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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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See an example

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 ).

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

Methodology

• 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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Biology library

Course: biology library   >   unit 1, the scientific method.

• Controlled experiments
• The scientific method and experimental design

Introduction

• Make an observation.
• Ask a question.
• Form a hypothesis , or testable explanation.
• Make a prediction based on the hypothesis.
• Test the prediction.
• Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation..

• Observation: the toaster won't toast.

2. Ask a question.

• Question: Why won't my toaster toast?

3. Propose a hypothesis.

• Hypothesis: Maybe the outlet is broken.

4. Make predictions.

• Prediction: If I plug the toaster into a different outlet, then it will toast the bread.

5. Test the predictions.

• Test of prediction: Plug the toaster into a different outlet and try again.
• If the toaster does toast, then the hypothesis is supported—likely correct.
• If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

• Iteration time!
• If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
• If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

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Hypothesis Testing Framework

Now that we've seen an example and explored some of the themes for hypothesis testing, let's specify the procedure that we will follow.

Hypothesis Testing Steps

The formal framework and steps for hypothesis testing are as follows:

• Identify and define the parameter of interest
• Define the competing hypotheses to test
• Set the evidence threshold, formally called the significance level
• Generate or use theory to specify the sampling distribution and check conditions
• Calculate the test statistic and p-value
• Evaluate your results and write a conclusion in the context of the problem.

We'll discuss each of these steps below.

Identify Parameter of Interest

First, I like to specify and define the parameter of interest. What is the population that we are interested in? What characteristic are we measuring?

By defining our population of interest, we can confirm that we are truly using sample data. If we find that we actually have population data, our inference procedures are not needed. We could proceed by summarizing our population data.

By identifying and defining the parameter of interest, we can confirm that we use appropriate methods to summarize our variable of interest. We can also focus on the specific process needed for our parameter of interest.

In our example from the last page, the parameter of interest would be the population mean time that a host has been on Airbnb for the population of all Chicago listings on Airbnb in March 2023. We could represent this parameter with the symbol $\mu$. It is best practice to fully define $\mu$ both with words and symbol.

Define the Hypotheses

For hypothesis testing, we need to decide between two competing theories. These theories must be statements about the parameter. Although we won't have the population data to definitively select the correct theory, we will use our sample data to determine how reasonable our "skeptic's theory" is.

The first hypothesis is called the null hypothesis, $H_0$. This can be thought of as the "status quo", the "skeptic's theory", or that nothing is happening.

Examples of null hypotheses include that the population proportion is equal to 0.5 ($p = 0.5$), the population median is equal to 12 ($M = 12$), or the population mean is equal to 14.5 ($\mu = 14.5$).

The second hypothesis is called the alternative hypothesis, $H_a$ or $H_1$. This can be thought of as the "researcher's hypothesis" or that something is happening. This is what we'd like to convince the skeptic to believe. In most cases, the desired outcome of the researcher is to conclude that the alternative hypothesis is reasonable to use moving forward.

Examples of alternative hypotheses include that the population proportion is greater than 0.5 ($p > 0.5$), the population median is less than 12 ($M < 12$), or the population mean is not equal to 14.5 ($\mu \neq 14.5$).

There are a few requirements for the hypotheses:

• the hypotheses must be about the same population parameter,
• the hypotheses must have the same null value (provided number to compare to),
• the null hypothesis must have the equality (the equals sign must be in the null hypothesis),
• the alternative hypothesis must not have the equality (the equals sign cannot be in the alternative hypothesis),
• there must be no overlap between the null and alternative hypothesis.

You may have previously seen null hypotheses that include more than an equality (e.g. $p \le 0.5$). As long as there is an equality in the null hypothesis, this is allowed. For our purposes, we will simplify this statement to ($p = 0.5$).

To summarize from above, possible hypotheses statements are:

$H_0: p = 0.5$ vs. $H_a: p > 0.5$

$H_0: M = 12$ vs. $H_a: M < 12$

$H_0: \mu = 14.5$ vs. $H_a: \mu \neq 14.5$

In our second example about Airbnb hosts, our hypotheses would be:

$H_0: \mu = 2100$ vs. $H_a: \mu > 2100$.

Set Threshold (Significance Level)

There is one more step to complete before looking at the data. This is to set the threshold needed to convince the skeptic. This threshold is defined as an $\alpha$ significance level. We'll define exactly what the $\alpha$ significance level means later. For now, smaller $\alpha$s correspond to more evidence being required to convince the skeptic.

A few common $\alpha$ levels include 0.1, 0.05, and 0.01.

For our Airbnb hosts example, we'll set the threshold as 0.02.

Determine the Sampling Distribution of the Sample Statistic

The first step (as outlined above) is the identify the parameter of interest. What is the best estimate of the parameter of interest? Typically, it will be the sample statistic that corresponds to the parameter. This sample statistic, along with other features of the distribution will prove especially helpful as we continue the hypothesis testing procedure.

However, we do have a decision at this step. We can choose to use simulations with a resampling approach or we can choose to rely on theory if we are using proportions or means. We then also need to confirm that our results and conclusions will be valid based on the available data.

Required Condition

The one required assumption, regardless of approach (resampling or theory), is that the sample is random and representative of the population of interest. In other words, we need our sample to be a reasonable sample of data from the population.

Using Simulations and Resampling

If we'd like to use a resampling approach, we have no (or minimal) additional assumptions to check. This is because we are relying on the available data instead of assumptions.

We do need to adjust our data to be consistent with the null hypothesis (or skeptic's claim). We can then rely on our resampling approach to estimate a plausible sampling distribution for our sample statistic.

Recall that we took this approach on the last page. Before simulating our estimated sampling distribution, we adjusted the mean of the data so that it matched with our skeptic's claim, shown in the code below.

We'll see a few more examples on the next page.

Using Theory

On the other hand, we could rely on theory in order to estimate the sampling distribution of our desired statistic. Recall that we had a few different options to rely on:

• the CLT for the sampling distribution of a sample mean
• the binomial distribution for the sampling distribution of a proportion (or count)
• the Normal approximation of a binomial distribution (using the CLT) for the sampling distribution of a proportion

If relying on the CLT to specify the underlying sampling distribution, you also need to confirm:

• having a random sample and
• having a sample size that is less than 10% of the population size if the sampling is done without replacement
• having a Normally distributed population for a quantitative variable OR
• having a large enough sample size (usually at least 25) for a quantitative variable
• having a large enough sample size for a categorical variable (defined by $np$ and $n(1-p)$ being at least 10)

If relying on the binomial distribution to specify the underlying sampling distribution, you need to confirm:

• having a set number of trials, $n$
• having the same probability of success, $p$ for each observation

After determining the appropriate theory to use, we should check our conditions and then specify the sampling distribution for our statistic.

For the Airbnb hosts example, we have what we've assumed to be a random sample. It is not taken with replacement, so we also need to assume that our sample size (700) is less than 10% of our population size. In other words, we need to assume that the population of Chicago Airbnbs in March 2023 was at least 7000. Since we do have our (presumed) population data available, we can confirm that there were at least 7000 Chicago Airbnbs in the population in 2023.

Additionally, we can confirm that normality of the sampling distribution applies for the CLT to apply. Our sample size is more than 25 and the parameter of interest is a mean, so this meets our necessary criteria for the normality condition to be valid.

With the conditions now met, we can estimate our sampling distribution. From the CLT, we know that the distribution for the sample mean should be $\bar{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$.

Now, we face our next challenge -- what to plug in as the mean and standard error for this distribution. Since we are adopting the skeptic's point of view for the purpose of this approach, we can plug in the value of $\mu_0 = 2100$. We also know that the sample size $n$ is 700. But what should we plug in for the population standard deviation $\sigma$?

When we don't know the value of a parameter, we will generally plug in our best estimate for the parameter. In this case, that corresponds to plugging in $\hat{\sigma}$, or our sample standard deviation.

Now, our estimated sampling distribution based on the CLT is: $\bar{X} \sim N(2100, 41.4045)$.

If we compare to our corresponding skeptic's sampling distribution on the last page, we can confirm that the theoretical sampling distribution is similar to the simulated sampling distribution based on resampling.

Assumptions not met

What do we do if the necessary conditions aren't met for the sampling distribution? Because the simulation-based resampling approach has minimal assumptions, we should be able to use this approach to produce valid results as long as the provided data is representative of the population.

The theory-based approach has more conditions, and we may not be able to meet all of the necessary conditions. For example, if our parameter is something other than a mean or proportion, we may not have appropriate theory. Additionally, we may not have a large enough sample size.

• First, we could consider changing approaches to the simulation-based one.
• Second, we might look at how we could meet the necessary conditions better. In some cases, we may be able to redefine groups or make adjustments so that the setup of the test is closer to what is needed.
• As a last resort, we may be able to continue following the hypothesis testing steps. In this case, your calculations may not be valid or exact; however, you might be able to use them as an estimate or an approximation. It would be crucial to specify the violation and approximation in any conclusions or discussion of the test.

Calculate the evidence with statistics and p-values

Now, it's time to calculate how much evidence the sample contains to convince the skeptic to change their mind. As we saw above, we can convince the skeptic to change their mind by demonstrating that our sample is unlikely to occur if their theory is correct.

How do we do this? We do this by calculating a probability associated with our observed value for the statistic.

For example, for our situation, we want to convince the skeptic that the population mean is actually greater than 2100 days. We do that by calculating the probability that a sample mean would be as large or larger than what we observed in our actual sample, which was 2188 days. Why do we need the larger portion? We use the larger portion because a sample mean of 2200 days also provides evidence that the population mean is larger than 2100 days; it isn't limited to exactly what we observed in our sample. We call this specific probability the p-value.

That is, the p-value is the probability of observing a test statistic as extreme or more extreme (as determined by the alternative hypothesis), assuming the null hypothesis is true.

Our observed p-value for the Airbnb host example demonstrates that the probability of getting a sample mean host time of 2188 days (the value from our sample) or more is 1.46%, assuming that the true population mean is 2100 days.

Test statistic

Notice that the formal definition of a p-value mentions a test statistic . In most cases, this word can be replaced with "statistic" or "sample" for an equivalent statement.

Oftentimes, we'll see that our sample statistic can be used directly as the test statistic, as it was above. We could equivalently adjust our statistic to calculate a test statistic. This test statistic is often calculated as:

$\text{test statistic} = \frac{\text{estimate} - \text{hypothesized value}}{\text{standard error of estimate}}$

P-value Calculation Options

Note also that the p-value definition includes a probability associated with a test statistic being as extreme or more extreme (as determined by the alternative hypothesis . How do we determine the area that we consider when calculating the probability. This decision is determined by the inequality in the alternative hypothesis.

For example, when we were trying to convince the skeptic that the population mean is greater than 2100 days, we only considered those sample means that we at least as large as what we observed -- 2188 days or more.

If instead we were trying to convince the skeptic that the population mean is less than 2100 days ($H_a: \mu < 2100$), we would consider all sample means that were at most what we observed - 2188 days or less. In this case, our p-value would be quite large; it would be around 99.5%. This large p-value demonstrates that our sample does not support the alternative hypothesis. In fact, our sample would encourage us to choose the null hypothesis instead of the alternative hypothesis of $\mu < 2100$, as our sample directly contradicts the statement in the alternative hypothesis.

If we wanted to convince the skeptic that they were wrong and that the population mean is anything other than 2100 days ($H_a: \mu \neq 2100$), then we would want to calculate the probability that a sample mean is at least 88 days away from 2100 days. That is, we would calculate the probability corresponding to 2188 days or more or 2012 days or less. In this case, our p-value would be roughly twice the previously calculated p-value.

We could calculate all of those probabilities using our sampling distributions, either simulated or theoretical, that we generated in the previous step. If we chose to calculate a test statistic as defined in the previous section, we could also rely on standard normal distributions to calculate our p-value.

Evaluate your results and write conclusion in context of problem

Once you've gathered your evidence, it's now time to make your final conclusions and determine how you might proceed.

In traditional hypothesis testing, you often make a decision. Recall that you have your threshold (significance level $\alpha$) and your level of evidence (p-value). We can compare the two to determine if your p-value is less than or equal to your threshold. If it is, you have enough evidence to persuade your skeptic to change their mind. If it is larger than the threshold, you don't have quite enough evidence to convince the skeptic.

Common formal conclusions (if given in context) would be:

• I have enough evidence to reject the null hypothesis (the skeptic's claim), and I have sufficient evidence to suggest that the alternative hypothesis is instead true.
• I do not have enough evidence to reject the null hypothesis (the skeptic's claim), and so I do not have sufficient evidence to suggest the alternative hypothesis is true.

The only decision that we can make is to either reject or fail to reject the null hypothesis (we cannot "accept" the null hypothesis). Because we aren't actively evaluating the alternative hypothesis, we don't want to make definitive decisions based on that hypothesis. However, when it comes to making our conclusion for what to use going forward, we frame this on whether we could successfully convince someone of the alternative hypothesis.

A less formal conclusion might look something like:

Based on our sample of Chicago Airbnb listings, it seems as if the mean time since a host has been on Airbnb (for all Chicago Airbnb listings) is more than 5.75 years.

Significance Level Interpretation

We've now seen how the significance level $\alpha$ is used as a threshold for hypothesis testing. What exactly is the significance level?

The significance level $\alpha$ has two primary definitions. One is that the significance level is the maximum probability required to reject the null hypothesis; this is based on how the significance level functions within the hypothesis testing framework. The second definition is that this is the probability of rejecting the null hypothesis when the null hypothesis is true; in other words, this is the probability of making a specific type of error called a Type I error.

Why do we have to be comfortable making a Type I error? There is always a chance that the skeptic was originally correct and we obtained a very unusual sample. We don't want to the skeptic to be so convinced of their theory that no evidence can convince them. In this case, we need the skeptic to be convinced as long as the evidence is strong enough . Typically, the probability threshold will be low, to reduce the number of errors made. This also means that a decent amount of evidence will be needed to convince the skeptic to abandon their position in favor of the alternative theory.

p-value Limitations and Misconceptions

In comparison to the $\alpha$ significance level, we also need to calculate the evidence against the null hypothesis with the p-value.

The p-value is the probability of getting a test statistic as extreme or more extreme (in the direction of the alternative hypothesis), assuming the null hypothesis is true.

Recently, p-values have gotten some bad press in terms of how they are used. However, that doesn't mean that p-values should be abandoned, as they still provide some helpful information. Below, we'll describe what p-values don't mean, and how they should or shouldn't be used to make decisions.

Factors that affect a p-value

What features affect the size of a p-value?

• the null value, or the value assumed under the null hypothesis
• the effect size (the difference between the null value under the null hypothesis and the true value of the parameter)
• the sample size

More evidence against the null hypothesis will be obtained if the effect size is larger and if the sample size is larger.

Misconceptions

We gave a definition for p-values above. What are some examples that p-values don't mean?

• A p-value is not the probability that the null hypothesis is correct
• A p-value is not the probability that the null hypothesis is incorrect
• A p-value is not the probability of getting your specific sample
• A p-value is not the probability that the alternative hypothesis is correct
• A p-value is not the probability that the alternative hypothesis is incorrect
• A p-value does not indicate the size of the effect

Our p-value is a way of measuring the evidence that your sample provides against the null hypothesis, assuming the null hypothesis is in fact correct.

Using the p-value to make a decision

Why is there bad press for a p-value? You may have heard about the standard $\alpha$ level of 0.05. That is, we would be comfortable with rejecting the null hypothesis once in 20 attempts when the null hypothesis is really true. Recall that we reject the null hypothesis when the p-value is less than or equal to the significance level.

Consider what would happen if you have two different p-values: 0.049 and 0.051.

In essence, these two p-values represent two very similar probabilities (4.9% vs. 5.1%) and very similar levels of evidence against the null hypothesis. However, when we make our decision based on our threshold, we would make two different decisions (reject and fail to reject, respectively). Should this decision really be so simplistic? I would argue that the difference shouldn't be so severe when the sample statistics are likely very similar. For this reason, I (and many other experts) strongly recommend using the p-value as a measure of evidence and including it with your conclusion.

Putting too much emphasis on the decision (and having a significant result) has created a culture of misusing p-values. For this reason, understanding your p-value itself is crucial.

Searching for p-values

The other concern with setting a definitive threshold of 0.05 is that some researchers will begin performing multiple tests until finding a p-value that is small enough. However, with a p-value of 0.05, we know that we will have a p-value less than 0.05 1 time out of every 20 times, even when the null hypothesis is true.

This means that if researchers start hunting for p-values that are small (sometimes called p-hacking), then they are likely to identify a small p-value every once in a while by chance alone. Researchers might then publish that result, even though the result is actually not informative. For this reason, it is recommended that researchers write a definitive analysis plan to prevent performing multiple tests in search of a result that occurs by chance alone.

Best Practices

With all of this in mind, what should we do when we have our p-value? How can we prevent or reduce misuse of a p-value?

• Report the p-value along with the conclusion
• Specify the effect size (the value of the statistic)
• Define an analysis plan before looking at the data
• Interpret the p-value clearly to specify what it indicates
• Consider using an alternate statistical approach, the confidence interval, discussed next, when appropriate

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8.1: Steps in Hypothesis Testing

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CHAPTER OBJECTIVES

By the end of this chapter, the student should be able to:

• Differentiate between Type I and Type II Errors
• Describe hypothesis testing in general and in practice
• Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.
• Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.
• Conduct and interpret hypothesis tests for a single population proportion

One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.

A statistician will make a decision about these claims. This process is called "hypothesis testing." A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician makes a decision as to whether or not there is sufficient evidence, based upon analysis of the data, to reject the null hypothesis. In this chapter, you will conduct hypothesis tests on single means and single proportions. You will also learn about the errors associated with these tests.

Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will:

• Set up two contradictory hypotheses.
• Collect sample data (in homework problems, the data or summary statistics will be given to you).
• Determine the correct distribution to perform the hypothesis test.
• Analyze sample data by performing the calculations that ultimately will allow you to reject or decline to reject the null hypothesis.
• Make a decision and write a meaningful conclusion.

To do the hypothesis test homework problems for this chapter and later chapters, make copies of the appropriate special solution sheets. See Appendix E .

• The desired confidence level.
• Information that is known about the distribution (for example, known standard deviation).
• The sample and its size.

Hypothesis Testing in 5 Steps (Introduction to Statistical Inference)

• Published September 26, 2022

This is an introduction to Statistical Inference, and its most useful tool—Hypothesis Testing.

We’ll start off with an overview of the field of Statistics this tool belongs to, as well as the basic concepts we need in order to understand it.

After that, you’ll learn how Hypothesis Testing works in 5 steps.

Let’s dive right in:

What is Statistical Inference?

Say you’re a farmer and just had your biggest harvest of apples ever. 2,000 shiny red fresh treats you want to sink your teeth in immediately.

Now, you want to measure the average size of your apples, as you believe that’s a good indicator of how healthy your apples are.

The problem? It’s not practical to measure a whole population of 2,000 apples one by one. It would take too long.

How do we solve this problem?

Statistical inference.

Inference is the same word as extrapolation—which is when you assume something based on something else.

Statistical inference allows us to draw conclusions about a population based on a sample of that population.

Most times, we want to measure something in a huge population. The problem is that is rarely possible due to its size. The solution? Samples.

Inferential Statistics can be contrasted with Descriptive Statistics —which is only concerned with the properties of the data we observe, like the average and the mean.

Descriptive statistics aims to summarize a sample, rather than use the data to learn about the population the sample of data is thought to represent .

If we could get to the whole population easily, Statistics would be just descriptive statistics.

In the case above, you would analyze 100 apples and draw conclusions for the whole population based on that smaller sample.

The main tools of statistical inference are Confidence Intervals and Hypothesis Testing .

But before we get into that, it’s important that we define the difference between Statistics and Parameters :

Statistics vs. Parameters

Parameters are Greek letters used to represent observations in the population .

Statistics represent observations in the sample . Instead of Greek letters, we use our dear Latin alphabet (the letters you’re reading right now).

Statistics help us estimate parameters.

Here’s a good article on how to tell the difference between statistics and parameters .

And here’s a table with the symbols of population parameters and their corresponding sample statistic :

The mean (also known as average) is the sum of all values divided by the number of values.

A population proportion is a fraction of the population that has a certain characteristic.

Variance refers to a measurement of the spread between numbers in a data set. In other words, how far each number in the set is from the mean.

How do you calculate variance? By taking the mean of the data points, subtracting the mean from each data point individually, squaring each of these results, and then calculating another mean of those squares.

Standard deviation is the square root (√) of the variance. It is easier to picture and apply. Why? Because the standard deviation is in the same unit of measurement as the data, unlike the variance.

Now, correlation and regression :

Correlation measures the degree to which two variables move in relation to each other. In other words, it indicates some form of association.

A regression relates a dependent variable to one or more independent (explanatory) variables.

It tells us whether changes in the independent variables explain the changes in the dependent variable. Sounds similar to correlation, right? Well, they’re not quite the same:

Correlation measures how strong the relationship between two variables is, whereas regression how one variable affects the other.

Now, sample statistics will likely vary from sample to sample.

You can draw multiple samples from the same population, and those samples will give you different results.

Because of this, sample statistics are also called random variables . Their value is uncertain every time you collect a new sample.

This means a sample will never be a perfect representation of its whole population .

We don’t know for sure how well the sample represents the population.

The difference we believe exists between the sample and the population is what we call the sampling error .

What’s the point of me telling you this?

I want to remind you that in inferential statistics you need to be careful in how you word the conclusions you take.

Data from a sample will never substitute data from a population. It simply helps us estimate what’s going on in the population.

Got it? Alright, let’s see how we can actually put this into practice with hypothesis testing:

Hypothesis Testing Explained in 5 Steps

When using Statistics to analyze financial markets, we need to know how to formulate and decide on hypothesis testing.

Hypothesis testing is the use of statistics to determine the probability that a given hypothesis (involving parameters or not) is true.

We can explain the process in 5 steps:

#1) Identify the Hypotheses

The first step is to specify the null hypothesis (H0) and the alternative hypothesis (H1).

In this context, the word “null” is kinda like default . The default hypothesis. The currently accepted value for a parameter.

And what you do is challenge that. You’ll come up with an alternative hypothesis you want to test.

Your null hypothesis is always going to assume whatever you’re researching has no effect, or isn’t true. It’s the hypothesis you “want” to reject and prove wrong .

However, the null hypothesis is “innocent until proven guilty.”

That’s why you start with the exact opposite of that—we assume the null hypothesis is true.

In general, the null hypothesis says there’s no difference between the means of two methods (H0: µ1−µ2=0). In that case, the alternative hypothesis is H1: µ1≠µ2.

Continuing the example of the apples… You know the average size of the apples in your harvest is usually around 8cm. How do you compute a hypothesis test to check if this year things are similar?

• H0: The average apple size is 8cm.
• H1: The average apple size is different than 8cm.

Simple as that.

You can also test the correlation between two variables. In this case, the null hypothesis states there is no correlation (H0: ρ=0) and the alternative hypothesis is H1: ρ≠0.

H0 and H1 are always mathematical opposites.

Keep in mind:

We’re not going to prove anything to be true. We’re just saying this is false or this is not false. The hypotheses are made about the population, not the sample.

#2) Collect a Sample from the Population

As we’ve seen above, measuring a whole population is most times difficult and time-consuming. Instead, you collect random sample data to draw a generalization about the population.

But how do you determine the sample from a population?

To extract valid conclusions from your test, you have to carefully select a sample that is representative of the group as a whole.

There are many ways to draw a sample , as it changes based on what you’re testing.

To test the mean size of your population of apples, you can’t pick a group of apples from the same tree. You need to go around your farm and pick a couple from each tree.

After that, you use information about the samples to decide whether there’s a difference between the means.

#3) Choose a Statistical Test

How do you actually test your hypothesis?

You do a statistical test to get a test statistic , which will tell you if the sample is believable given the null hypothesis.

The test statistic is calculated from sample data and helps you decide whether you reject H0 or not.

It’s important to choose the right statistical test for your hypothesis, as it varies according to the sample size and parameter you’re trying to measure.

Statistical tests assume the null hypothesis. They assume there is no relationship or no difference between groups.

Then, they determine if the observed data matches the values from the null hypothesis.

In other words, it will compare the null hypothesis to the value you get from the sample, and determine if the values are different enough to say they’re different.

The test statistic tells you if the data you get from the sample is statistically significant enough to reject the null hypothesis or not.

“Statistically significant” —what do you mean by that? ( Druski voice.)

#4) Choose a Level of Confidence

You test a hypothesis and decide to reject it. How confident are you in that decision?

The level of confidence represents how sure you are that you made the right decision.

Doing a test with 99% confidence means that if you reject the null hypothesis, you’re 99% sure it was the correct thing to do.

In general, this value is either 90%, 95%, or 99%.

The complement to this is the level of significance (also called alpha , and represented by this symbol: α).

To get alpha, you simply subtract the level of confidence to 1.

So, the level of significance for a confidence level of 95% is 1-95%=5%.

The sum of the level of confidence with the level of significance is always 1. So they both tell you the same thing:

How sure are you that you’re making the right decision?

This is basically where you “draw the line.”

The average size of your apples is usually 8cm. This year you measure a sample, and get an average of 7.6cm. You want big apples. Should you be concerned? Maybe not.

But what if instead of 7.6, the average size of the sample is 6.5cm? Ok, there may be something going on. But still, not necessarily small apples, right?

What if it’s 5cm? Wow! From 8cm to 5cm. Most people would agree that now you have a problem. Something is different in this year’s harvest.

Do you see the problem? Where do you draw the line?

It’s subjective. Everyone has different opinions. And that cannot happen in Statistics.

We need a concrete way to look at the null hypothesis, collect data, and decide when to reject.

That’s what a hypothesis test does:

It collects the data from a sample, puts it in an equation, and gives you a number ( p-value ) that will help you decide when that test statistic is too high or too low—and when to reject or not.

Without having to guess. It gives you concrete boundaries.

How sure do you want to be of your decision?

Now, here’s what we do with those values:

#5) Look at the P-value and Decide

So, how do we know if we should accept the alternative hypothesis or default to the null hypothesis because the data isn’t convincing?

We look at the probability of getting the results the null hypothesis indicates.

If that probability is super small and insignificant, then the null hypothesis probably isn’t true.

We would then reject the null hypothesis and believe the alternative hypothesis.

The p-value estimates that probability. It answers this question:

How likely is it that I will see the difference described by the test statistic if the null hypothesis is true?

The most common significance level is 5%, so if the p-value is below that, you can reject H0.

The Bottom Line

Half the challenge with hypothesis testing is turning a real life problem into an hypothesis. Then, it’s all about figuring out the test you need to study it.

This is the thing that will give you the p-value—helping to decide whether to reject your null hypothesis.

In Statistics, a result is called statistically significant if it is unlikely to have occurred by chance.

Hugo Moreira

Currently finishing a Master's degree in Finance. I'm happy to be able to spend my free time writing and explaining financial concepts to you. You can learn more by visiting the About page.

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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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5 Steps of Hypothesis Testing with Examples – A Beginner’s Guide

Hypothesis testing is a statistical technique used to draw conclusions about a population based on sample data. It is a fundamental tool in research and data analysis, allowing researchers to test their assumptions and make inferences about the larger population. I this blog post, I will discuss in-depth guide for hypothesis testing.

What Is Hypothesis Testing and Why Is It Important?

Hypothesis testing is a statistical method used to determine whether a hypothesis about a population parameter is supported by the data. In simpler terms, it’s a way to test if a claim you make about a group or a situation is likely to be true. By using hypothesis testing, you can evaluate the evidence and make decisions based on the data we collect. It helps you to identify relationships, predict outcomes, and make informed decisions.

For example, a financial analyst might want to test the hypothesis that a particular investment portfolio outperforms a benchmark index. They would collect data on the returns of the portfolio and the index over a period of time and use hypothesis testing to determine whether the difference in returns is statistically significant. If the test results indicate that the portfolio does outperform the index, the analyst can be more confident in recommending that portfolio to investors.

In short, hypothesis testing is important because it allows us to make informed decisions based on evidence. Without hypothesis testing, we would be left with guesswork and intuition, which can often lead to costly mistakes.

5 Key Steps of Hypothesis Testing: A Simple Overview

Hypothesis testing typically involves five key steps that are used to evaluate whether a hypothesis is supported by the evidence . Here’s a simple overview of the five key steps:

• State the Null and Alternative Hypotheses : The first step in hypothesis testing is to state the null hypothesis (H 0 ) and the alternative hypothesis (H a ). The null hypothesis is the hypothesis that there is no significant difference between the population parameter and the sample . The alternative hypothesis is the hypothesis that there is a significant difference .
• Set the Significance Level : The next step is to determine the significance level (alpha) that will be used in the hypothesis test. The significance level is the probability of rejecting the null hypothesis when it is actually true. The most commonly used significance level is 0.05. Mostly, researchers use three significance levels, i.e., 0.01, 0.05, and 0.1.
• Collect the Data : The third step is to collect the data that will be used to test the hypothesis. The data can be collected through experiments, surveys, or other research methods.
• Calculate the Test Statistic : The fourth step is to calculate the test statistic, which is a measure of how far the sample statistic is from the hypothesized population parameter. The test statistic is used to determine the p-value.
• Make a Decision : The final step is to make a decision based on the p-value. If the p-value is less than the significance level, we reject the null hypothesis and accept the alternative hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis .

In summary, the five key steps of hypothesis testing are to state the hypotheses, set the significance level, collect the data, calculate the test statistic, and make a decision based on the p-value. By following these steps, you can determine whether a hypothesis is supported by the evidence and make informed decisions based on the data you collected.

Understanding the Difference Between Null and Alternative Hypotheses

In hypothesis testing, we typically compare two hypotheses: the null hypothesis and the alternative hypothesis. Understanding the difference between these two hypotheses is critical to performing hypothesis testing correctly.

What is Null Hypothesis?

The null hypothesis (H 0 ) is the hypothesis that there is no significant difference between the population parameter and the sample. In other words, the null hypothesis states that any differences observed between the sample and population are due to chance. Let’s say an investor is considering investing in Portfolio A or Portfolio B and wants to determine which one has a higher return. The null hypothesis would be that there is no significant difference between the two portfolios in terms of returns, and any observed differences are due to chance.

What is Alternative Hypothesis?

On the other hand, the alternative hypothesis (H a ) is the hypothesis that there is a significant difference between the population parameter and the sample. The alternative hypothesis states that any differences observed between the sample and population are not due to chance. In the above portfolio example, the alternative hypothesis might be that there is significan t difference between the two portfolios.

Null and Alternative Hypothesis with An example

To illustrate the difference between the null and alternative hypotheses, let’s consider a simple example of testing the effectiveness of a new investment strategy. The null hypothesis would be that the new investment strategy has no significant effect on returns compared to the existing strategy, while the alternative hypothesis would be that the new strategy has a significant positive effect on returns. If we apply the new investment strategy for a period of time and find that the returns are not significantly different from those of the existing strategy, we might fail to reject the null hypothesis and conclude that the new strategy is not effective. However, if we find that the returns are significantly higher with the new strategy, we might reject the null hypothesis and conclude that the new strategy is effective in generating higher returns.

In summary, the null hypothesis is the hypothesis that any differences observed between the sample and population are due to chance, while the alternative hypothesis is the hypothesis that any differences observed are not due to chance. By understanding the difference between these two hypotheses, we can correctly perform hypothesis testing and draw accurate conclusions based on the evidence.

One-Tailed vs. Two-Tailed Tests: How to Choose the Right One

When performing hypothesis testing, it is important to choose the right type of test to use. Two common types of tests are one-tailed tests and two-tailed tests. Understanding the difference between these two types of tests is important to ensure accurate hypothesis testing.

One-tailed test

A one-tailed test is a hypothesis test in which the alternative hypothesis specifies the direction of the effect, and we are interested in determining if the observed effect is significant in that specific direction. In finance, a common example of a one-tailed test is testing whether a new investment strategy generates higher returns than an existing strategy. The alternative hypothesis in this case would be directional, specifying that the new strategy generates higher returns than the existing one. We would use a one-tailed test to determine if the observed effect is significant in the expected direction.

Two-tailed test

A two-tailed test is a hypothesis test in which the alternative hypothesis does not specify the direction of the effect. A common example of a two-tailed test is testing whether the mean returns of a stock portfolio are different from a certain value (e.g., zero). The null hypothesis would be that the mean returns are equal to the specified value, and the alternative hypothesis would be that the mean returns are not equal to the specified value. Since the alternative hypothesis does not specify a particular direction, we would use a two-tailed test to determine if the observed effect is significant in either direction (i.e., if the mean returns are significantly greater or significantly less than the specified value).

How to choose right one?

So how do we choose the right type of test to use? The choice depends on the research question and the specific hypotheses being tested. If we have a specific direction in mind for the alternative hypothesis, we would use a one-tailed test. If we do not have a specific direction in mind, we would use a two-tailed test.

In summary, when performing hypothesis testing, it is important to choose the right type of test to use. One-tailed tests are used when we have a specific direction in mind for the alternative hypothesis, while two-tailed tests are used when we do not have a specific direction in mind. By choosing the right type of test, we can ensure accurate hypothesis testing and draw accurate conclusions based on the evidence.

How to Calculate p-Values and What They Mean

When performing hypothesis testing, we often calculate a p-value, which tells us the probability of obtaining a result as extreme as the one we observed, assuming that the null hypothesis is true. The smaller the p-value, the stronger the evidence against the null hypothesis.

To calculate a p-value, we first need to calculate the test statistic. The test statistic is a value that measures the distance between the sample and the null hypothesis. The choice of test statistic depends on the type of hypothesis test being performed. For example, if we are testing the mean of a population, we might use the t-test as our test statistic .

Once we have calculated the test statistic, we can use a p-value table or statistical software to find the p-value (Stata software automatically calculates this value for us in statistical analysis). The p-value is the probability of obtaining a test statistic as extreme as the one we observed, assuming that the null hypothesis is true. For example, if we observe a t-test statistic of 2.0 with a degree of freedom of 10 and our alternative hypothesis is two-tailed, we might find a p-value of 0.06 . This would mean that if the null hypothesis is true, there is a 6% chance of observing a test statistic as extreme as the one we observed.

It is important to remember that the p-value is not the probability that the null hypothesis is true. Instead, it is the probability of obtaining a result as extreme as the one we observed, assuming that the null hypothesis is true. The smaller the p-value, the stronger the evidence against the null hypothesis . A commonly used threshold for statistical significance is a p-value of 0.05, which means that there is a 5% chance of obtaining a result as extreme as the one we observed, assuming that the null hypothesis is true. In summary, p-values are an important part of hypothesis testing that tells us the probability of obtaining a result as extreme as the one we observed, assuming that the null hypothesis is true. By understanding how to calculate p-values and what they mean, we can draw accurate conclusions based on the evidence and make informed decisions in various fields, such as healthcare, finance, and social sciences.

Common Hypothesis Testing Errors to Watch Out For

When conducting hypothesis testing, it is important to be aware of common errors that can occur. Here are a few examples of errors to watch out for:

• Type I Error : This occurs when we reject the null hypothesis even though it is true. In other words, we conclude that there is a significant effect when there is not one. Type I error is also known as a false positive . The probability of making a Type I error is denoted by the Greek letter alpha (α) and is often set to 0.05.
• Type II Error : This occurs when we fail to reject the null hypothesis even though it is false. In other words, we conclude that there is no significant effect when there actually is one. Type II error is also known as a false negative . The probability of making a Type II error is denoted by the Greek letter beta (β).
• Insufficient sample size : A sample size that is too small may lead to inaccurate conclusions. For example, a small sample size may result in a Type II error where we fail to reject the null hypothesis even though it is false.
• Biased sampling : If the sample is not representative of the population, the results of the hypothesis test may not be accurate.
• Misinterpretation of results : It is important to interpret the results of the hypothesis test correctly. A common mistake is to interpret a non-significant result as evidence that the null hypothesis is true, when in fact it simply means that there is not enough evidence to reject it.

By being aware of these common errors, we can take steps to avoid them and conduct hypothesis testing with greater accuracy and confidence. It is important to carefully design experiments, choose appropriate hypothesis tests, and interpret results correctly in order to draw valid conclusions.

Examples of Hypothesis Testing in Real-World Scenarios

Hypothesis testing is a powerful tool that can be used to make decisions and draw conclusions in a wide variety of real-world scenarios. Here are a few examples of how hypothesis testing is used in practice:

• Medical Research : Hypothesis testing is commonly used in medical research to test the effectiveness of new treatments or interventions. For example, a researcher might test the hypothesis that a new drug is more effective at treating a certain condition than an existing drug. By comparing the results of the two treatments using statistical analysis , the researcher can determine whether the new drug is significantly more effective than the existing drug.
• Quality Control : Hypothesis testing is also used in quality control to ensure that a product or process meets certain specifications. For example, a manufacturing company might test the hypothesis that the average weight of their product is equal to a certain target weight. By taking a sample of the product and testing the hypothesis using statistical analysis, the company can determine whether the product meets the required specifications.
• Finance : Hypothesis testing is used in finance to test various investment strategies. For example, a financial analyst might test the hypothesis that a particular stock is likely to outperform the market based on certain criteria. By analyzing historical data and testing the hypothesis, the analyst can determine whether the stock is a good investment.
• Environmental Studies : Hypothesis testing is also used in environmental studies to test hypotheses related to environmental issues. For example, a researcher might test the hypothesis that a certain chemical is causing harm to a particular ecosystem. By analyzing data and testing the hypothesis, the researcher can determine whether the chemical is having a significant impact on the ecosystem.

These are just a few examples of the many real-world scenarios in which hypothesis testing is used. By using statistical analysis to test hypotheses, researchers and decision-makers can make informed choices and draw valid conclusions based on data.

Tips for Designing Effective Hypothesis Testing Experiments

Designing effective experiments is a crucial part of hypothesis testing. Here are some tips for designing effective hypothesis testing experiments:

• Clearly define the research question : It is important to clearly define the research question before designing the experiment. The research question should be specific, measurable, and focused on a clear objective.
• Choose an appropriate hypothesis test : Once the research question is defined, it is important to choose an appropriate hypothesis test that will provide the most relevant information. Different hypothesis tests are used for different types of data and research questions, so it is important to choose the right test for the specific situation.
• Determine the sample size : The sample size should be large enough to ensure that the results of the experiment are accurate and representative of the population. A small sample size may lead to inaccurate conclusions, while a large sample size may be unnecessary and time-consuming.
• Randomize the sample : To ensure that the sample is representative of the population, it is important to randomize the selection of subjects. This helps to reduce bias and ensure that the sample is as representative as possible.
• Control for confounding variables : Confounding variables are factors that may affect the outcome of the experiment, but are not the focus of the research question. It is important to control for these variables in order to ensure that the results are as accurate as possible.
• Analyze the data : Once the experiment is conducted and the data is collected, it is important to analyze the data using appropriate statistical methods. This helps to draw valid conclusions and avoid errors in interpretation.

By following these tips, you can design effective hypothesis testing experiments that provide relevant and accurate information. Careful planning and attention to detail are key to conducting successful experiments and drawing valid conclusions.

Frequently Asked Questions About Hypothesis Testing

Here are some frequently asked questions about hypothesis testing:

A hypothesis is a statement that is tested in a hypothesis test. It is typically a statement about a population parameter, such as the mean or proportion.

The null hypothesis is a statement that assumes there is no significant difference between a population parameter and a sample statistic. It is the starting point for hypothesis testing.

The alternative hypothesis is a statement that assumes there is a significant difference between a population parameter and a sample statistic. It is the hypothesis that researchers are trying to support with their data.

The p-value is a probability that measures the strength of evidence against the null hypothesis. It is used to determine whether the results of a hypothesis test are statistically significant or not.

A p-value less than 0.05 (or whatever significance level is chosen) indicates that the null hypothesis should be rejected, and the alternative hypothesis should be supported. A p-value greater than the significance level indicates that there is not enough evidence to reject the null hypothesis.

Type I error occurs when a true null hypothesis is incorrectly rejected, while type II error occurs when a false null hypothesis is not rejected. Type I errors are usually more serious than type II errors.

Statistical power is the probability of rejecting the null hypothesis when it is false. It is affected by the sample size, significance level, effect size, and variability in the data.

The significance level is typically set at 0.05, but it can be set at any level depending on the nature of the research question and the consequences of a type I error. A higher significance level increases the risk of type I error but decreases the risk of type II error, while a lower significance level does the opposite.

Next Steps: How to Build on Your Hypothesis Testing Knowledge

If you’re interested in building on your hypothesis testing knowledge, here are some steps you can take:

• Practice, practice, practice : The best way to improve your hypothesis testing skills is to practice as much as possible. You can find many examples and practice problems online or in textbooks. If you found it difficult or struck anywhere, do contact me . I will answer your questions.
• Discuss your project with an Expert : If you are struggling to understand your hypothesis testing project, do contact with a statistical analysis expert. Do not hold yourself back and make it a headache. Get expert help from me .
• Learn advanced techniques : Once you’ve mastered the basics of hypothesis testing, you can move on to more advanced techniques such as ANOVA, regression analysis , and Bayesian inference.
• Attend workshops or courses : Attending workshops or courses can be a great way to learn new techniques, get feedback from experts, and network with other researchers.
• Collaborate with others : Collaborating with other researchers can be a great way to learn from others, share your knowledge, and work on more complex problems.
• Read research papers : Reading research papers that use hypothesis testing can help you learn about the practical applications of these techniques in various fields.

In conclusion, hypothesis testing is a fundamental tool in research that enables us to make data-driven decisions and draw conclusions about the population based on a sample. By following the five key steps of hypothesis testing, understanding the difference between null and alternative hypotheses, choosing the right type of test, and interpreting p-values correctly, researchers can make meaningful inferences and conclusions from their data. However, it’s important to be aware of the common pitfalls and errors associated with hypothesis testing and to design effective experiments that produce reliable results. By continuing to practice and learn about hypothesis testing, you can enhance your skills and improve your ability to conduct sound research. Ultimately, hypothesis testing can help us gain insights, make better decisions, and contribute to the advancement of knowledge in your respective fields such as Finance .

Stata Data Analyst

I am a Finance Research Analyst and help students learn Stata. I am working in the finance industry for the past 7 years. I love to write on Statistical Analysis in Research with Stata software. I have assisted more than 150+ Finance Projects.

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Learn How To Write A Hypothesis For Your Next Research Project!

Undoubtedly, research plays a crucial role in substantiating or refuting our assumptions. These assumptions act as potential answers to our questions. Such assumptions, also known as hypotheses, are considered key aspects of research. In this blog, we delve into the significance of hypotheses. And provide insights on how to write them effectively. So, let’s dive in and explore the art of writing hypotheses together.

Table of Contents

What is a Hypothesis?

A hypothesis is a crucial starting point in scientific research. It is an educated guess about the relationship between two or more variables. In other words, a hypothesis acts as a foundation for a researcher to build their study.

Here are some examples of well-crafted hypotheses:

• Increased exposure to natural sunlight improves sleep quality in adults.

A positive relationship between natural sunlight exposure and sleep quality in adult individuals.

• Playing puzzle games on a regular basis enhances problem-solving abilities in children.

Engaging in frequent puzzle gameplay leads to improved problem-solving skills in children.

• Students and improved learning hecks.

S tudents using online  paper writing service  platforms (as a learning tool for receiving personalized feedback and guidance) will demonstrate improved writing skills. (compared to those who do not utilize such platforms).

• The use of APA format in research papers. 

Using the  APA format  helps students stay organized when writing research papers. Organized students can focus better on their topics and, as a result, produce better quality work.

The Building Blocks of a Hypothesis

To better understand the concept of a hypothesis, let’s break it down into its basic components:

• Variables . A hypothesis involves at least two variables. An independent variable and a dependent variable. The independent variable is the one being changed or manipulated, while the dependent variable is the one being measured or observed.
• Relationship : A hypothesis proposes a relationship or connection between the variables. This could be a cause-and-effect relationship or a correlation between them.
• Testability : A hypothesis should be testable and falsifiable, meaning it can be proven right or wrong through experimentation or observation.

Types of Hypotheses

When learning how to write a hypothesis, it’s essential to understand its main types. These include; alternative hypotheses and null hypotheses. In the following section, we explore both types of hypotheses with examples. 

Alternative Hypothesis (H1)

This kind of hypothesis suggests a relationship or effect between the variables. It is the main focus of the study. The researcher wants to either prove or disprove it. Many research divides this hypothesis into two subsections: 

• Directional 

This type of H1 predicts a specific outcome. Many researchers use this hypothesis to explore the relationship between variables rather than the groups. 

• Non-directional

You can take a guess from the name. This type of H1 does not provide a specific prediction for the research outcome. 

Here are some examples for your better understanding of how to write a hypothesis.

• Consuming caffeine improves cognitive performance.  (This hypothesis predicts that there is a positive relationship between caffeine consumption and cognitive performance.)
• Aerobic exercise leads to reduced blood pressure.  (This hypothesis suggests that engaging in aerobic exercise results in lower blood pressure readings.)
• Exposure to nature reduces stress levels among employees.  (Here, the hypothesis proposes that employees exposed to natural environments will experience decreased stress levels.)
• Listening to classical music while studying increases memory retention.  (This hypothesis speculates that studying with classical music playing in the background boosts students’ ability to retain information.)
• Early literacy intervention improves reading skills in children.  (This hypothesis claims that providing early literacy assistance to children results in enhanced reading abilities.)
• Time management in nursing students. ( Students who use a  nursing research paper writing service  have more time to focus on their studies and can achieve better grades in other subjects. )

Null Hypothesis (H0)

A null hypothesis assumes no relationship or effect between the variables. If the alternative hypothesis is proven to be false, the null hypothesis is considered to be true. Usually a null hypothesis shows no direct correlation between the defined variables. 

Here are some of the examples

• The consumption of herbal tea has no effect on sleep quality.  (This hypothesis assumes that herbal tea consumption does not impact the quality of sleep.)
• The number of hours spent playing video games is unrelated to academic performance.  (Here, the null hypothesis suggests that no relationship exists between video gameplay duration and academic achievement.)
• Implementing flexible work schedules has no influence on employee job satisfaction.  (This hypothesis contends that providing flexible schedules does not affect how satisfied employees are with their jobs.)
• Writing ability of a 7th grader is not affected by reading editorial example. ( There is no relationship between reading an  editorial example  and improving a 7th grader’s writing abilities.) 
• The type of lighting in a room does not affect people’s mood.  (In this null hypothesis, there is no connection between the kind of lighting in a room and the mood of those present.)
• The use of social media during break time does not impact productivity at work.  (This hypothesis proposes that social media usage during breaks has no effect on work productivity.)

As you learn how to write a hypothesis, remember that aiming for clarity, testability, and relevance to your research question is vital. By mastering this skill, you’re well on your way to conducting impactful scientific research. Good luck!

Importance of a Hypothesis in Research

A well-structured hypothesis is a vital part of any research project for several reasons:

• It provides clear direction for the study by setting its focus and purpose.
• It outlines expectations of the research, making it easier to measure results.
• It helps identify any potential limitations in the study, allowing researchers to refine their approach.

In conclusion, a hypothesis plays a fundamental role in the research process. By understanding its concept and constructing a well-thought-out hypothesis, researchers lay the groundwork for a successful, scientifically sound investigation.

How to Write a Hypothesis?

Here are five steps that you can follow to write an effective hypothesis. 

Step 1: Identify Your Research Question

The first step in learning how to compose a hypothesis is to clearly define your research question. This question is the central focus of your study and will help you determine the direction of your hypothesis.

Step 2: Determine the Variables

When exploring how to write a hypothesis, it’s crucial to identify the variables involved in your study. You’ll need at least two variables:

• Independent variable : The factor you manipulate or change in your experiment.
• Dependent variable : The outcome or result you observe or measure, which is influenced by the independent variable.

Step 3: Build the Hypothetical Relationship

In understanding how to compose a hypothesis, constructing the relationship between the variables is key. Based on your research question and variables, predict the expected outcome or connection. This prediction should be specific, testable, and, if possible, expressed in the “If…then” format.

Step 4: Write the Null Hypothesis

When mastering how to write a hypothesis, it’s important to create a null hypothesis as well. The null hypothesis assumes no relationship or effect between the variables, acting as a counterpoint to your primary hypothesis.

Step 5: Review Your Hypothesis

Finally, when learning how to compose a hypothesis, it’s essential to review your hypothesis for clarity, testability, and relevance to your research question. Make any necessary adjustments to ensure it provides a solid basis for your study.

In conclusion, understanding how to write a hypothesis is crucial for conducting successful scientific research. By focusing on your research question and carefully building relationships between variables, you will lay a strong foundation for advancing research and knowledge in your field.

Hypothesis vs. Prediction: What’s the Difference?

Understanding the differences between a hypothesis and a prediction is crucial in scientific research. Often, these terms are used interchangeably, but they have distinct meanings and functions. This segment aims to clarify these differences and explain how to compose a hypothesis correctly, helping you improve the quality of your research projects.

Hypothesis: The Foundation of Your Research

A hypothesis is an educated guess about the relationship between two or more variables. It provides the basis for your research question and is a starting point for an experiment or observational study.

The critical elements for a hypothesis include:

• Specificity: A clear and concise statement that describes the relationship between variables.
• Testability: The ability to test the hypothesis through experimentation or observation.

To learn how to write a hypothesis, it’s essential to identify your research question first and then predict the relationship between the variables.

Prediction: The Expected Outcome

A prediction is a statement about a specific outcome you expect to see in your experiment or observational study. It’s derived from the hypothesis and provides a measurable way to test the relationship between variables.

Here’s an example of how to write a hypothesis and a related prediction:

• Hypothesis: Consuming a high-sugar diet leads to weight gain.
• Prediction: People who consume a high-sugar diet for six weeks will gain more weight than those who maintain a low-sugar diet during the same period.

Key Differences Between a Hypothesis and a Prediction

While a hypothesis and prediction are both essential components of scientific research, there are some key differences to keep in mind:

• A hypothesis is an educated guess that suggests a relationship between variables, while a prediction is a specific and measurable outcome based on that hypothesis.
• A hypothesis can give rise to multiple experiment or observational study predictions.

To conclude, understanding the differences between a hypothesis and a prediction, and learning how to write a hypothesis, are essential steps to form a robust foundation for your research. By creating clear, testable hypotheses along with specific, measurable predictions, you lay the groundwork for scientifically sound investigations.

Here’s a wrap-up for this guide on how to write a hypothesis. We’re confident this article was helpful for many of you. We understand that many students struggle with writing their school research . However, we hope to continue assisting you through our blog tutorial on writing different aspects of academic assignments.

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Steps of the Scientific Method 2

The scientific method is a system scientists and other people use to ask and answer questions about the natural world. In a nutshell, the scientific method works by making observations, asking a question or identifying a problem, and then designing and analyzing an experiment to test a prediction of what you expect will happen. It’s a powerful analytical tool because once you draw conclusions, you may be able to answer a question and make predictions about future events.

These are the steps of the scientific method:

• Make observations.

Sometimes this step is omitted in the list, but you always make observations before asking a question, whether you recognize it or not. You always have some background information about a topic. However, it’s a good idea to be systematic about your observations and to record them in a lab book or another way. Often, these initial observations can help you identify a question. Later on, this information may help you decide on another area of investigation of a topic.

• Ask a question, identify a problem, or state an objective.

There are various forms of this step. Sometimes you may want to state an objective and a problem and then phrase it in the form of a question. The reason it’s good to state a question is because it’s easiest to design an experiment to answer a question. A question helps you form a hypothesis, which focuses your study.

• Research the topic.

You should conduct background research on your topic to learn as much as you can about it. This can occur both before and after you state an objective and form a hypothesis. In fact, you may find yourself researching the topic throughout the entire process.

• Formulate a hypothesis.

A hypothesis is a formal prediction. There are two forms of a hypothesis that are particularly easy to test. One is to state the hypothesis as an “if, then” statement. An example of an if-then hypothesis is: “If plants are grown under red light, then they will be taller than plants grown under white light.” Another good type of hypothesis is what is called a “ null hypothesis ” or “no difference” hypothesis. An example of a null hypothesis is: “There is no difference in the rate of growth of plants grown under red light compared with plants grown under white light.”

• Design and perform an experiment to test the hypothesis.

Once you have a hypothesis, you need to find a way to test it. This involves an experiment . There are many ways to set up an experiment. A basic experiment contains variables, which are factors you can measure. The two main variables are the independent variable (the one you control or change) and the dependent variable (the one you measure to see if it is affected when you change the independent variable).

• Record and analyze the data you obtain from the experiment.

It’s a good idea to record notes alongside your data, stating anything unusual or unexpected. Once you have the data, draw a chart, table, or graph to present your results. Next, analyze the results to understand what it all means.

• Determine whether you accept or reject the hypothesis.

Do the results support the hypothesis or not? Keep in mind, it’s okay if the hypothesis is not supported, especially if you are testing a null hypothesis. Sometimes excluding an explanation answers your question! There is no “right” or “wrong” here. However, if you obtain an unexpected result, you might want to perform another experiment.

• Draw a conclusion and report the results of the experiment.

What good is knowing something if you keep it to yourself? You should report the outcome of the experiment, even if it’s just in a notebook. What did you learn from the experiment?

How Many Steps Are There?

You may be asked to list the 5 steps of the scientific method or the 6 steps of the method or some other number. There are different ways of grouping together the steps outlined here, so it’s a good idea to learn the way an instructor wants you to list the steps. No matter how many steps there are, the order is always the same.

Related Posts

2 thoughts on “ steps of the scientific method ”.

You raise a valid point, but peer review has its limitations. Consider the case of Galileo, for example.

That’s a good point too. But that was a rare limitation due to religion, and scientific consensus prevailed in the end. It’s nowhere near a reason to doubt scientific consensus in general. I’m thinking about issues such as climate change where so many people are skeptical despite 97% consensus among climate scientists. I was just surprised to see that this is not included as an important part of the process.

Comments are closed.

The 5 Easy Steps to Hypothesis Testing

I would like to make the process of understanding hypothesis testing much simpler for students need help learning statistics . Hypothesis testing is a five-step procedure. Let’s address the difficulties of students while they learn the topic of hypothesis testing.

Step 1: Identifying the claim and designing null and alternative hypothesis

Students should first identify the research claim: A research claim is a statement or condition that is being tested.

Now if the claim is to test that there is NO difference between or to test if the given value is EQUAL to any number, in this case, we consider the claim as a null hypothesis.

In contrast, if the claim is to test that there is a difference or to test if the given number is NOT equal to/greater than/less than any given number, in this case, we consider the claim as an alternative hypothesis.

We represent the Null hypothesis symbolically with H0 and the alternative hypothesis with Ha or H1

Step 2: Identifying the tail of the test and notifying the significance level if given

Here, students are posed with the question: how do I identify the tail of the f test?

• It is simple if the alternative hypothesis is directional with the statement (greater than or less than) then the claim is ONE tailed.
• If the claim is with the statement NOT equal to-it is TWO tailed.

So when the claim is directional, it is a one-tailed test and when the claim is non-directional, it is a two-tailed test!

Step 3: Identifying the type of statistical test to be identified and to compute test statistic

Well there are different test statistics we compute while working with test statistics.

To start off, if we are testing one sample mean when the sample size is small (less than 30) and the standard deviation is unknown, we compute test statistic t for the same condition. When the standard deviation is known, we compute test statistic Z. We have different formulas listed for computing the Z test for one sample proportion and the difference between means and then the difference between proportions, so here to compute the test statistic we must identify the type of statistical test to be performed.

Step 4: Writing decisions

This is again a very confusing part to most of the students. There are two methods to write decisions, so students should be familiar with the method taught in class.

The first method is: P-Value Approach In the p-value approach, we compare the p-value of the test statistic with the alpha/significance level.

• When the p-value is <(less than) Alpha we reject H0
• When the p-value is >(greater than) Alpha we fail to reject H0

The second method is: Critical Value Approach So in this method, we compare test statistics obtained with the critical value of the test conducted

• When the test statistic is less than (<) critical value of the test we fail to reject H0
• When the test statistic is greater than(>) critical value of the test we reject H0

Step 5: Drawing conclusions

Students should match the decision results while making conclusions when we reject the null hypothesis we conclude that we have enough evidence.

To support the claim (in this case the claim will be an alternative hypothesis), we say the test is statistically significant.

When we reject the null hypothesis and say that we do not have enough evidence to support the claim (in this case the null hypothesis is the claim), we say the test is not statistically significant.

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Research Paper Hypothesis

Last updated on: Mar 27, 2024

How To Write A Hypothesis In A Research Paper - A Simple Guide

By: Barbara P.

Reviewed By:

Published on: Mar 6, 2024

Writing a good hypothesis can be tricky, especially for new researchers. If your hypothesis isn't clear, your research paper might confuse readers about what you're studying and what are the anticipated outcomes of your study.

This confusion not only makes your research less trustworthy but also makes it harder for others to repeat or build on your work.

This blog post is here to help you understand how to state a hypothesis in a research paper. We'll go through it step by step, so you can learn to craft the important parts, like how you identify variables and formulate a clear hypothesis. 

With these skills, you can make sure your hypothesis is clear and can be tested. So, get ready to craft a strong hypothesis!

On this Page

What is a Hypothesis in Research? 

A hypothesis in research paper is a clear and testable statement or prediction that proposes a relationship between two or more variables. 

It serves as a foundation for scientific investigations, guiding researchers in designing experiments and collecting data to either support or refute the hypothesis.

Research Question vs. Hypothesis vs. Thesis Statement 

Research Question, Hypothesis, and Thesis Statement are three distinct elements in the research process, each serving a specific purpose. 

Here's a breakdown of their differences:

Components of a Hypothesis 

If you are wondering what to write in a research hypothesis, here is the breakdown:

Different Types of Hypothesis 

Hypotheses come in various forms, each tailored to address different aspects of research. 

Simple Hypothesis

This hypothesis proposes a straightforward relationship between two variables.  For example, "Increasing sunlight will lead to increased plant growth."

Complex Hypothesis 

In contrast, a complex hypothesis involves multiple variables and intricate relationships.  An example could be "The interaction of sunlight, soil quality, and water availability collectively influences plant growth."

Directional Hypothesis 

A directional hypothesis predicts a specific outcome.  For instance, "Higher levels of education will result in increased job satisfaction."

Non-directional Hypothesis 

Conversely, a non-directional hypothesis suggests a relationship without specifying the expected direction.  An example is "There is a correlation between exercise and weight loss."

Associative Hypothesis 

This type suggests a relationship between variables without implying causation.  For example, "There is an association between ice cream sales and drowning incidents."

Causal Hypothesis

Unlike associative hypotheses, causal hypotheses propose a cause-and-effect relationship. For instance, "Increasing water intake causes improvements in skin hydration."

Null Hypothesis (H0) 

The null hypothesis assumes no effect or relationship between variables.  An example is, "There is no significant difference in test scores between students who receive extra tutoring and those who do not."

Alternative Hypothesis 

The alternative hypothesis suggests a specific effect or relationship. It contrasts with the null hypothesis.  For instance, "There is a significant difference in test scores between students who receive extra tutoring and those who do not."

5 Steps of Writing a Strong Hypothesis

A strong hypothesis gives the reader a clear view of your research. In this section, we will explore the steps of writing a strong hypothesis in detail:

Step 1: Understand the Research Question

Before diving into hypothesis crafting, take time to comprehend your research problem . Break it down into its core components. 

For instance, if your research question is, 

"How does caffeine consumption affect students' test performance?":

• Identify the Main Focus: Clearly pinpoint the main aspect of the research question. In this case, it's the impact of caffeine consumption.
• Define Variables : Recognize the key variables involved. In our example, the independent variable is "caffeine consumption," and the dependent variable is "students' test performance."
• Refine the Question: Ask yourself what specific information you want to uncover. Is it the overall effect, a comparison between different levels of caffeine intake, or perhaps the timing of consumption? This refinement sets the stage for a more focused hypothesis.

Step 2: Identify the Variables

Understanding the variables of your research is crucial for defining the key roles and what changes you're anticipating. 

They are the backbone of your hypothesis and create a focused and meaningful research approach.

• Independent Variable (The What You Tweak): Pinpoint the factor you're going to manipulate. For instance, if you're exploring the impact of fertilizer on plant growth, fertilizer becomes your independent variable.
• Dependent Variable (The What You Measure): Identify the factor you're measuring, the one expected to change due to the manipulation. In the plant growth example, it could be the height of the plants after a specific period—this is your dependent variable.

Step 3: Formulate a Clear Statement

Precision is the key to shaping a concise and strong hypothesis. To create a well-structured hypothesis, condense your thoughts into a single, easy-to-follow sentence. 

Also, do not forget to clearly express the expected connection between your independent and dependent variables.

Step 4: Consider the Type of Hypothesis

In this step, you decide on the type of your hypothesis—whether it's giving a specific prediction or leaving room for surprises.

• Example of Directional Hypothesis: "Increasing product advertising will result in higher sales."
• Example of Non-Directional Hypothesis: "There is a significant correlation between stress levels and job performance."

Step 5: Predict the Outcome

Predicting the outcome is like offering a sneak peek into the conclusion of your research narrative.

By following these five steps, you'll be well-equipped to create a strong and effective hypothesis, providing a solid foundation for your research.

Check out this example of hypothesis for a research paper for better understanding:

Example Of Hypothesis In Research Proposal PDF

How to Write a Null Hypothesis In A Research Paper

Writing a null hypothesis in a research paper involves stating a proposition that there is no significant difference or effect. 

Here are some tips for writing a null hypothesis:

• Reverse the Statement: Formulate the null hypothesis by reversing the statement of the research hypothesis to suggest no significant difference or effect.
• Use Equality Sign: Express the null hypothesis using an equality sign, such as "equals" or "is not significantly different from."
• Be Specific and Testable: Make the null hypothesis specific and testable, ensuring it can be evaluated through data analysis.
• Consider the Context: Ensure that the null hypothesis is appropriate for the context of your research.

Here is an example of a null hypothesis:

How to Write an Alternative Hypothesis? 

Writing an alternative hypothesis, also known as the research hypothesis, involves stating a proposition that suggests a significant difference or effect between variables. 

Here are some tips for writing an alternative hypothesis:

• Formulate a Prediction: Formulate a clear prediction or expectation regarding the relationship or effect between the variables.
• Express the Relationship: Clearly express the anticipated relationship or effect using specific terms, such as "greater than," "less than," or "different from."
• Use Inequality Sign: Utilize an inequality sign (>, <, ?) to represent the direction of the expected difference or effect.

Here's a PDF example for an alternative hypothesis:

How to Write an Alternative Hypothesis

In a nutshell, hypotheses aren't just words; they guide us in discovering new things. So, as you dive into your own research, use clear hypotheses to represent yours to illuminate your research question.

But if you face any problem in creating a meaningful hypothesis or any section of your research paper, get help from the top paper writing service online .

Our expert writers will help you in creating an outstanding research paper that will show your command over the topic.

So, don’t waste time! Get your research papers from experts today! 

Barbara has a Ph.D. in public health from an Ivy League university and extensive experience working in the medical field. With her practical experience conducting research on various health issues, she is skilled in writing innovative papers on healthcare. Her many works have been published in multiple publications.

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Each academic research revolves around specific statement or problem — a research hypothesis. 

A hypothesis is a suggested prediction for a phenomenon or observed event, based on prior knowledge or research. It is a tentative statement that can be tested through further investigation and analysis. A hypothesis usually takes the form of a statement that suggests a relationship between two or more variables.

Every research project, be it a a term paper, research paper or a dissertation, should begin with defining a hypothesis. While this may seem simple, in reality beginners face a lot of problems. This includes difficulty with formulating a hypothesis accurately and capturing the main idea. In this blog post, we will tell you how to write a hypothesis so it is accurate and correct.

What Is a Research Hypothesis: Expanded Definition

A research hypothesis is a statement or assumption that answers a question you asked earlier but haven't tested yet. In fact, this is basis of your work which you use to prove or reject your assumption. Major research projects most often deal with several hypotheses. These relate to various aspects of an issue under study. Thus, you will divide assumptions by research sectors and study them in a segmented manner. When making an assignment, one must work based on an existing theory and gained knowledge. One must also take into account that it must be testable. That is, it can be rejected or confirmed with methods of scientific research. Hypothesis example may look like this:

In your work, you must prove or reject this hypothesis by providing survey results. Show some statistical analysis , study of reports and other processed data.

Remeber that you can hire a paper writer who will integrate survey outcomes and conduct statistical analysis in your research paper hypothesis. 

Variables in Hypotheses

To make a qualitative guess, you should consider variables in your hypothesis. They can be divided into independent and dependent ones. In fact, you must establish causal relationship between two or more variables. Independent ( confounding variable ) is what researcher can control or change, i.e. initial condition. Dependent ( extraneous variable ) is what researcher studies. It is observed in created conditions. Before you start learning how to write an assignment with independent and dependent variables, you should define the main idea of your work. For example, you take an assumption that eating hedgehog meat reduces risk of cardiovascular disease. Independent variable is hedgehog meat consumption, which is cause. Improvement in cardiovascular health is a dependent variable – an intended effect.

How to Write a Hypothesis: 5 Simple Writing Steps

Novice researchers most frequently ask how to write a hypothesis statement. This is a complex process that includes compilation of laconic predictions. These are based on conducted experiments. We can support you in this task. We have developed 5 steps for researchers so they can write a high-quality and comprehensive assignment.

Step 1. Generate a Question Before Writing Your Hypothesis

At the first stage of writing a hypothesis for a research paper you must define a research question that you need to answer. It should be focused on particular problem. Try to make it specific and yet suitable for research within framework of your project. To write quality assignment, you must use 6 classic statements. Thus, you must clarify: who, what, where, when, why and how. You must make question understandable in terms of positioning problem. Example of correct hypothesis:

Step 2. Gather Preliminary Research for Your Hypothesis

Before writing a research hypothesis, conduct some preliminary research to find out if your assumption is working and can be proved. You will get the key insights through observations or experiments. You can also use results of your colleagues who have already studied this issue. Thus, you will build a concept with formulated variables. You will study them and identify relationships between them.

Step 3. Write a Strong Hypothesis

With results of preliminary preparation and research questions, you can study how to write a strong hypothesis . First of all, highlight the main testing problem. You must formulate it as briefly as possible. Try to avoid stretching statements in an attempt to make paper longer. Be as clear as possible, avoid vague judgments. For example:

This is not good option. It is better to apply hypothesis in the form of:

This is a clear sentence that is devoid of unnecessary details. It allows you to immediately see an expected effect. Get practical help in writing research paper if you wish for more quality.

Step 4. Refine Your Research Hypothesis

Make sure a hypothesis for a research proposal formulated correctly. You must check if it has following elements:

• Dependent and independent variables.
• An object or phenomenon for testing.
• Expected outcome of study that you plan to work through. This must be part of an experiment or an observation.

This way, you will specify question under study. You also will be able to verify it if needed. That is, you will move from general to particular.

Step 5. Write a Null Hypothesis

You may need to write a null hypothesis. Why and when, you may ask? When you use this method for processing specific statistics. You should specify if you plan to prove your point on its basis. In fact, it is clear position that doesn’t establish links between variables. For example, this statement is null hypothesis:

It is basis for presenting one's own opinion. It allows to build an evidence base stemming from researcher's evidence.

What Is the Difference Between a Null Hypothesis and an Alternative Hypothesis

To better understand how to write null and alternative hypothesis that will form backbone of study, examine testable statements. Based on results, null hypothesis is prepared. It is a statement with no connection between variables. At the same time, scientists usually work with an alternative hypothesis. Here, they have already found a connection between phenomena. Ever considered custom research paper writing service ? So, the above statement about frequency of doctor visits can be modified to research of: 

Hypothesis Examples

Quite often, researchers find it difficult to formulate basis for  writing a research paper . Therefore, some examples of hypothesis will be useful for them. This will correspond to if-then connections. With their help you will also briefly outline the main part of current research. We will help you in formulating an assignment and offer several working options:

Tips on Writing a Hypothesis

It’s difficult to start writing a hypothesis for a research proposal. Especially for aspiring academics! After all, it is important that an assignment is clear and specific. It must also be viable for further development. Here are some tips to help you formulate your statement:

• Analyze interesting aspects. Review current studies and problems on the selected topic. Highlight what you wanted to explore, perhaps it will be a concept close to your previous works.
• Clarify the details. Spend time on preliminary analysis. You must also highlight controversial aspects and contemporary issues. Sometimes, even well-researched phenomena can be promising.
• Focus on your own work. It’s always easier to continue than to start anew. At the same time, you might not have considered all the theses in the previous study.
• Make the variables clear. Avoid ambiguous statements.

Sounds a bit difficult? College paper help is there for you.

How to Write a Scientific Hypothesis: Final Thoughts

So, if you've come this far, you should already know how to how to write a hypothesis step by step. Before starting writing, analyze the problem and the topic. You should highlight the thesis that can be developed further. We recommend going through the following steps:

• Define the question you expect to receive an answer to.
• Do some preliminary research.
• Write it strongly.
• Refine it with variables, subject and phenomenon, and expected result.
• Make a null hypothesis and consider a different option.

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Frequently Asked Questions About Writing a Good Hypothesis

1. how can i improve my hypothesis.

To make the hypothesis working and of high quality, be sure you select both independent and dependent variables and add them to the statement. Examine the relationships of these elements. Think if you can prove them and explain them in further research.

2. Is there a maximum number of hypotheses that is allowed in one research paper?

You can write as many hypotheses as you want for your paper, because it all depends on your view on the topic and the desire to develop it in several directions. The main thing is that your project shouldn't be overloaded with too many hypotheses and that you pay enough attention to each of them.

3. How do I test my hypothesis?

It’s easy to test the statement before you write a hypothesis for a research proposal. Do an experiment: ask your question and try answering it. If you succeed, this assignment can be used for more detailed study.

4. How long is a hypothesis?

While writing the hypothesis, you must make it as direct as possible and, at the same time, clear it of extraneous judgments. Typically, it's 20 words long. We don’t recommend exceeding this volume, so as not to face difficulties in interpretation.

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