

3. Chi-Square Test:

The Chi-Square test stands distinct from the previous tests, primarily focusing on categorical data rather than means. This statistical test is instrumental when analyzing categorical variables to determine if observed data aligns with expected outcomes as posited by the null hypothesis. 

By assessing the differences between observed and expected frequencies within categorical data, the Chi-Square test offers insights into whether discrepancies are statistically significant. Whether used in social sciences to evaluate survey responses or in quality control to assess product defects, the Chi-Square test remains pivotal for hypothesis testing in diverse scenarios.

Also Read: Python vs Java: Which is Best for Machine learning algorithm

Hypothesis Testing in Statistics

Hypothesis testing is a fundamental concept in statistics used to make decisions or inferences about a population based on a sample of data. The process involves setting up two competing hypotheses, the null hypothesis H 0​ and the alternative hypothesis H 1​. 

Through various statistical tests, such as the t-test, z-test, or Chi-square test, analysts evaluate sample data to determine whether there’s enough evidence to reject the null hypothesis in favor of the alternative. The aim is to draw conclusions about population parameters or to test theories, claims, or hypotheses.

Hypothesis Testing in Research

In research, hypothesis testing serves as a structured approach to validate or refute theories or claims. Researchers formulate a clear hypothesis based on existing literature or preliminary observations. They then collect data through experiments, surveys, or observational studies. 

Using statistical methods, researchers analyze this data to determine if there’s sufficient evidence to reject the null hypothesis. By doing so, they can draw meaningful conclusions, make predictions, or recommend actions based on empirical evidence rather than mere speculation.

Hypothesis Testing in R

R, a powerful programming language and environment for statistical computing and graphics, offers a wide array of functions and packages specifically designed for hypothesis testing. Here’s how hypothesis testing is conducted in R:

• Data Collection : Before conducting any test, you need to gather your data and ensure it’s appropriately structured in R.
• Choose the Right Test : Depending on your research question and data type, select the appropriate hypothesis test. For instance, use the t.test() function for a t-test or chisq.test() for a Chi-square test.
• Set Hypotheses : Define your null and alternative hypotheses. Using R’s syntax, you can specify these hypotheses and run the corresponding test.
• Execute the Test : Utilize built-in functions in R to perform the hypothesis test on your data. For instance, if you want to compare two means, you can use the t.test() function, providing the necessary arguments like the data vectors and type of t-test (one-sample, two-sample, paired, etc.).
• Interpret Results : Once the test is executed, R will provide output, including test statistics, p-values, and confidence intervals. Based on these results and a predetermined significance level (often 0.05), you can decide whether to reject the null hypothesis.
• Visualization : R’s graphical capabilities allow users to visualize data distributions, confidence intervals, or test statistics, aiding in the interpretation and presentation of results.

Hypothesis testing is an integral part of statistics and research, offering a systematic approach to validate hypotheses. Leveraging R’s capabilities, researchers and analysts can efficiently conduct and interpret various hypothesis tests, ensuring robust and reliable conclusions from their data.

Do Data Scientists do Hypothesis Testing?

Yes, data scientists frequently engage in hypothesis testing as part of their analytical toolkit. Hypothesis testing is a foundational statistical technique used to make data-driven decisions, validate assumptions, and draw conclusions from data. Here’s how data scientists utilize hypothesis testing:

• Validating Assumptions : Before diving into complex analyses or building predictive models, data scientists often need to verify certain assumptions about the data. Hypothesis testing provides a structured approach to test these assumptions, ensuring that subsequent analyses or models are valid.
• Feature Selection : In machine learning and predictive modeling, data scientists use hypothesis tests to determine which features (or variables) are most relevant or significant in predicting a particular outcome. By testing hypotheses related to feature importance or correlation, they can streamline the modeling process and enhance prediction accuracy.
• A/B Testing : A/B testing is a common technique in marketing, product development, and user experience design. Data scientists employ hypothesis testing to compare two versions (A and B) of a product, feature, or marketing strategy to determine which performs better in terms of a specified metric (e.g., conversion rate, user engagement).
• Research and Exploration : In exploratory data analysis (EDA) or when investigating specific research questions, data scientists formulate hypotheses to test certain relationships or patterns within the data. By conducting hypothesis tests, they can validate these relationships, uncover insights, and drive data-driven decision-making.
• Model Evaluation : After building machine learning or statistical models, data scientists use hypothesis testing to evaluate the model’s performance, assess its predictive power, or compare different models. For instance, hypothesis tests like the t-test or F-test can help determine if a new model significantly outperforms an existing one based on certain metrics.
• Business Decision-making : Beyond technical analyses, data scientists employ hypothesis testing to support business decisions. Whether it’s evaluating the effectiveness of a marketing campaign, assessing customer preferences, or optimizing operational processes, hypothesis testing provides a rigorous framework to validate assumptions and guide strategic initiatives.

Hypothesis Testing Examples and Solutions

Let’s delve into some common examples of hypothesis testing and provide solutions or interpretations for each scenario.

Example: Testing the Mean

Scenario : A coffee shop owner believes that the average waiting time for customers during peak hours is 5 minutes. To test this, the owner takes a random sample of 30 customer waiting times and wants to determine if the average waiting time is indeed 5 minutes.

Hypotheses :

• H 0​ (Null Hypothesis): 5 μ =5 minutes (The average waiting time is 5 minutes)
• H 1​ (Alternative Hypothesis): 5 μ =5 minutes (The average waiting time is not 5 minutes)

Solution : Using a t-test (assuming population variance is unknown), calculate the t-statistic based on the sample mean, sample standard deviation, and sample size. Then, determine the p-value and compare it with a significance level (e.g., 0.05) to decide whether to reject the null hypothesis.

Example: A/B Testing in Marketing

Scenario : An e-commerce company wants to determine if changing the color of a “Buy Now” button from blue to green increases the conversion rate.

• H 0​: Changing the button color does not affect the conversion rate.
• H 1​: Changing the button color affects the conversion rate.

Solution : Split website visitors into two groups: one sees the blue button (control group), and the other sees the green button (test group). Track the conversion rates for both groups over a specified period. Then, use a chi-square test or z-test (for large sample sizes) to determine if there’s a statistically significant difference in conversion rates between the two groups.

Hypothesis Testing Formula

The formula for hypothesis testing typically depends on the type of test (e.g., z-test, t-test, chi-square test) and the nature of the data (e.g., mean, proportion, variance). Below are the basic formulas for some common hypothesis tests:

Z-Test for Population Mean :

Z=(σ/n​)(xˉ−μ0​)​

• ˉ x ˉ = Sample mean
• 0 μ 0​ = Population mean under the null hypothesis
• σ = Population standard deviation
• n = Sample size

T-Test for Population Mean :

t= (s/ n ​ ) ( x ˉ −μ 0 ​ ) ​ 

s = Sample standard deviation 

Chi-Square Test for Goodness of Fit :

χ2=∑Ei​(Oi​−Ei​)2​

• Oi ​ = Observed frequency
• Ei ​ = Expected frequency

Also Read: Full Form of OOPS

Hypothesis Testing Calculator

While you can perform hypothesis testing manually using the above formulas and statistical tables, many online tools and software packages simplify this process. Here’s how you might use a calculator or software:

• Z-Test and T-Test Calculators : These tools typically require you to input sample statistics (like sample mean, population mean, standard deviation, and sample size). Once you input these values, the calculator will provide you with the test statistic (Z or t) and a p-value.
• Chi-Square Calculator : For chi-square tests, you’d input observed and expected frequencies for different categories or groups. The calculator then computes the chi-square statistic and provides a p-value.
• Software Packages (e.g., R, Python with libraries like scipy, or statistical software like SPSS) : These platforms offer more comprehensive tools for hypothesis testing. You can run various tests, get detailed outputs, and even perform advanced analyses, including regression models, ANOVA, and more.

When using any calculator or software, always ensure you understand the underlying assumptions of the test, interpret the results correctly, and consider the broader context of your research or analysis.

Hypothesis Testing FAQs

What are the key components of a hypothesis test.

The key components include: Null Hypothesis (H0): A statement of no effect or no difference. Alternative Hypothesis (H1 or Ha): A statement that contradicts the null hypothesis. Test Statistic: A value computed from the sample data to test the null hypothesis. Significance Level (α): The threshold for rejecting the null hypothesis. P-value: The probability of observing the given data, assuming the null hypothesis is true.

What is the significance level in hypothesis testing?

The significance level (often denoted as α) is the probability threshold used to determine whether to reject the null hypothesis. Commonly used values for α include 0.05, 0.01, and 0.10, representing a 5%, 1%, or 10% chance of rejecting the null hypothesis when it's actually true.

How do I choose between a one-tailed and two-tailed test?

The choice between one-tailed and two-tailed tests depends on your research question and hypothesis. Use a one-tailed test when you're specifically interested in one direction of an effect (e.g., greater than or less than). Use a two-tailed test when you want to determine if there's a significant difference in either direction.

What is a p-value, and how is it interpreted?

The p-value is a probability value that helps determine the strength of evidence against the null hypothesis. A low p-value (typically ≤ 0.05) suggests that the observed data is inconsistent with the null hypothesis, leading to its rejection. Conversely, a high p-value suggests that the data is consistent with the null hypothesis, leading to no rejection.

Can hypothesis testing prove a hypothesis true?

No, hypothesis testing cannot prove a hypothesis true. Instead, it helps assess the likelihood of observing a given set of data under the assumption that the null hypothesis is true. Based on this assessment, you either reject or fail to reject the null hypothesis.

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Sat / act prep online guides and tips, what is a hypothesis and how do i write one.

General Education

Think about something strange and unexplainable in your life. Maybe you get a headache right before it rains, or maybe you think your favorite sports team wins when you wear a certain color. If you wanted to see whether these are just coincidences or scientific fact, you would form a hypothesis, then create an experiment to see whether that hypothesis is true or not.

But what is a hypothesis, anyway? If you’re not sure about what a hypothesis is--or how to test for one!--you’re in the right place. This article will teach you everything you need to know about hypotheses, including: 

• Defining the term “hypothesis” 
• Providing hypothesis examples 
• Giving you tips for how to write your own hypothesis

So let’s get started!

What Is a Hypothesis?

Merriam Webster defines a hypothesis as “an assumption or concession made for the sake of argument.” In other words, a hypothesis is an educated guess . Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it’s true or not. Keep in mind that in science, a hypothesis should be testable. You have to be able to design an experiment that tests your hypothesis in order for it to be valid. 

As you could assume from that statement, it’s easy to make a bad hypothesis. But when you’re holding an experiment, it’s even more important that your guesses be good...after all, you’re spending time (and maybe money!) to figure out more about your observation. That’s why we refer to a hypothesis as an educated guess--good hypotheses are based on existing data and research to make them as sound as possible.

Hypotheses are one part of what’s called the scientific method .  Every (good) experiment or study is based in the scientific method. The scientific method gives order and structure to experiments and ensures that interference from scientists or outside influences does not skew the results. It’s important that you understand the concepts of the scientific method before holding your own experiment. Though it may vary among scientists, the scientific method is generally made up of six steps (in order):

• Observation
• Asking questions
• Forming a hypothesis
• Analyze the data
• Communicate your results

You’ll notice that the hypothesis comes pretty early on when conducting an experiment. That’s because experiments work best when they’re trying to answer one specific question. And you can’t conduct an experiment until you know what you’re trying to prove!

Independent and Dependent Variables 

After doing your research, you’re ready for another important step in forming your hypothesis: identifying variables. Variables are basically any factor that could influence the outcome of your experiment . Variables have to be measurable and related to the topic being studied.

There are two types of variables:  independent variables and dependent variables. I ndependent variables remain constant . For example, age is an independent variable; it will stay the same, and researchers can look at different ages to see if it has an effect on the dependent variable. 

Speaking of dependent variables... dependent variables are subject to the influence of the independent variable , meaning that they are not constant. Let’s say you want to test whether a person’s age affects how much sleep they need. In that case, the independent variable is age (like we mentioned above), and the dependent variable is how much sleep a person gets. 

Variables will be crucial in writing your hypothesis. You need to be able to identify which variable is which, as both the independent and dependent variables will be written into your hypothesis. For instance, in a study about exercise, the independent variable might be the speed at which the respondents walk for thirty minutes, and the dependent variable would be their heart rate. In your study and in your hypothesis, you’re trying to understand the relationship between the two variables.

Elements of a Good Hypothesis

The best hypotheses start by asking the right questions . For instance, if you’ve observed that the grass is greener when it rains twice a week, you could ask what kind of grass it is, what elevation it’s at, and if the grass across the street responds to rain in the same way. Any of these questions could become the backbone of experiments to test why the grass gets greener when it rains fairly frequently.

As you’re asking more questions about your first observation, make sure you’re also making more observations . If it doesn’t rain for two weeks and the grass still looks green, that’s an important observation that could influence your hypothesis. You'll continue observing all throughout your experiment, but until the hypothesis is finalized, every observation should be noted.

Finally, you should consult secondary research before writing your hypothesis . Secondary research is comprised of results found and published by other people. You can usually find this information online or at your library. Additionally, m ake sure the research you find is credible and related to your topic. If you’re studying the correlation between rain and grass growth, it would help you to research rain patterns over the past twenty years for your county, published by a local agricultural association. You should also research the types of grass common in your area, the type of grass in your lawn, and whether anyone else has conducted experiments about your hypothesis. Also be sure you’re checking the quality of your research . Research done by a middle school student about what minerals can be found in rainwater would be less useful than an article published by a local university.

Writing Your Hypothesis

Once you’ve considered all of the factors above, you’re ready to start writing your hypothesis. Hypotheses usually take a certain form when they’re written out in a research report.

When you boil down your hypothesis statement, you are writing down your best guess and not the question at hand . This means that your statement should be written as if it is fact already, even though you are simply testing it.

The reason for this is that, after you have completed your study, you'll either accept or reject your if-then or your null hypothesis. All hypothesis testing examples should be measurable and able to be confirmed or denied. You cannot confirm a question, only a statement! 

In fact, you come up with hypothesis examples all the time! For instance, when you guess on the outcome of a basketball game, you don’t say, “Will the Miami Heat beat the Boston Celtics?” but instead, “I think the Miami Heat will beat the Boston Celtics.” You state it as if it is already true, even if it turns out you’re wrong. You do the same thing when writing your hypothesis.

Additionally, keep in mind that hypotheses can range from very specific to very broad.  These hypotheses can be specific, but if your hypothesis testing examples involve a broad range of causes and effects, your hypothesis can also be broad.  

The Two Types of Hypotheses

Now that you understand what goes into a hypothesis, it’s time to look more closely at the two most common types of hypothesis: the if-then hypothesis and the null hypothesis.

#1: If-Then Hypotheses

First of all, if-then hypotheses typically follow this formula:

If ____ happens, then ____ will happen.

The goal of this type of hypothesis is to test the causal relationship between the independent and dependent variable. It’s fairly simple, and each hypothesis can vary in how detailed it can be. We create if-then hypotheses all the time with our daily predictions. Here are some examples of hypotheses that use an if-then structure from daily life: 

• If I get enough sleep, I’ll be able to get more work done tomorrow.
• If the bus is on time, I can make it to my friend’s birthday party. 
• If I study every night this week, I’ll get a better grade on my exam. 

In each of these situations, you’re making a guess on how an independent variable (sleep, time, or studying) will affect a dependent variable (the amount of work you can do, making it to a party on time, or getting better grades). 

You may still be asking, “What is an example of a hypothesis used in scientific research?” Take one of the hypothesis examples from a real-world study on whether using technology before bed affects children’s sleep patterns. The hypothesis read s:

“We hypothesized that increased hours of tablet- and phone-based screen time at bedtime would be inversely correlated with sleep quality and child attention.”

It might not look like it, but this is an if-then statement. The researchers basically said, “If children have more screen usage at bedtime, then their quality of sleep and attention will be worse.” The sleep quality and attention are the dependent variables and the screen usage is the independent variable. (Usually, the independent variable comes after the “if” and the dependent variable comes after the “then,” as it is the independent variable that affects the dependent variable.) This is an excellent example of how flexible hypothesis statements can be, as long as the general idea of “if-then” and the independent and dependent variables are present.

#2: Null Hypotheses

Your if-then hypothesis is not the only one needed to complete a successful experiment, however. You also need a null hypothesis to test it against. In its most basic form, the null hypothesis is the opposite of your if-then hypothesis . When you write your null hypothesis, you are writing a hypothesis that suggests that your guess is not true, and that the independent and dependent variables have no relationship .

One null hypothesis for the cell phone and sleep study from the last section might say: 

“If children have more screen usage at bedtime, their quality of sleep and attention will not be worse.” 

In this case, this is a null hypothesis because it’s asking the opposite of the original thesis! 

Conversely, if your if-then hypothesis suggests that your two variables have no relationship, then your null hypothesis would suggest that there is one. So, pretend that there is a study that is asking the question, “Does the amount of followers on Instagram influence how long people spend on the app?” The independent variable is the amount of followers, and the dependent variable is the time spent. But if you, as the researcher, don’t think there is a relationship between the number of followers and time spent, you might write an if-then hypothesis that reads:

“If people have many followers on Instagram, they will not spend more time on the app than people who have less.”

In this case, the if-then suggests there isn’t a relationship between the variables. In that case, one of the null hypothesis examples might say:

“If people have many followers on Instagram, they will spend more time on the app than people who have less.”

You then test both the if-then and the null hypothesis to gauge if there is a relationship between the variables, and if so, how much of a relationship. 

4 Tips to Write the Best Hypothesis

If you’re going to take the time to hold an experiment, whether in school or by yourself, you’re also going to want to take the time to make sure your hypothesis is a good one. The best hypotheses have four major elements in common: plausibility, defined concepts, observability, and general explanation.

#1: Plausibility

At first glance, this quality of a hypothesis might seem obvious. When your hypothesis is plausible, that means it’s possible given what we know about science and general common sense. However, improbable hypotheses are more common than you might think. 

Imagine you’re studying weight gain and television watching habits. If you hypothesize that people who watch more than  twenty hours of television a week will gain two hundred pounds or more over the course of a year, this might be improbable (though it’s potentially possible). Consequently, c ommon sense can tell us the results of the study before the study even begins.

Improbable hypotheses generally go against  science, as well. Take this hypothesis example: 

“If a person smokes one cigarette a day, then they will have lungs just as healthy as the average person’s.” 

This hypothesis is obviously untrue, as studies have shown again and again that cigarettes negatively affect lung health. You must be careful that your hypotheses do not reflect your own personal opinion more than they do scientifically-supported findings. This plausibility points to the necessity of research before the hypothesis is written to make sure that your hypothesis has not already been disproven.

#2: Defined Concepts

The more advanced you are in your studies, the more likely that the terms you’re using in your hypothesis are specific to a limited set of knowledge. One of the hypothesis testing examples might include the readability of printed text in newspapers, where you might use words like “kerning” and “x-height.” Unless your readers have a background in graphic design, it’s likely that they won’t know what you mean by these terms. Thus, it’s important to either write what they mean in the hypothesis itself or in the report before the hypothesis.

Here’s what we mean. Which of the following sentences makes more sense to the common person?

If the kerning is greater than average, more words will be read per minute.

If the space between letters is greater than average, more words will be read per minute.

For people reading your report that are not experts in typography, simply adding a few more words will be helpful in clarifying exactly what the experiment is all about. It’s always a good idea to make your research and findings as accessible as possible. 

Good hypotheses ensure that you can observe the results. 

#3: Observability

In order to measure the truth or falsity of your hypothesis, you must be able to see your variables and the way they interact. For instance, if your hypothesis is that the flight patterns of satellites affect the strength of certain television signals, yet you don’t have a telescope to view the satellites or a television to monitor the signal strength, you cannot properly observe your hypothesis and thus cannot continue your study.

Some variables may seem easy to observe, but if you do not have a system of measurement in place, you cannot observe your hypothesis properly. Here’s an example: if you’re experimenting on the effect of healthy food on overall happiness, but you don’t have a way to monitor and measure what “overall happiness” means, your results will not reflect the truth. Monitoring how often someone smiles for a whole day is not reasonably observable, but having the participants state how happy they feel on a scale of one to ten is more observable. 

In writing your hypothesis, always keep in mind how you'll execute the experiment.

#4: Generalizability 

Perhaps you’d like to study what color your best friend wears the most often by observing and documenting the colors she wears each day of the week. This might be fun information for her and you to know, but beyond you two, there aren’t many people who could benefit from this experiment. When you start an experiment, you should note how generalizable your findings may be if they are confirmed. Generalizability is basically how common a particular phenomenon is to other people’s everyday life.

Let’s say you’re asking a question about the health benefits of eating an apple for one day only, you need to realize that the experiment may be too specific to be helpful. It does not help to explain a phenomenon that many people experience. If you find yourself with too specific of a hypothesis, go back to asking the big question: what is it that you want to know, and what do you think will happen between your two variables?

Hypothesis Testing Examples

We know it can be hard to write a good hypothesis unless you’ve seen some good hypothesis examples. We’ve included four hypothesis examples based on some made-up experiments. Use these as templates or launch pads for coming up with your own hypotheses.

Experiment #1: Students Studying Outside (Writing a Hypothesis)

You are a student at PrepScholar University. When you walk around campus, you notice that, when the temperature is above 60 degrees, more students study in the quad. You want to know when your fellow students are more likely to study outside. With this information, how do you make the best hypothesis possible?

You must remember to make additional observations and do secondary research before writing your hypothesis. In doing so, you notice that no one studies outside when it’s 75 degrees and raining, so this should be included in your experiment. Also, studies done on the topic beforehand suggested that students are more likely to study in temperatures less than 85 degrees. With this in mind, you feel confident that you can identify your variables and write your hypotheses:

If-then: “If the temperature in Fahrenheit is less than 60 degrees, significantly fewer students will study outside.”

Null: “If the temperature in Fahrenheit is less than 60 degrees, the same number of students will study outside as when it is more than 60 degrees.”

These hypotheses are plausible, as the temperatures are reasonably within the bounds of what is possible. The number of people in the quad is also easily observable. It is also not a phenomenon specific to only one person or at one time, but instead can explain a phenomenon for a broader group of people.

To complete this experiment, you pick the month of October to observe the quad. Every day (except on the days where it’s raining)from 3 to 4 PM, when most classes have released for the day, you observe how many people are on the quad. You measure how many people come  and how many leave. You also write down the temperature on the hour. 

After writing down all of your observations and putting them on a graph, you find that the most students study on the quad when it is 70 degrees outside, and that the number of students drops a lot once the temperature reaches 60 degrees or below. In this case, your research report would state that you accept or “failed to reject” your first hypothesis with your findings.

Experiment #2: The Cupcake Store (Forming a Simple Experiment)

Let’s say that you work at a bakery. You specialize in cupcakes, and you make only two colors of frosting: yellow and purple. You want to know what kind of customers are more likely to buy what kind of cupcake, so you set up an experiment. Your independent variable is the customer’s gender, and the dependent variable is the color of the frosting. What is an example of a hypothesis that might answer the question of this study?

Here’s what your hypotheses might look like: 

If-then: “If customers’ gender is female, then they will buy more yellow cupcakes than purple cupcakes.”

Null: “If customers’ gender is female, then they will be just as likely to buy purple cupcakes as yellow cupcakes.”

This is a pretty simple experiment! It passes the test of plausibility (there could easily be a difference), defined concepts (there’s nothing complicated about cupcakes!), observability (both color and gender can be easily observed), and general explanation ( this would potentially help you make better business decisions ).

Experiment #3: Backyard Bird Feeders (Integrating Multiple Variables and Rejecting the If-Then Hypothesis)

While watching your backyard bird feeder, you realized that different birds come on the days when you change the types of seeds. You decide that you want to see more cardinals in your backyard, so you decide to see what type of food they like the best and set up an experiment. 

However, one morning, you notice that, while some cardinals are present, blue jays are eating out of your backyard feeder filled with millet. You decide that, of all of the other birds, you would like to see the blue jays the least. This means you'll have more than one variable in your hypothesis. Your new hypotheses might look like this: 

If-then: “If sunflower seeds are placed in the bird feeders, then more cardinals will come than blue jays. If millet is placed in the bird feeders, then more blue jays will come than cardinals.”

Null: “If either sunflower seeds or millet are placed in the bird, equal numbers of cardinals and blue jays will come.”

Through simple observation, you actually find that cardinals come as often as blue jays when sunflower seeds or millet is in the bird feeder. In this case, you would reject your “if-then” hypothesis and “fail to reject” your null hypothesis . You cannot accept your first hypothesis, because it’s clearly not true. Instead you found that there was actually no relation between your different variables. Consequently, you would need to run more experiments with different variables to see if the new variables impact the results.

Experiment #4: In-Class Survey (Including an Alternative Hypothesis)

You’re about to give a speech in one of your classes about the importance of paying attention. You want to take this opportunity to test a hypothesis you’ve had for a while: 

If-then: If students sit in the first two rows of the classroom, then they will listen better than students who do not.

Null: If students sit in the first two rows of the classroom, then they will not listen better or worse than students who do not.

You give your speech and then ask your teacher if you can hand out a short survey to the class. On the survey, you’ve included questions about some of the topics you talked about. When you get back the results, you’re surprised to see that not only do the students in the first two rows not pay better attention, but they also scored worse than students in other parts of the classroom! Here, both your if-then and your null hypotheses are not representative of your findings. What do you do?

This is when you reject both your if-then and null hypotheses and instead create an alternative hypothesis . This type of hypothesis is used in the rare circumstance that neither of your hypotheses is able to capture your findings . Now you can use what you’ve learned to draft new hypotheses and test again! 

Key Takeaways: Hypothesis Writing

The more comfortable you become with writing hypotheses, the better they will become. The structure of hypotheses is flexible and may need to be changed depending on what topic you are studying. The most important thing to remember is the purpose of your hypothesis and the difference between the if-then and the null . From there, in forming your hypothesis, you should constantly be asking questions, making observations, doing secondary research, and considering your variables. After you have written your hypothesis, be sure to edit it so that it is plausible, clearly defined, observable, and helpful in explaining a general phenomenon.

Writing a hypothesis is something that everyone, from elementary school children competing in a science fair to professional scientists in a lab, needs to know how to do. Hypotheses are vital in experiments and in properly executing the scientific method . When done correctly, hypotheses will set up your studies for success and help you to understand the world a little better, one experiment at a time.

What’s Next?

If you’re studying for the science portion of the ACT, there’s definitely a lot you need to know. We’ve got the tools to help, though! Start by checking out our ultimate study guide for the ACT Science subject test. Once you read through that, be sure to download our recommended ACT Science practice tests , since they’re one of the most foolproof ways to improve your score. (And don’t forget to check out our expert guide book , too.)

If you love science and want to major in a scientific field, you should start preparing in high school . Here are the science classes you should take to set yourself up for success.

If you’re trying to think of science experiments you can do for class (or for a science fair!), here’s a list of 37 awesome science experiments you can do at home

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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Hypothesis testing involves formulating assumptions about population parameters based on sample statistics and rigorously evaluating these assumptions against empirical evidence. This article sheds light on the significance of hypothesis testing and the critical steps involved in the process.

What is Hypothesis Testing?

Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. 

Example: You say an average height in the class is 30 or a boy is taller than a girl. All of these is an assumption that we are assuming, and we need some statistical way to prove these. We need some mathematical conclusion whatever we are assuming is true.

Defining Hypotheses

Key Terms of Hypothesis Testing

• P-value: The P value , or calculated probability, is the probability of finding the observed/extreme results when the null hypothesis(H0) of a study-given problem is true. If your P-value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample claims to support the alternative hypothesis.
• Test Statistic: The test statistic is a numerical value calculated from sample data during a hypothesis test, used to determine whether to reject the null hypothesis. It is compared to a critical value or p-value to make decisions about the statistical significance of the observed results.
• Critical value : The critical value in statistics is a threshold or cutoff point used to determine whether to reject the null hypothesis in a hypothesis test.
• Degrees of freedom: Degrees of freedom are associated with the variability or freedom one has in estimating a parameter. The degrees of freedom are related to the sample size and determine the shape.

Why do we use Hypothesis Testing?

Hypothesis testing is an important procedure in statistics. Hypothesis testing evaluates two mutually exclusive population statements to determine which statement is most supported by sample data. When we say that the findings are statistically significant, thanks to hypothesis testing. 

One-Tailed and Two-Tailed Test

One tailed test focuses on one direction, either greater than or less than a specified value. We use a one-tailed test when there is a clear directional expectation based on prior knowledge or theory. The critical region is located on only one side of the distribution curve. If the sample falls into this critical region, the null hypothesis is rejected in favor of the alternative hypothesis.

One-Tailed Test

There are two types of one-tailed test:

Two-Tailed Test

A two-tailed test considers both directions, greater than and less than a specified value.We use a two-tailed test when there is no specific directional expectation, and want to detect any significant difference.

What are Type 1 and Type 2 errors in Hypothesis Testing?

In hypothesis testing, Type I and Type II errors are two possible errors that researchers can make when drawing conclusions about a population based on a sample of data. These errors are associated with the decisions made regarding the null hypothesis and the alternative hypothesis.

How does Hypothesis Testing work?

Step 1: define null and alternative hypothesis.

We first identify the problem about which we want to make an assumption keeping in mind that our assumption should be contradictory to one another, assuming Normally distributed data.

Step 2 – Choose significance level

Step 3 – Collect and Analyze data.

Gather relevant data through observation or experimentation. Analyze the data using appropriate statistical methods to obtain a test statistic.

Step 4-Calculate Test Statistic

The data for the tests are evaluated in this step we look for various scores based on the characteristics of data. The choice of the test statistic depends on the type of hypothesis test being conducted.

There are various hypothesis tests, each appropriate for various goal to calculate our test. This could be a Z-test , Chi-square , T-test , and so on.

• Z-test : If population means and standard deviations are known. Z-statistic is commonly used.
• t-test : If population standard deviations are unknown. and sample size is small than t-test statistic is more appropriate.
• Chi-square test : Chi-square test is used for categorical data or for testing independence in contingency tables
• F-test : F-test is often used in analysis of variance (ANOVA) to compare variances or test the equality of means across multiple groups.

We have a smaller dataset, So, T-test is more appropriate to test our hypothesis.

T-statistic is a measure of the difference between the means of two groups relative to the variability within each group. It is calculated as the difference between the sample means divided by the standard error of the difference. It is also known as the t-value or t-score.

Step 5 – Comparing Test Statistic:

In this stage, we decide where we should accept the null hypothesis or reject the null hypothesis. There are two ways to decide where we should accept or reject the null hypothesis.

Method A: Using Crtical values

Comparing the test statistic and tabulated critical value we have,

• If Test Statistic>Critical Value: Reject the null hypothesis.
• If Test Statistic≤Critical Value: Fail to reject the null hypothesis.

Note: Critical values are predetermined threshold values that are used to make a decision in hypothesis testing. To determine critical values for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Method B: Using P-values

We can also come to an conclusion using the p-value,

Note : The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed in the sample, assuming the null hypothesis is true. To determine p-value for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Step 7- Interpret the Results

At last, we can conclude our experiment using method A or B.

Calculating test statistic

To validate our hypothesis about a population parameter we use statistical functions . We use the z-score, p-value, and level of significance(alpha) to make evidence for our hypothesis for normally distributed data .

1. Z-statistics:

When population means and standard deviations are known.

• μ represents the population mean, 
• σ is the standard deviation
• and n is the size of the sample.

2. T-Statistics

T test is used when n<30,

t-statistic calculation is given by:

• t = t-score,
• x̄ = sample mean
• μ = population mean,
• s = standard deviation of the sample,
• n = sample size

3. Chi-Square Test

Chi-Square Test for Independence categorical Data (Non-normally distributed) using:

• i,j are the rows and columns index respectively.

Real life Hypothesis Testing example

Let’s examine hypothesis testing using two real life situations,

Case A: D oes a New Drug Affect Blood Pressure?

Imagine a pharmaceutical company has developed a new drug that they believe can effectively lower blood pressure in patients with hypertension. Before bringing the drug to market, they need to conduct a study to assess its impact on blood pressure.

• Before Treatment: 120, 122, 118, 130, 125, 128, 115, 121, 123, 119
• After Treatment: 115, 120, 112, 128, 122, 125, 110, 117, 119, 114

Step 1 : Define the Hypothesis

• Null Hypothesis : (H 0 )The new drug has no effect on blood pressure.
• Alternate Hypothesis : (H 1 )The new drug has an effect on blood pressure.

Step 2: Define the Significance level

Let’s consider the Significance level at 0.05, indicating rejection of the null hypothesis.

If the evidence suggests less than a 5% chance of observing the results due to random variation.

Step 3 : Compute the test statistic

Using paired T-test analyze the data to obtain a test statistic and a p-value.

The test statistic (e.g., T-statistic) is calculated based on the differences between blood pressure measurements before and after treatment.

t = m/(s/√n)

• m  = mean of the difference i.e X after, X before
• s  = standard deviation of the difference (d) i.e d i ​= X after, i ​− X before,
• n  = sample size,

then, m= -3.9, s= 1.8 and n= 10

we, calculate the , T-statistic = -9 based on the formula for paired t test

Step 4: Find the p-value

The calculated t-statistic is -9 and degrees of freedom df = 9, you can find the p-value using statistical software or a t-distribution table.

thus, p-value = 8.538051223166285e-06

Step 5: Result

• If the p-value is less than or equal to 0.05, the researchers reject the null hypothesis.
• If the p-value is greater than 0.05, they fail to reject the null hypothesis.

Conclusion: Since the p-value (8.538051223166285e-06) is less than the significance level (0.05), the researchers reject the null hypothesis. There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

Python Implementation of Hypothesis Testing

Let’s create hypothesis testing with python, where we are testing whether a new drug affects blood pressure. For this example, we will use a paired T-test. We’ll use the scipy.stats library for the T-test.

Scipy is a mathematical library in Python that is mostly used for mathematical equations and computations.

We will implement our first real life problem via python,

In the above example, given the T-statistic of approximately -9 and an extremely small p-value, the results indicate a strong case to reject the null hypothesis at a significance level of 0.05. 

• The results suggest that the new drug, treatment, or intervention has a significant effect on lowering blood pressure.
• The negative T-statistic indicates that the mean blood pressure after treatment is significantly lower than the assumed population mean before treatment.

Case B : Cholesterol level in a population

Data: A sample of 25 individuals is taken, and their cholesterol levels are measured.

Cholesterol Levels (mg/dL): 205, 198, 210, 190, 215, 205, 200, 192, 198, 205, 198, 202, 208, 200, 205, 198, 205, 210, 192, 205, 198, 205, 210, 192, 205.

Populations Mean = 200

Population Standard Deviation (σ): 5 mg/dL(given for this problem)

Step 1: Define the Hypothesis

• Null Hypothesis (H 0 ): The average cholesterol level in a population is 200 mg/dL.
• Alternate Hypothesis (H 1 ): The average cholesterol level in a population is different from 200 mg/dL.

As the direction of deviation is not given , we assume a two-tailed test, and based on a normal distribution table, the critical values for a significance level of 0.05 (two-tailed) can be calculated through the z-table and are approximately -1.96 and 1.96.

Step 4: Result

Since the absolute value of the test statistic (2.04) is greater than the critical value (1.96), we reject the null hypothesis. And conclude that, there is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL

Limitations of Hypothesis Testing

• Although a useful technique, hypothesis testing does not offer a comprehensive grasp of the topic being studied. Without fully reflecting the intricacy or whole context of the phenomena, it concentrates on certain hypotheses and statistical significance.
• The accuracy of hypothesis testing results is contingent on the quality of available data and the appropriateness of statistical methods used. Inaccurate data or poorly formulated hypotheses can lead to incorrect conclusions.
• Relying solely on hypothesis testing may cause analysts to overlook significant patterns or relationships in the data that are not captured by the specific hypotheses being tested. This limitation underscores the importance of complimenting hypothesis testing with other analytical approaches.

Hypothesis testing stands as a cornerstone in statistical analysis, enabling data scientists to navigate uncertainties and draw credible inferences from sample data. By systematically defining null and alternative hypotheses, choosing significance levels, and leveraging statistical tests, researchers can assess the validity of their assumptions. The article also elucidates the critical distinction between Type I and Type II errors, providing a comprehensive understanding of the nuanced decision-making process inherent in hypothesis testing. The real-life example of testing a new drug’s effect on blood pressure using a paired T-test showcases the practical application of these principles, underscoring the importance of statistical rigor in data-driven decision-making.

Frequently Asked Questions (FAQs)

1. what are the 3 types of hypothesis test.

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed. Right-tailed tests assess if a parameter is greater, left-tailed if lesser. Two-tailed tests check for non-directional differences, greater or lesser.

2.What are the 4 components of hypothesis testing?

Null Hypothesis ( ): No effect or difference exists. Alternative Hypothesis ( ): An effect or difference exists. Significance Level ( ): Risk of rejecting null hypothesis when it’s true (Type I error). Test Statistic: Numerical value representing observed evidence against null hypothesis.

3.What is hypothesis testing in ML?

Statistical method to evaluate the performance and validity of machine learning models. Tests specific hypotheses about model behavior, like whether features influence predictions or if a model generalizes well to unseen data.

4.What is the difference between Pytest and hypothesis in Python?

Pytest purposes general testing framework for Python code while Hypothesis is a Property-based testing framework for Python, focusing on generating test cases based on specified properties of the code.

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Practicing Hypothesis-Driven Development in Azure DevOps

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I like to think of Scrum Product Owners as mini-CEOs of their product. As such, they should be empowered to drive value in any direction that they desire. This often requires a Product Owner to hypothesize about an outcome and then run an experiment to prove or disprove it. Rather than just building features blindly, a Professional Product Owner bases their decisions on data.

Hypothesis-Driven Development

Hypothesis-Driven Development (HDD) is a complementary practice that incorporates an experimentation-based approach to product development. With HDD, each Product Backlog item (e.g. feature or user story) begins with a clearly defined hypothesis that predicts how this new capability will impact user behavior or achieve specific outcomes. The results from these experiments guide the next steps: whether to iterate, pivot, or abandon - all based on actual data rather than just guessing.

“Test-Driven Development is a great excuse to think about the problem before you think about the solution. Hypothesis-Driven Development is a great opportunity to test what you think the problem is before you work on the solution.” Kent Beck, creator of eXtreme Programming

HDD, based on Lean principles, can enhance Scrum's iterative nature by ensuring that the development of risky/costly items is based on empirical evidence and real user feedback, fostering a more focused and adaptive product development process.

Practicing Hypothesis-Driven Development

There are several ways to practice HDD and craft a hypothesis. I like the format put forward in this Thoughtworks post by Barry O'Reilly as it's akin to the user-story description format ...

Creating a Hypothesis work item type in Azure DevOps

The first step is to create a custom work item type in your Azure DevOps project. You will need to have the appropriate permissions to do this. Refer to this page for more information. I will, of course, create an inherited process based on the Scrum process, naming it Hypothesis-Driven Scrum and adding a new Hypothesis work item type ...

Next, I'll add the supporting fields and make any other tweaks (such as hiding the Description field) ...

I'll also edit the Backlog levels and include the new Hypothesis work item type on the Backlog items backlog ...

This is an optional step, but if you don't do this, then you will need to create a custom work item query to retrieve all of your Hypothesis work items. You might want to do this anyway so that you could have a dedicated dashboard showing the various hypotheses.

Forming and testing a hypothesis

Next, I'll create a new Azure DevOps project (or convert an existing one to use the new process). This provides me access to the new work item type, which I can start using to form, track, and manage my hypotheses, such as this one ...

Should you practice HDD with every item in the Product Backlog? I wouldn't. But, for those tricky, risky, and expensive features, I would definitely consider this approach, or at least starting to think in terms of hypothesis (and the expected, measurable outcomes), to help ensure that the product aligns with user needs as well as business and product goals.

Leveraging empirical evidence to make informed decisions? Sounds like good Scrum to me!

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Title: vulcan: retreading a tired hypothesis with the 2024 total solar eclipse.

Abstract: The number of planets in the solar system over the last three centuries has, perhaps surprisingly, been less of a fixed value than one would think it should be. In this paper, we look at the specific case of Vulcan, which was both a planet before Pluto was a planet and discarded from being a planet before Pluto was downgraded. We examine the historical context that led to its discovery in the 19th century, the decades of observations that were taken of it, and its eventual fall from glory. By applying a more modern understanding of astrophysics, we provide multiple mechanisms that may have changed the orbit of Vulcan sufficiently that it would have been outside the footprint of early 20th century searches for it. Finally, we discuss how the April 8, 2024 eclipse provides a renewed opportunity to rediscover this lost planet after more than a century of having been overlooked.

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Dr. Marty Makary: “We’ll Have Herd Immunity by April” & “It’s Okay To Have an Incorrect Scientific Hypothesis. But When New Data Proves It Wrong, You Have To Adapt.”

Part 1: Doctors who said the pandemic ended 3-years ago now have the audacity to lament the “damaged public trust in the medical profession.”

Unfortunately, many elected leaders and public health officials have held on far too long to the hypothesis that natural immunity offers unreliable protection against covid-19 — a contention that is being rapidly debunked by science.

On September 15th, 2021, Dr. Marty Makary authored an article titled Natural Immunity to Covid Is Powerful. Policymakers Seem Afraid to Say So . It started by saying:

It’s okay to have an incorrect scientific hypothesis. But when new data proves it wrong, you have to adapt. Unfortunately, many elected leaders and public health officials have held on far too long to the hypothesis that natural immunity offers unreliable protection against covid-19 — a contention that is being rapidly debunked by science.

These three sentences have an interesting relationship, don’t they?

We’ll Have Herd Immunity by April

I’ll return to them in a bit, but first let’s flashback to February 2021. 450,000 Americans died of COVID in in the pandemic’s first year, overwhelming hospitals and morgues. The worst wave, where over 3,000 Americans died per day, was just receding. The virus was just 1 year-old, and it had given us plenty of reasons to respect it so far.

Not everyone felt that way.

On February 18th, Dr. Markary authored an article titled We’ll Have Herd Immunity by April . He was very confident about this new virus. “Experts should level with the public about the good news,” he said. He said:

Some medical experts privately agreed with my prediction that there may be very little Covid-19 by April but suggested that I not to talk publicly about herd immunity because people might become complacent and fail to take precautions or might decline the vaccine. But scientists shouldn’t try to manipulate the public by hiding the truth…Herd immunity is the inevitable result of viral spread and vaccination. When the chain of virus transmission has been broken in multiple places, it’s harder for it to spread—and that includes the new strains.

Then in March, he authored an article titled Herd Immunity Is Near, Despite Fauci’s Denial . He said:

Anthony Fauci has been saying that the country needs to vaccinate 70% to 85% of the population to reach herd immunity from Covid-19. But he inexplicably ignores natural immunity. If you account for previous infections, herd immunity is likely close at hand.

In May, Dr. Makary continued his media blitz to announce big news . He had been right. Herd immunity had arrived, and it was time to “stop living in fear”. In an article titled Don’t Buy The Fearmongering: The COVID-19 Threat Is Waning he said “On a clinical level, we simply have not seen significant re-infections at any concerning rate.” “The public-health threat is now defanged”, he added.

In another article titled Risk Of COVID Is Now Very Low — It’s Time To Stop Living In Fear: Doctor he said:

COVID cases are collapsing in front of our eyes…Yet some people want the pandemic to stretch out longer

During an interview on Fox New that month, he dismissed the concerns about variants and said the main priority was to not “scare people”. “People need something to look forward to,” he said. He also had this exchange :

Question : You talked about this a couple of months ago.  You said look, we are two months away from herd immunity. Are we there, are we closer, is it ever going to be full realized in your estimation? Answer : Well unfortunately, we have this perception now that’s being created by some public health leaders that we reach to total eradication.  And we’re not going to get to total risk elimination. That is a false goal and quite honestly it’s being used to manipulate the public. We heard today if get to 70% vaccination, then we can see restrictions. That’s dishonest.  Most of the country is at herd immunity.  Other parts will get there later this month… I call that herd immunity.

I don’t remember anyone serious talking about “total risk elimination” in May 2021, though through this straw man argument, Dr. Makary sought to convince his audience that “public health leaders” were dishonest manipulators out to scare people. In contrast, he was a straight shooter, willing to tell bravely the truth- most of the country is at herd immunity .

In June, Dr. Makary formalized his thoughts in an article called The Power of Natural Immunity , another article that paid homage to the “power” of being infected with a potentially deadly virus. He said:

The news about the U.S. Covid pandemic is even better than you’ve heard… There’s ample scientific evidence that natural immunity is effective and durable, and public-health leaders should pay it heed.

With more than 8 in 10 adults protected from either contracting or transmitting the virus, it can’t readily propagate by jumping around in the population. In public health, we call that herd immunity, defined broadly on the Johns Hopkins Covid information webpage as “when most of a population is immune.” It’s not eradication, but it’s powerful.

Dr. Makary concluded:

It’s time to stop the fear mongering and level with the public. 

So far this year, nearly 2.8 million cases of COVID have been reported in the U.S.

Let’s return to those three sentences from Dr. Makary’s article Natural Immunity to Covid Is Powerful. Policymakers Seem Afraid to Say So :

We all know what happened next.

Since February 2021, when Dr. Makary penned We’ll Have Herd Immunity by April, around 700,000 Americans have died of COVID and millions more have been injured by it. It’s not over yet. Unfortunately, those “elected leaders and public health officials” turned out to be right. Natural immunity offers unreliable protection against COVID, and reinfections are hardly rare events. Despite the abundance and “power” of natural immunity, we still do not have herd immunity.

Delta is downgraded to a mild seasonal virus that causes mild common cold-like symptoms.

So, did Dr. Makary adapt when new data proved his scientific hypothesis was incorrect? Not that I’ve seen. I have not seen him acknowledge his bizarre fetishization of the “power of natural immunity” was misplaced. I have not seen him revisit his doomed declarations of herd immunity. I have not seen him retract his unprofessional slurs that “public health leaders” were “dishonest” and trying to “manipulate the public” because they wanted the pandemic to continue.

He’s not alone.

Many doctors sounded exactly like Dr. Makary in 2021. These “free-thinking” doctors also claimed that natural immunity was a “ triumph ,” that vaccines were a panacea for those who needed them, that variants were nothing to “panic” about, and that kid’s didn’t need the COVID vaccine because the pandemic was ending . They too disparaged anyone who disagreed as having an “ addiction to doom and gloom. ”

Yet, when the pandemic failed to end, these doctors just barreled on full-steam ahead as if none of that ever happened. Their confident, optimistic proclamations- most of the country is at herd immunity – were made and then instantly forgotten, without a moment’s recognition of error or the slightest expression of regret to those they smeared as “fear mongers.”

In fact, doctors who said the pandemic was winding down in the first half of 2021, devoted the second half of that year not to pausing their COVID commentary and reflecting on their failed forecasts, but rather by doubling down and minimizing the variants that obliterated their pollyannaish predictions. No matter what was happening on the ground, they just kept robotically repeating the exact same things they’d always said. There was always “ reassuring data “. It was always time to stop “ living in fear “. They were all completely predictable.

• Dr. Jay Bhattacharya, who said in March, “We should not be particularly concerned about the variants,” said in July , “I don’t think the Delta variant changes the calculus or the evidence in any fundamental way.” Then in December, he starred in a podcast titled Why No One Should Panic About the Omicron Variant , in which he said “this is not something to panic about.”
• Dr. Monica Gandhi, who gave an interview titled Pandemic Exit Interviews: Stop Panicking About the COVID-19 Variants, Says UCSF’s Monica Gandhi in February, wrote an article titled The Reassuring Data on the Delta Variant in July. Then in December, she gave an interview titled, The Cautious Case for Omicron Optimism Dr. Monica Gandhi Says There’s Reason to Trust Preliminary Reports of Mild Illness .
• Dr. Zubin Damania, who recorded a podcast with Dr. Gandhi called The End of the Pandemic in February, wrote an article titled The Delta Surge May Collapse Faster Than You Think in August. Then, in January 2022, he said the Omicron variant was “Omi-cold, and we generate immunity from being infected by it”.
• Dr. Lucy McBride, who wrote I’ve Been Yearning For An End To The Pandemic. Now That It’s Here, I’m A Little Afraid in March, wrote an article about the Delta variant titled Fear of COVID-19 in Kids Is Getting Ahead of the Data in August, as if waiting for “data” before reacting to a deadly virus is always wise.

Articles from February, July, and December 2021

Like these doctors, Dr. Makary also failed to adapt to new data when the Delta variant arrived, wrecking his declarations of herd immunity. As it ripped through much the country , he just kept robotically repeating the exact same things he’d always said. He gave in interview in June titled Dr. Marty Makary Pans ‘Fear-Mongering’ Over Delta Variant , and in August he said :

If you’re one of the 99%+ of kids that are unvaccinated…those kids don’t need to worry…For most people right now, Delta is downgraded to a mild seasonal virus that causes mild common cold-like symptoms…The vaccines have been perfectly consistent against all of the variants.

Of course, Dr. Makary and these other doctors were wrong about the Delta variant, which caused “ record deaths ” in many parts of the country and hit children harder than ever before, especially unvaccinated ones .

Predictably, Dr. Makary also failed to adapt to new data when the Omicron variant arrived. As it ripped through much the country , he just kept robotically repeating the exact same things he’d always said. In December, he glorified the Omicron variant as “ nature’s vaccine ” and in an interview on Fox News titled Omicron Fear Fueling a ‘Second Pandemic of Lunacy’ said:

We’re seeing this massive new wave of fear that is fueling our second pandemic after COVID-19, which is a pandemic of lunacy, which is omicron. Now I call it omi-cold… This new scientific data from the lab explains the epidemiological data and the bedside observation of doctors that this is far more mild… and that’s why I call it omi-cold.

Of course, Dr. Makary and these other doctors were wrong about the Omicron variant, as the articles During the Omicron Wave, Death Rates Soared for Older People and Hospitalizations Of Young Children With The Virus Surged During The U.S. Omicron Wave explain.

All that from the doctor who instructed others :

It’s okay to have an incorrect scientific hypothesis. But when new data proves it wrong, you have to adapt.

Public health officials actively propagated misinformation that ruined lives and forever damaged public trust in the medical profession.

Many people adapted to new data and relinquished their optimistic pandemic estimations when immune-evading variants arrived in the summer of 2021. These doctors did not. Minimizing COVID was a pure reflex for them. It was literally all they could do. What more could the virus have done to make them say, “ OOPS! I was wrong to have said the pandemic was over “? The answer, of course, is “nothing.”

To my knowledge, just one of these doctors has ever acknowledged error for prematurely declaring the pandemic over. He’s also stopped doing this. Good for him. However, I can’t recall any doctor who said the pandemic ended in spring 2021 who later had the integrity to honestly reckon with the consequences of blasting out that false message in major media outlets for months on end. Million of Americans trusted these highly-credential doctors who spoke with great confidence when they said what we all wanted to hear.

How are these people doing today? Did all they all turn out OK?

Predictably, instead of showing even a hint of concern about the fate of their audience and introspecting for a nanosecond, these doctors keep robotically repeating the exact same things they’ve always said. Despite his inglorious track record, Dr. Makary still fancies himself a brave truth-teller, entitled to sanctimoniously scold those dastardly “public health officials”. In an article from February 2023, ironically titled 10 Myths Told by COVID Experts — And Now Debunked , Dr. Makary spread blatant anti-vaccine falsities and continued to lavish praise on “natural immunity”. He also said this:

Imagine the utter audacity, shamelessness, and lack of self-awareness it takes for the author of We’ll Have Herd Immunity by April to write that contemptible slur about people who were right about herd immunity 3-years ago. Nonetheless, I won’t disagree with him for saying:

That’s actually a really good idea.

Articles from February, May, June, and December 2021

Dr. Jonathan Howard is a neurologist and psychiatrist who has been interested in vaccines since long before COVID-19. He is the author of "We Want Them Infected: How the failed quest for herd immunity led doctors to embrace the anti-vaccine movement and blinded Americans to the threat of COVID."

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• Posted in: Science and Medicine

Posted by Jonathan Howard