type 1 error in research example

Type 1 and Type 2 Errors in Statistics

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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A statistically significant result cannot prove that a research hypothesis is correct (which implies 100% certainty). Because a p -value is based on probabilities, there is always a chance of making an incorrect conclusion regarding accepting or rejecting the null hypothesis ( H 0 ).

Anytime we make a decision using statistics, there are four possible outcomes, with two representing correct decisions and two representing errors.

The chances of committing these two types of errors are inversely proportional: that is, decreasing type I error rate increases type II error rate and vice versa.

As the significance level (α) increases, it becomes easier to reject the null hypothesis, decreasing the chance of missing a real effect (Type II error, β). If the significance level (α) goes down, it becomes harder to reject the null hypothesis , increasing the chance of missing an effect while reducing the risk of falsely finding one (Type I error).

Type I error 

A type 1 error is also known as a false positive and occurs when a researcher incorrectly rejects a true null hypothesis. Simply put, it’s a false alarm.

This means that you report that your findings are significant when they have occurred by chance.

The probability of making a type 1 error is represented by your alpha level (α), the p- value below which you reject the null hypothesis.

A p -value of 0.05 indicates that you are willing to accept a 5% chance of getting the observed data (or something more extreme) when the null hypothesis is true.

You can reduce your risk of committing a type 1 error by setting a lower alpha level (like α = 0.01). For example, a p-value of 0.01 would mean there is a 1% chance of committing a Type I error.

However, using a lower value for alpha means that you will be less likely to detect a true difference if one really exists (thus risking a type II error).

Scenario: Drug Efficacy Study

Imagine a pharmaceutical company is testing a new drug, named “MediCure”, to determine if it’s more effective than a placebo at reducing fever. They experimented with two groups: one receives MediCure, and the other received a placebo.

• Null Hypothesis (H0) : MediCure is no more effective at reducing fever than the placebo.
• Alternative Hypothesis (H1) : MediCure is more effective at reducing fever than the placebo.

After conducting the study and analyzing the results, the researchers found a p-value of 0.04.

If they use an alpha (α) level of 0.05, this p-value is considered statistically significant, leading them to reject the null hypothesis and conclude that MediCure is more effective than the placebo.

However, MediCure has no actual effect, and the observed difference was due to random variation or some other confounding factor. In this case, the researchers have incorrectly rejected a true null hypothesis.

Error : The researchers have made a Type 1 error by concluding that MediCure is more effective when it isn’t.

Implications

Resource Allocation : Making a Type I error can lead to wastage of resources. If a business believes a new strategy is effective when it’s not (based on a Type I error), they might allocate significant financial and human resources toward that ineffective strategy.

Unnecessary Interventions : In medical trials, a Type I error might lead to the belief that a new treatment is effective when it isn’t. As a result, patients might undergo unnecessary treatments, risking potential side effects without any benefit.

Reputation and Credibility : For researchers, making repeated Type I errors can harm their professional reputation. If they frequently claim groundbreaking results that are later refuted, their credibility in the scientific community might diminish.

Type II error

A type 2 error (or false negative) happens when you accept the null hypothesis when it should actually be rejected.

Here, a researcher concludes there is not a significant effect when actually there really is.

The probability of making a type II error is called Beta (β), which is related to the power of the statistical test (power = 1- β). You can decrease your risk of committing a type II error by ensuring your test has enough power.

You can do this by ensuring your sample size is large enough to detect a practical difference when one truly exists.

Scenario: Efficacy of a New Teaching Method

Educational psychologists are investigating the potential benefits of a new interactive teaching method, named “EduInteract”, which utilizes virtual reality (VR) technology to teach history to middle school students.

They hypothesize that this method will lead to better retention and understanding compared to the traditional textbook-based approach.

• Null Hypothesis (H0) : The EduInteract VR teaching method does not result in significantly better retention and understanding of history content than the traditional textbook method.
• Alternative Hypothesis (H1) : The EduInteract VR teaching method results in significantly better retention and understanding of history content than the traditional textbook method.

The researchers designed an experiment where one group of students learns a history module using the EduInteract VR method, while a control group learns the same module using a traditional textbook.

After a week, the student’s retention and understanding are tested using a standardized assessment.

Upon analyzing the results, the psychologists found a p-value of 0.06. Using an alpha (α) level of 0.05, this p-value isn’t statistically significant.

Therefore, they fail to reject the null hypothesis and conclude that the EduInteract VR method isn’t more effective than the traditional textbook approach.

However, let’s assume that in the real world, the EduInteract VR truly enhances retention and understanding, but the study failed to detect this benefit due to reasons like small sample size, variability in students’ prior knowledge, or perhaps the assessment wasn’t sensitive enough to detect the nuances of VR-based learning.

Error : By concluding that the EduInteract VR method isn’t more effective than the traditional method when it is, the researchers have made a Type 2 error.

This could prevent schools from adopting a potentially superior teaching method that might benefit students’ learning experiences.

Missed Opportunities : A Type II error can lead to missed opportunities for improvement or innovation. For example, in education, if a more effective teaching method is overlooked because of a Type II error, students might miss out on a better learning experience.

Potential Risks : In healthcare, a Type II error might mean overlooking a harmful side effect of a medication because the research didn’t detect its harmful impacts. As a result, patients might continue using a harmful treatment.

Stagnation : In the business world, making a Type II error can result in continued investment in outdated or less efficient methods. This can lead to stagnation and the inability to compete effectively in the marketplace.

How do Type I and Type II errors relate to psychological research and experiments?

Type I errors are like false alarms, while Type II errors are like missed opportunities. Both errors can impact the validity and reliability of psychological findings, so researchers strive to minimize them to draw accurate conclusions from their studies.

How does sample size influence the likelihood of Type I and Type II errors in psychological research?

Sample size in psychological research influences the likelihood of Type I and Type II errors. A larger sample size reduces the chances of Type I errors, which means researchers are less likely to mistakenly find a significant effect when there isn’t one.

A larger sample size also increases the chances of detecting true effects, reducing the likelihood of Type II errors.

Are there any ethical implications associated with Type I and Type II errors in psychological research?

Yes, there are ethical implications associated with Type I and Type II errors in psychological research.

Type I errors may lead to false positive findings, resulting in misleading conclusions and potentially wasting resources on ineffective interventions. This can harm individuals who are falsely diagnosed or receive unnecessary treatments.

Type II errors, on the other hand, may result in missed opportunities to identify important effects or relationships, leading to a lack of appropriate interventions or support. This can also have negative consequences for individuals who genuinely require assistance.

Therefore, minimizing these errors is crucial for ethical research and ensuring the well-being of participants.

Further Information

• Publication manual of the American Psychological Association
• Statistics for Psychology Book Download

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• Type I & Type II Errors | Differences, Examples, Visualizations

Type I & Type II Errors | Differences, Examples, Visualizations

Published on 18 January 2021 by Pritha Bhandari . Revised on 2 February 2023.

In statistics , a Type I error is a false positive conclusion, while a Type II error is a false negative conclusion.

Making a statistical decision always involves uncertainties, so the risks of making these errors are unavoidable in hypothesis testing .

The probability of making a Type I error is the significance level , or alpha (α), while the probability of making a Type II error is beta (β). These risks can be minimized through careful planning in your study design.

• Type I error (false positive) : the test result says you have coronavirus, but you actually don’t.
• Type II error (false negative) : the test result says you don’t have coronavirus, but you actually do.

Table of contents

Error in statistical decision-making, type i error, type ii error, trade-off between type i and type ii errors, is a type i or type ii error worse, frequently asked questions about type i and ii errors.

Using hypothesis testing, you can make decisions about whether your data support or refute your research predictions with null and alternative hypotheses .

Hypothesis testing starts with the assumption of no difference between groups or no relationship between variables in the population—this is the null hypothesis . It’s always paired with an alternative hypothesis , which is your research prediction of an actual difference between groups or a true relationship between variables .

In this case:

• The null hypothesis (H 0 ) is that the new drug has no effect on symptoms of the disease.
• The alternative hypothesis (H 1 ) is that the drug is effective for alleviating symptoms of the disease.

Then , you decide whether the null hypothesis can be rejected based on your data and the results of a statistical test . Since these decisions are based on probabilities, there is always a risk of making the wrong conclusion.

• If your results show statistical significance , that means they are very unlikely to occur if the null hypothesis is true. In this case, you would reject your null hypothesis. But sometimes, this may actually be a Type I error.
• If your findings do not show statistical significance, they have a high chance of occurring if the null hypothesis is true. Therefore, you fail to reject your null hypothesis. But sometimes, this may be a Type II error.

A Type I error means rejecting the null hypothesis when it’s actually true. It means concluding that results are statistically significant when, in reality, they came about purely by chance or because of unrelated factors.

The risk of committing this error is the significance level (alpha or α) you choose. That’s a value that you set at the beginning of your study to assess the statistical probability of obtaining your results ( p value).

The significance level is usually set at 0.05 or 5%. This means that your results only have a 5% chance of occurring, or less, if the null hypothesis is actually true.

If the p value of your test is lower than the significance level, it means your results are statistically significant and consistent with the alternative hypothesis. If your p value is higher than the significance level, then your results are considered statistically non-significant.

To reduce the Type I error probability, you can simply set a lower significance level.

Type I error rate

The null hypothesis distribution curve below shows the probabilities of obtaining all possible results if the study were repeated with new samples and the null hypothesis were true in the population .

At the tail end, the shaded area represents alpha. It’s also called a critical region in statistics.

If your results fall in the critical region of this curve, they are considered statistically significant and the null hypothesis is rejected. However, this is a false positive conclusion, because the null hypothesis is actually true in this case!

A Type II error means not rejecting the null hypothesis when it’s actually false. This is not quite the same as “accepting” the null hypothesis, because hypothesis testing can only tell you whether to reject the null hypothesis.

Instead, a Type II error means failing to conclude there was an effect when there actually was. In reality, your study may not have had enough statistical power to detect an effect of a certain size.

Power is the extent to which a test can correctly detect a real effect when there is one. A power level of 80% or higher is usually considered acceptable.

The risk of a Type II error is inversely related to the statistical power of a study. The higher the statistical power, the lower the probability of making a Type II error.

Statistical power is determined by:

• Size of the effect : Larger effects are more easily detected.
• Measurement error : Systematic and random errors in recorded data reduce power.
• Sample size : Larger samples reduce sampling error and increase power.
• Significance level : Increasing the significance level increases power.

To (indirectly) reduce the risk of a Type II error, you can increase the sample size or the significance level.

Type II error rate

The alternative hypothesis distribution curve below shows the probabilities of obtaining all possible results if the study were repeated with new samples and the alternative hypothesis were true in the population .

The Type II error rate is beta (β), represented by the shaded area on the left side. The remaining area under the curve represents statistical power, which is 1 – β.

Increasing the statistical power of your test directly decreases the risk of making a Type II error.

The Type I and Type II error rates influence each other. That’s because the significance level (the Type I error rate) affects statistical power, which is inversely related to the Type II error rate.

This means there’s an important tradeoff between Type I and Type II errors:

• Setting a lower significance level decreases a Type I error risk, but increases a Type II error risk.
• Increasing the power of a test decreases a Type II error risk, but increases a Type I error risk.

This trade-off is visualized in the graph below. It shows two curves:

• The null hypothesis distribution shows all possible results you’d obtain if the null hypothesis is true. The correct conclusion for any point on this distribution means not rejecting the null hypothesis.
• The alternative hypothesis distribution shows all possible results you’d obtain if the alternative hypothesis is true. The correct conclusion for any point on this distribution means rejecting the null hypothesis.

Type I and Type II errors occur where these two distributions overlap. The blue shaded area represents alpha, the Type I error rate, and the green shaded area represents beta, the Type II error rate.

By setting the Type I error rate, you indirectly influence the size of the Type II error rate as well.

It’s important to strike a balance between the risks of making Type I and Type II errors. Reducing the alpha always comes at the cost of increasing beta, and vice versa .

For statisticians, a Type I error is usually worse. In practical terms, however, either type of error could be worse depending on your research context.

A Type I error means mistakenly going against the main statistical assumption of a null hypothesis. This may lead to new policies, practices or treatments that are inadequate or a waste of resources.

In contrast, a Type II error means failing to reject a null hypothesis. It may only result in missed opportunities to innovate, but these can also have important practical consequences.

In statistics, a Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s actually false.

The risk of making a Type I error is the significance level (or alpha) that you choose. That’s a value that you set at the beginning of your study to assess the statistical probability of obtaining your results ( p value ).

To reduce the Type I error probability, you can set a lower significance level.

The risk of making a Type II error is inversely related to the statistical power of a test. Power is the extent to which a test can correctly detect a real effect when there is one.

To (indirectly) reduce the risk of a Type II error, you can increase the sample size or the significance level to increase statistical power.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

In statistics, power refers to the likelihood of a hypothesis test detecting a true effect if there is one. A statistically powerful test is more likely to reject a false negative (a Type II error).

If you don’t ensure enough power in your study, you may not be able to detect a statistically significant result even when it has practical significance. Your study might not have the ability to answer your research question.

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What Is a Type I Error?

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Type 1 Error: Definition, False Positives, and Examples

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In statistical research, a type 1 error is when the null hypothesis is rejected, which incorrectly leads to the study stating that notable differences were found in the variables when actually there were no differences. Put simply, a type I error is a false positive result.

Making a type I error often can't be avoided because of the degree of uncertainty involved. A null hypothesis is established during hypothesis testing before a test begins. In some cases, a type I error assumes there's no cause-and-effect relationship between the tested item and the stimuli to trigger an outcome to the test.

Key Takeaways

• A type I error occurs during hypothesis testing when a null hypothesis is rejected, even though it is accurate and should not be rejected.
• Hypothesis testing is a testing process that uses sample data.
• The null hypothesis assumes no cause-and-effect relationship between the tested item and the stimuli applied during the test.
• A type I error is a false positive leading to an incorrect rejection of the null hypothesis.
• A false positive can occur if something other than the stimuli causes the outcome of the test.

How a Type I Error Works

Hypothesis testing is a testing process that uses sample data. The test is designed to provide evidence that the hypothesis or conjecture is supported by the data being tested. A null hypothesis is a belief that there is no statistical significance or effect between the two data sets, variables, or populations being considered in the hypothesis. A researcher would generally try to disprove the null hypothesis.

For example, let's say the null hypothesis states that an investment strategy doesn't perform any better than a market index like the S&P 500 . The researcher would take samples of data and test the historical performance of the investment strategy to determine if the strategy performed at a higher level than the S&P. If the test results show that the strategy performed at a higher rate than the index, the null hypothesis is rejected.

This condition is denoted as n=0. If the result seems to indicate that the stimuli applied to the test subject caused a reaction when the test is conducted, the null hypothesis stating that the stimuli do not affect the test subject then needs to be rejected.

A null hypothesis should ideally never be rejected if it's found to be true. It should always be rejected if it's found to be false. However, there are situations when errors can occur.

False Positive Type I Error

A type I error is also called a false positive result. This result leads to an incorrect rejection of the null hypothesis. It rejects an idea that shouldn't have been rejected in the first place.

Rejecting the null hypothesis under the assumption that there is no relationship between the test subject, the stimuli, and the outcome may sometimes be incorrect. If something other than the stimuli causes the outcome of the test, it can cause a false positive result.

Examples of Type I Errors

Let's look at a couple of hypothetical examples to show how type I errors occur.

Criminal Trials

Type I errors commonly occur in criminal trials, where juries are required to come up with a verdict of either innocent or guilty. In this case, the null hypothesis is that the person is innocent, while the alternative is guilty. A jury may come up with a type I error if the members find that the person is found guilty and is sent to jail, despite actually being innocent.

Medical Testing

In medical testing, a type I error would cause the appearance that a treatment for a disease has the effect of reducing the severity of the disease when, in fact, it does not. When a new medicine is being tested, the null hypothesis will be that the medicine does not affect the progression of the disease.

Let's say a lab is researching a new cancer drug . Their null hypothesis might be that the drug does not affect the growth rate of cancer cells.

After applying the drug to the cancer cells, the cancer cells stop growing. This would cause the researchers to reject their null hypothesis that the drug would have no effect. If the drug caused the growth stoppage, the conclusion to reject the null, in this case, would be correct.

However, if something else during the test caused the growth stoppage instead of the administered drug, this would be an example of an incorrect rejection of the null hypothesis (i.e., a type I error).

How Does a Type I Error Occur?

A type I error occurs when the null hypothesis, which is the belief that there is no statistical significance or effect between the data sets considered in the hypothesis, is mistakenly rejected. The type I error should never be rejected even though it's accurate. It is also known as a false positive result.

What Is the Difference Between a Type I and Type II Error?

Type I and type II errors occur during statistical hypothesis testing. While the type I error (a false positive) rejects a null hypothesis when it is, in fact, correct, the type II error (a false negative) fails to reject a false null hypothesis. For example, a type I error would convict someone of a crime when they are actually innocent. A type II error would acquit a guilty individual when they are guilty of a crime.

What Is a Null Hypothesis?

A null hypothesis occurs in statistical hypothesis testing. It states that no relationship exists between two data sets or populations. When a null hypothesis is accurate and rejected, the result is a false positive or a type I error. When it is false and fails to be rejected, a false negative occurs. This is also referred to as a type II error.

What's the Difference Between a Type I Error and a False Positive?

A type I error is often called a false positive. This occurs when the null hypothesis is rejected even though it's correct. The rejection takes place because of the assumption that there is no relationship between the data sets and the stimuli. As such, the outcome is assumed to be incorrect.

Hypothesis testing is a form of testing that uses data sets to either accept or determine a specific outcome using a null hypothesis. Although we often don't realize it, we use hypothesis testing in our everyday lives.

This comes in many areas, such as making investment decisions or deciding the fate of a person in a criminal trial. Sometimes, the result may be a type I error. This false positive is the incorrect rejection of the null hypothesis even when it is true.

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6.1 - type i and type ii errors.

When conducting a hypothesis test there are two possible decisions: reject the null hypothesis or fail to reject the null hypothesis. You should remember though, hypothesis testing uses data from a sample to make an inference about a population. When conducting a hypothesis test we do not know the population parameters. In most cases, we don't know if our inference is correct or incorrect.

When we reject the null hypothesis there are two possibilities. There could really be a difference in the population, in which case we made a correct decision. Or, it is possible that there is not a difference in the population (i.e., \(H_0\) is true) but our sample was different from the hypothesized value due to random sampling variation. In that case we made an error. This is known as a Type I error.

When we fail to reject the null hypothesis there are also two possibilities. If the null hypothesis is really true, and there is not a difference in the population, then we made the correct decision. If there is a difference in the population, and we failed to reject it, then we made a Type II error.

Rejecting \(H_0\) when \(H_0\) is really true, denoted by \(\alpha\) ("alpha") and commonly set at .05

     \(\alpha=P(Type\;I\;error)\)

Failing to reject \(H_0\) when \(H_0\) is really false, denoted by \(\beta\) ("beta")

     \(\beta=P(Type\;II\;error)\)

Example: Trial Section  

A man goes to trial where he is being tried for the murder of his wife.

We can put it in a hypothesis testing framework. The hypotheses being tested are:

• \(H_0\) : Not Guilty
• \(H_a\) : Guilty

Type I error  is committed if we reject \(H_0\) when it is true. In other words, did not kill his wife but was found guilty and is punished for a crime he did not really commit.

Type II error  is committed if we fail to reject \(H_0\) when it is false. In other words, if the man did kill his wife but was found not guilty and was not punished.

Example: Culinary Arts Study Section  

A group of culinary arts students is comparing two methods for preparing asparagus: traditional steaming and a new frying method. They want to know if patrons of their school restaurant prefer their new frying method over the traditional steaming method. A sample of patrons are given asparagus prepared using each method and asked to select their preference. A statistical analysis is performed to determine if more than 50% of participants prefer the new frying method:

• \(H_{0}: p = .50\)
• \(H_{a}: p>.50\)

Type I error  occurs if they reject the null hypothesis and conclude that their new frying method is preferred when in reality is it not. This may occur if, by random sampling error, they happen to get a sample that prefers the new frying method more than the overall population does. If this does occur, the consequence is that the students will have an incorrect belief that their new method of frying asparagus is superior to the traditional method of steaming.

Type II error  occurs if they fail to reject the null hypothesis and conclude that their new method is not superior when in reality it is. If this does occur, the consequence is that the students will have an incorrect belief that their new method is not superior to the traditional method when in reality it is.

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A guide to type 1 errors: Examples and best practices

When managing products, product managers often use statistical testing to evaluate the impact of new features, user interface adjustments, or other product modifications. Statistical testing provides evidence to help product managers make informed decisions based on data, indicating whether a change has significantly affected user behavior, engagement, or other relevant metrics.

However, statistical tests aren’t always accurate, and there is a risk of type 1 errors, also known as “false positives,” in statistics. A type 1 error occurs when a null hypothesis is wrongly rejected, even if it’s true.

PMs must consider the risk of type 1 errors when conducting statistical tests. If the significance level is set too high or multiple tests are performed without adjusting for multiple comparisons, the chance of false positives increases. This could lead to incorrect conclusions and waste resources on changes that don’t significantly affect the product.

In this article, you will learn what a type 1 error is, the factors that contribute to one, and best practices for minimizing the risks associated with it.

What is a type 1 error?

A type 1 error, also known as a “false positive,” occurs when you mistakenly reject a null hypothesis as true. The null hypothesis assumes no significant relationship or effect between variables, while the alternative hypothesis suggests the opposite.

For example, a product manager wants to determine if a new call to action (CTA) button implementation on a web app leads to a statistically significant increase in new customer acquisition.

The null hypothesis (H₀) states no significant effect on acquiring new customers on a web app after implementing a new feature, and an alternative hypothesis (H₁) suggests a significant increase in customer acquisition. To confirm their hypothesis, the product managers gather information on user acquisition metrics, like the daily number of active users, repeat customers, click through rate (CTR), churn rate, and conversion rates, both before and after the feature’s implementation.

After collecting data on the acquisition metrics from two different periods and running a statistical evaluation using a t-test or chi-square test, the PM * * falsely believes that the new CTA button is effective based on the sample data. In this case, a type 1 error occurs as he rejected the H₀ even though it has no impact on the population as a whole.

A PM must carefully interpret data, control the significance level, and perform appropriate sample size calculations to avoid this. Product managers, researchers, and practitioners must also take these steps to reduce the likelihood of making type 1 errors:

Type 1 vs. type 2 errors

Before comparing type 1 and type 2 errors, let’s first focus on type 2 errors . Unlike type 1 errors, type 2 errors occur when an effect is present but not detected. This means a null hypothesis (Ho) is not rejected even though it is false.

In product management, type 1 errors lead to incorrect decisions, wasted resources, and unsuccessful products, while type 2 errors result in missed opportunities, stunted growth, and suboptimal decision-making. For a comprehensive comparison between type 1 and type 2 errors with product development and management, please refer to the following:

To understand the comparison table above, it’s necessary to grasp the relationship between type 1 and type 2 errors. This is where the concept of statistical power comes in handy.

Statistical power refers to the likelihood of accurately rejecting a null hypothesis( Ho) when it’s false. This likelihood is influenced by factors such as sample size, effect size, and the chosen level of significance, alpha ( α ).

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With hypothesis testing, there’s often a trade-off between type 1 and type 2 errors. By setting a more stringent significance level with a lower α, you can decrease the chance of type 1 errors, but increase the chance of Type 2 errors.

On the other hand, by setting a less stringent significance level with a higher α, we can decrease the chance of type 2 errors, but increase the chance of type 1 errors.

It’s crucial to consider the consequences of each type of error in the specific context of the study or decision being made. The importance of avoiding one type of error over the other will depend on the field of study, the costs associated with the errors, and the goals of the analysis.

Factors that contribute to type 1 errors

Type 1 errors can be caused by a range of different factors, but the following are some of the most common reasons:

Insufficient sample size

Multiple comparisons, publication bias, inadequate control groups or comparison conditions, human judgment and bias.

When sample sizes are too small, there is a greater chance of type 1 errors. This is because random variation may affect the observed results rather than an actual effect. To avoid this, studies should be conducted with larger sample sizes, which increases statistical power and decreases the risk of type 1 errors.

When multiple statistical tests or comparisons are conducted simultaneously without appropriate adjustments, the likelihood of encountering false positives increases. Conducting numerous tests without correcting for multiple comparisons can lead to an inflated type 1 error rate.

Techniques like Bonferroni correction or false discovery rate control should be employed to address this issue.

Publication bias is when studies with statistically significant results are more likely to be published than those with non-significant or null findings. This can lead to misleading perceptions of the true effect sizes or relationships. To mitigate this bias, meta-analyses or systematic reviews consider all available evidence, including unpublished studies.

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When conducting experimental studies, selecting the wrong control group or comparison condition can lead to inaccurate results. Without a suitable control group, distinguishing the actual impact of the intervention from other variables becomes difficult, which raises the likelihood of making type 1 errors.

When researchers allow their personal opinions or assumptions to influence their analysis, they can make type 1 errors. This is especially true when researchers favor results that align with their expectations, known as confirmation bias.

To reduce the chances of type 1 errors, it’s crucial to consider these factors and utilize appropriate research design, statistical analysis methods, and reporting protocols.

Type 1 error examples

In software product management, minimizing type 1 errors is important. To help you better understand, here are some examples of type 1 errors from product management in the context of null hypothesis (Ho) validation, alongside strategies to mitigate them:

False positive impact of a new feature

False positive correlation between metrics, false positive for performance improvement, overstating the effectiveness of an algorithm.

Here, the assumption is that specific features of your software would greatly improve user involvement. To test this hypothesis, a PM conducts experiments and observes increased user involvement. However, it later becomes clear that the boost was not solely due to the feature, but also other factors, such as a simultaneous marketing campaign.

This results in a type 1 error.

Experiments focusing solely on the analyzed feature are important to avoid mistakes. One effective method is A/B testing , where you randomly divide users into two groups — one group with the new feature and the other without. By comparing the outcomes of both groups, you can accurately attribute any observed effects to the feature being tested.

In this case, a PM believes there is a direct connection between the number of bug fixes and customer satisfaction scores (CSAT) . However, after examining the data, you find a correlation that appears to support your hypothesis that could just be coincidental.

This leads to a Type 1 error, where bug fixes have no direct impact on CSAT.

It’s important to use rigorous statistical analysis techniques to reduce errors. This includes employing appropriate statistical tests like correlation coefficients and evaluating the statistical significance of the correlations observed.

Another potential instance comes when a hypothesis states that the performance of the software can be greatly enhanced by implementing a particular optimization technique. However, if the optimization technique is implemented and there is no noticeable improvement in the software’s performance, a type 1 error has occured.

To ensure the successful implementation of optimization techniques, it is important to conduct thorough benchmarking and profiling beforehand. This will help identify any existing bottlenecks.

A type 1 error occurs when an algorithm claims to predict user behavior or outcomes with high accuracy and then often falls short in real-life situations.

To ensure the effectiveness of algorithms, conduct extensive testing in real-world settings, using diverse datasets and consider various edge cases. Additionally, evaluate the algorithm’s performance against relevant metrics and benchmarks before making any bold claims.

Designing rigorous experiments, using proper statistical analysis techniques, controlling for confounding variables, and incorporating qualitative data are important to reduce the risk of type 1 error.

Best practices to minimize type 1 errors

To reduce the chances of type 1 errors, product managers should take the following measures:

• Careful experiment design — To increase the reliability of results, it is important to prioritize well-designed experiments, clear hypotheses, and have appropriate sample sizes
• Set a significance level — The significance level determines the threshold for rejecting the null hypothesis. The most commonly used values are 0.05 or 0.01. These values represent a 5 percent or 1 percent chance of making a type 1 error. Opting for a lower significance level can decrease the probability of mistakenly rejecting the null hypothesis
• Correcting for multiple comparisons — To control the overall type 1 error rate, statistical techniques like Bonferroni correction or the false discovery rate (FDR) can be helpful when performing multiple tests simultaneously, such as testing several features or variants
• Replication and validation — To ensure accuracy and minimize false positives, it’s important to repeat important findings in future experiments
• Use appropriate sample sizes — Sufficient sample size is important for accurate results. Determine the required size of the sample based on effect size, desired power, and significance level. A suitable sample size improves the chances of detecting actual effects and reduces type 2 errors

Product managers must grasp the importance of type 1 errors in statistical testing. By recognizing the possibility of false positives, you can make better evidence-based decisions and avoid wasting resources on changes that do not truly benefit the product or its users. Employing appropriate statistical techniques, considering effect sizes, replicating findings, and conducting rigorous experiments can help mitigate the risk of type 1 errors and ensure reliable decision-making in product management.

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Type 1 and Type 2 Errors

What is type 1 error.

A Type 1 error, also known as a false positive, is when a test incorrectly indicates that a condition is present when it is not.

For example, if a new drug is tested and the null hypothesis is that the drug is ineffective but actually effective, then a Type 1 error has occurred. This error can have serious consequences, as patients may be needlessly exposed to harmful side effects or may miss out on treatment altogether.

Type 1 errors are often due to chance, but they can also be caused by errors in the testing process itself. For example, if the sample size is too small or there is bias in the selection of participants, this can increase the likelihood of a Type 1 error. It's important to consider these factors when designing a study, as they can greatly impact the results.

When interpreting results from a test, it's important to consider the potential for Type 1 errors. If the consequences of a false positive are serious, then a higher level of proof may be needed to make sure that the results are accurate. On the other hand, if the consequences of a false positive are not so serious, then a lower level of proof may be acceptable.

It's also worth considering the Type 2 error, which is when a test incorrectly indicates that a condition is not present when it actually is. This error can have just as serious consequences as a Type 1 error, so it's important to be aware of both when interpreting test results.

Type 1 and Type 2 errors can be reduced by using more reliable tests and increasing the sample size. However, it's not always possible to completely eliminate these errors, so it's important to be aware of their potential impact when interpreting test results.

What Causes a Type 1 Error

There are several factors that can contribute to a type 1 error.

First, the researcher sets the level of significance (alpha). The higher the alpha level, the more likely it is that a type 1 error will occur.

Second, the sample size also plays a role in the likelihood of a type 1 error. The larger the sample size, the less likely it is that a type 1 error will occur.

Third, the power of the test also affects the likelihood of a type 1 error. The higher the power of the test, the less likely it is that a type 1 error will occur.

Finally, if there are multiple tests being conducted, the Bonferroni correction can be used to control for the possibility of a type 1 error.

All of these factors contribute to the likelihood of a type 1 error. The level of significance, sample size, power of the test, and the Bonferroni correction are all important considerations when trying to avoid a type 1 error.

Why Is It Important to Understand Type 1 Errors

It's important to understand type 1 errors because it can help you avoid making decisions based on incorrect information. If you know that there's a chance of a false positive, you can be more cautious in your interpretation of results. This is especially important when the consequences of a wrong decision could be serious.

Type 1 error is also important to understand from a statistical standpoint. When designing studies and analyzing data, researchers need to account for the possibility of false positives. Otherwise, their results could be skewed.

Overall, it's essential to have a good understanding of type 1 errors. It can help you avoid making incorrect decisions and ensure accurate research studies.

How to Reduce Type 1 Errors

Type 1 errors, also known as false positives, can occur when a test or experiment rejects the null hypothesis incorrectly. This means that there is evidence to support the alternative hypothesis when in reality, there is none. Type 1 errors can have serious consequences, especially in the field of medicine or criminal justice. For example, if a new drug is tested and found to be effective but later discovered that it actually causes more harm than good, this would be a type 1 error.

There are several ways to reduce the risk of making a type 1 error:

Use a larger sample size: The larger the sample size, the less likely it is that a type 1 error will occur. This is because there is more data to work with, and the results are more likely to be representative of the population as a whole.

Use a stricter criterion: A stricter criterion means that there is less of a chance that a false positive will be found. For example, if a medical test is looking for a very rare disease, setting a high threshold for what constitutes a positive result will help reduce the chances of a type 1 error.

Replicate the study: If possible, try to replicate the study using a different sample or method. This can help to confirm the results and reduce the chance of error.

Use multiple testing methods: Using more than one method to test for something can also help to reduce the chances of error. For example, animal and human subjects can help confirm the results if a new drug is being tested.

Be aware of potential biases: Many different types of bias can affect a study's results. Try to be aware of these and take steps to avoid them.

Use objective measures: If possible, use objective measures rather than subjective ones. Objective measures are less likely to be influenced by personal biases or preconceptions.

Be cautious in interpreting results: Remember that even if a study shows significant results, this does not necessarily mean that the null hypothesis is false. There could still be some other explanation for the results. Therefore, it is important to be cautious in interpreting the results of any study.

Type 1 errors can have serious consequences, but there are ways to reduce the risk of making one. By using large sample size, setting a strict criterion, replicating the study, or using multiple testing methods, the chances of making a type 1 error can be reduced. However, it is also important to be aware of potential biases and to interpret the results of any study cautiously.

What Is Type 2 Error

A Type II error is when we fail to reject a null hypothesis when it is actually false. This error is also known as a false negative.

Type II errors are much more serious than Type I errors. This is because if we make a Type II error, we may be making a decision that could have harmful consequences. For example, imagine that we are testing a new drug to see if it is effective in treating cancer. If we make a Type I error, we may give the drug to patients who don’t actually need it. This may not be harmful, as the drug may have no side effects. However, if we make a Type II error, we may fail to give the drug to patients who could benefit from it. This could have deadly consequences.

It is important to note that, while Type I and Type II errors are both possible, it is impossible to make both errors at the same time. This is because they are opposite errors; if we reject the null hypothesis when it is true, then we cannot fail to reject the null hypothesis when it is false (and vice versa).

What Causes a Type 2 Error

A type 2 error occurs when you fail to reject the null hypothesis, even though it is false. In other words, you conclude that there is no difference when there actually is a difference. Type 2 errors are often called false negatives.

There are several reasons why a type 2 error can occur. One reason is that the sample size is too small. With a small sample size, there is simply not enough power to detect a difference, even if one exists.

Another reason for a type 2 error is poor study design. If the study is not well-designed, it may be biased in such a way that it fails to detect a difference that actually exists. For example, if there is selection bias in the recruitment of participants, this can lead to a type 2 error.

Finally, chance plays a role in all statistical tests. Even with a large sample size and a well-designed study, there is always a possibility that a type 2 error will occur simply by chance. This is why it is important to report the p-value in addition to the significance level when presenting the results of a statistical test. The p-value tells you how likely it is that a type 2 error has occurred.

Why Is It Important to Understand Type 2 Errors

It's important to understand type 2 errors because, if you don't, you could make some serious mistakes in your research. Type 2 error is when you conclude that there is no difference between two groups when there actually is a difference. This might not seem like a big deal, but it can have some pretty serious consequences.

For example, let's say you're doing a study on the effect of a new drug. You give the drug to one group of people and a placebo to another group. After taking the drug, you measure how well each group does on a test. If there's no difference between the two groups, you might conclude that the drug doesn't work. But if there is actually a difference, and you just didn't see it because of a type 2 error, you might be keeping people from getting the help they need.

How to Reduce Type 2 Errors

There are several ways to reduce the likelihood of making a Type II error in hypothesis testing. One way is to ensure that the null and alternative hypotheses are well-defined and that the test statistic is appropriately chosen.

Another way to reduce Type II error is to increase the power of the test. This can be done by increasing the sample size or by using a more powerful test statistic.

Ultimately, it is important to consider the consequences of both Type I and Type II errors when designing a hypothesis test. Both types of errors can have serious implications, so it is important to choose a test that will minimize the probability of both types of errors.

What Is the Difference Between a Type 1 and Type 2 Error?

Two types of errors can occur when conducting statistical tests: type 1 and type 2. These terms are often used interchangeably, but there is a crucial distinction between them.

A type 1 error, also known as a false positive, occurs when the test incorrectly rejects the null hypothesis. In other words, a type 1 error means that you've concluded there is a difference when in reality, there isn't one.

A type 2 error, or false negative, happens when the test fails to reject the null hypothesis when there actually is a difference. So a type 2 error represents missing an important opportunity.

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Fundamentals of Statistics

3. type i and type ii errors.

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9.2: Outcomes, Type I and Type II Errors

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When you perform a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis  H 0 and the decision to reject or not.

The outcomes are summarized in the following table:

The four possible outcomes in the table are:

• The decision is  not to reject H 0 when H 0 is true (correct decision) .
• The decision is to reject H 0 when H 0 is true (incorrect decision known as a Type I error ).
• The decision is not to reject H 0 when  H 0 is false (incorrect decision known as a Type II error ).
• The decision is to reject H 0 when H 0 is false ( correct decision whose probability is called the Power of the Test ).

Each of the errors occurs with a particular probability. The Greek letters  α and β represent the probabilities.

α = probability of a Type I error = P (Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

β = probability of a Type II error = P (Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

α and β should be as small as possible because they are probabilities of errors. They are rarely zero.

The Power of the Test is 1 –  β . Since β is probability of making type II error, we want this probability to be small. In other words, we want the value 1 –  β  to be as closed to one as possible. Increasing the sample size can increase the Power of the Test.

Suppose the null hypothesis,  H 0 , is: Frank’s rock climbing equipment is safe.

• Ty pe I error: Frank thinks that his rock climbing equipment may not be safe when, in fact, it really is safe.
• Type II error: Frank thinks that his rock climbing equipment may be safe when, in fact, it is not safe.

α = Probability that Frank thinks his rock climbing equipment may not be safe when it really is safe. β = Probability that Frank thinks his rock climbing equipment may be safe when it is not safe.

Notice that, in this case, the error with the greater consequence is the Type II error. (If Frank thinks his rock climbing equipment is safe, he will go ahead and use it.)

Suppose the null hypothesis,  H 0 , is: the blood cultures contain no traces of pathogen X . State the Type I and Type II errors.

[practice-area rows=”2″][/practice-area] [reveal-answer q=”313018″]Solution[/reveal-answer] [hidden-answer a=”313018″]

Type I error : The researcher thinks the blood cultures do contain traces of pathogen X, when in fact, they do not. Type II error : The researcher thinks the blood cultures do not contain traces of pathogen X, when in fact, they do.

[/hidden-answer]

Suppose the null hypothesis,  H 0 : The victim of an automobile accident is alive when he arrives at the emergency room of a hospital. State the 4 possible outcomes of performing a hypothesis test.

α = probability that the emergency crew thinks the victim is dead when, in fact, he is really alive = P (Type I error). β = probability that the emergency crew does not know if the victim is alive when, in fact, the victim is dead = P (Type II error).

The error with the greater consequence is the Type I error. (If the emergency crew thinks the victim is dead, they will not treat him.)

A YouTube element has been excluded from this version of the text. You can view it online here: http://pb.libretexts.org/esm/?p=120

Suppose the null hypothesis, H 0 , is: A patient is not sick. Which type of error has the greater consequence, Type I or Type II?

[practice-area rows=”1=2″][/practice-area] [reveal-answer q=”3933″]Solution[/reveal-answer] [hidden-answer a=”3933″]

Type I Error: The patient will not be thought well when, in fact, he is not sick.

Type II Error: The patient will be thought well when, in fact, he is sick.

The error with the greater consequence is the Type II error: the patient will be thought well when, in fact, he is sick. He will not be able to get treatment.[/hidden-answer]

Boy Genetic Labs claim to be able to increase the likelihood that a pregnancy will result in a boy being born. Statisticians want to test the claim. Suppose that the null hypothesis,  H 0 , is: Boy Genetic Labs has no effect on gender outcome. Which type of error has the greater consequence, Type I or Type II?

H 0 : Boy Genetic Labs has no effect on gender outcome.

H a : Boy Genetic Labs has effect on gender outcome.

• Type I error: This results when a true null hypothesis is rejected. In the context of this scenario, we would state that we believe that Boy Genetic Labs influences the gender outcome, when in fact it has no effect. The probability of this error occurring is denoted by the Greek letter alpha, α .
• Type II error: This results when we fail to reject a false null hypothesis. In context, we would state that Boy Genetic Labs does not influence the gender outcome of a pregnancy when, in fact, it does. The probability of this error occurring is denoted by the Greek letter beta, β .

The error of greater consequence would be the Type I error since couples would use the Boy Genetic Labs product in hopes of increasing the chances of having a boy.

“Red tide” is a bloom of poison-producing algae–a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living in the area develop dangerous levels of a paralysis-inducing toxin. In Massachusetts, the Division of Marine Fisheries (DMF) monitors levels of the toxin in shellfish by regular sampling of shellfish along the coastline. If the mean level of toxin in clams exceeds 800 μg (micrograms) of toxin per kg of clam meat in any area, clam harvesting is banned there until the bloom is over and levels of toxin in clams subside. Describe both a Type I and a Type II error in this context, and state which error has the greater consequence.

[reveal-answer q=”432609″]Solution[/reveal-answer] [hidden-answer a=”432609″]

In this scenario, an appropriate null hypothesis would be H 0 : the mean level of toxins is at most 800 μg. ( H 0 : μ 0 ≤ 800 μg ) H a : the mean level of toxins exceeds 800 μg. (H a : μ 0  > 800 μg )

Type I error: The DMF believes that toxin levels are still too high when, in fact, toxin levels are at most 800 μg. The DMF continues the harvesting ban. Type II error: The DMF believes that toxin levels are within acceptable levels (are at least 800 μg) when, in fact, toxin levels are still too high (more than 800 μg). The DMF lifts the harvesting ban.

This error could be the most serious. If the ban is lifted and clams are still toxic, consumers could possibly eat tainted food. In summary, the more dangerous error would be to commit a Type II error, because this error involves the availability of tainted clams for consumption.[/hidden-answer]

A certain experimental drug claims a cure rate of higher than 75% for males with prostate cancer.

Describe both the Type I and Type II errors in context. Which error is the more serious?

H 0 : The cure rate is less than 75%.

H a : The cure rate is higher than 75%.

• Type I: A cancer patient believes the cure rate for the drug is more than 75% when the cure rate actually is less than 75%.
• Type II: A cancer patient believes the the cure rate is less than 75% cure rate when the cure rate is actually higher than 75%.

In this scenario, the Type II error contains the more severe consequence. If a patient believes the drug works at least 75% of the time, this most likely will influence the patient’s (and doctor’s) choice about whether to use the drug as a treatment option.

Determine both Type I and Type II errors for the following scenario:

Assume a null hypothesis, H 0 , that states the percentage of adults with jobs is at least 88%.

Identify the Type I and Type II errors from these four statements.

a)Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88% when that percentage is actually less than 88%

b)Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88% when the percentage is actually at least 88%.

c)Reject the null hypothesis that the percentage of adults who have jobs is at least 88% when the percentage is actually at least 88%.

d)Reject the null hypothesis that the percentage of adults who have jobs is at least 88% when that percentage is actually less than 88%.

[reveal-answer q=”76062″]Type I error:[/reveal-answer] [hidden-answer a=”76062″]c [/hidden-answer] [reveal-answer q=”975662″]Type II error:[/reveal-answer] [hidden-answer a=”975662″]b[/hidden-answer]

If H 0 : The percentage of adults with jobs is at least 88%, then H a : The percentage of adults with jobs is less than 88%.

[reveal-answer q=”864484″]Type I error: [/reveal-answer] [hidden-answer a=”864484″]c [/hidden-answer] [reveal-answer q=”126260″]Type II error:[/reveal-answer] [hidden-answer a=”126260″]b[/hidden-answer]

Concept Review

In every hypothesis test, the outcomes are dependent on a correct interpretation of the data. Incorrect calculations or misunderstood summary statistics can yield errors that affect the results. A  Type I error occurs when a true null hypothesis is rejected. A Type II error occurs when a false null hypothesis is not rejected.

The probabilities of these errors are denoted by the Greek letters  α and β , for a Type I and a Type II error respectively. The power of the test, 1 – β , quantifies the likelihood that a test will yield the correct result of a true alternative hypothesis being accepted. A high power is desirable.

Formula Review

• OpenStax, Statistics, Outcomes and the Type I and Type II Errors. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution
• Introductory Statistics . Authored by : Barbara Illowski, Susan Dean. Provided by : Open Stax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]
• Type 1 errors | Inferential statistics | Probability and Statistics | Khan Academy. Authored by : Khan Academy. Located at : https://youtu.be/EowIec7Y8HM . License : All Rights Reserved . License Terms : Standard YouTube License

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Curbing type I and type II errors

Kenneth j. rothman.

RTI Health Solutions, Research Triangle Park, NC USA

The statistical education of scientists emphasizes a flawed approach to data analysis that should have been discarded long ago. This defective method is statistical significance testing. It degrades quantitative findings into a qualitative decision about the data. Its underlying statistic, the P -value, conflates two important but distinct aspects of the data, effect size and precision [ 1 ]. It has produced countless misinterpretations of data that are often amusing for their folly, but also hair-raising in view of the serious consequences.

Significance testing maintains its hold through brilliant marketing tactics—the appeal of having a “significant” result is nearly irresistible—and through a herd mentality. Novices quickly learn that significant findings are the key to publication and promotion, and that statistical significance is the mantra of many senior scientists who will judge their efforts. Stang et al. [ 2 ], in this issue of the journal, liken the grip of statistical significance testing on the biomedical sciences to tyranny, as did Loftus in the social sciences two decades ago [ 3 ]. The tyranny depends on collaborators to maintain its stranglehold. Some collude because they do not know better. Others do so because they lack the backbone to swim against the tide.

Students of significance testing are warned about two types of errors, type I and II, also known as alpha and beta errors. A type I error is a false positive, rejecting a null hypothesis that is correct. A type II error is a false negative, a failure to reject a null hypothesis that is false. A large literature, much of it devoted to the topic of multiple comparisons, subgroup analysis, pre-specification of hypotheses, and related topics, are aimed at reducing type I errors [ 4 ]. This lopsided emphasis on type I errors comes at the expense of type II errors. The type I error, the false positive, is only possible if the null hypothesis is true. If the null hypothesis is false, a type I error is impossible, but a type II error, the false negative, can occur.

Type I and type II errors are the product of forcing the results of a quantitative analysis into the mold of a decision, which is whether to reject or not to reject the null hypothesis. Reducing interpretations to a dichotomy, however, seriously degrades the information. The consequence is often a misinterpretation of study results, stemming from a failure to separate effect size from precision. Both effect size and precision need to be assessed, but they need to be assessed separately, rather than blended into the P -value, which is then degraded into a dichotomous decision about statistical significance.

As an example of what can happen when significance testing is exalted beyond reason, consider the case of the Wall Street Journal investigative reporter who broke the news of a scandal about a medical device maker, Boston Scientific, having supposedly distorted study results [ 5 ]. Boston Scientific reported to the FDA that a new device was better than a competing device. They based their conclusion in part on results from a randomized trial in which the significance test showing the superiority of their device had a P -value of 0.049, just under the criterion of 0.05 that the FDA used statistical significance. The reporter found, however, that the P -value was not significant when calculated using 16 other test procedures that he tried. The P -values from those procedures averaged 0.051. According to the news story, that small difference between the reported P -value of 0.049 and the journalist’s recalculated P -value of 0.051 was “the difference between success and failure” [ 5 ]. Regardless of what the “correct” P -value is for the data in question, it should be obvious that it is absurd to classify the success or failure of this new device according to whether or not the P -value falls barely on one side or the other of an arbitrary line, especially when the discussion revolves around the third decimal place of the P -value. No sensible interpretation of the data from the study should be affected by the news in this newspaper report. Unfortunately, the arbitrary standard imposed by regulatory agencies, which foster that focus on the P -value, reduces the prospects for more sensible evaluations.

In their article, Stang et al. [ 2 ] not only describe the problems with significance testing, but also allude to the solution, which is to rely on estimation using confidence intervals. Sadly, although the use of confidence intervals is increasing, for many readers and authors they are used only as surrogate tests of statistical significance [ 6 ], to note whether the null hypothesis value falls inside the interval or not. This dichotomy is equivalent to the dichotomous interpretation that results from significance testing. When confidence intervals are misused in this way, the entire conclusion can depend on whether the boundary of the interval is located precisely on one side or the other of an artificial criterion point. This is just the kind of mistake that tripped up the Wall Street Journal reporter. Using a confidence interval as a significance test is an opportunity lost.

How should a confidence interval be interpreted? It should be approached in the spirit of a quantitative estimate. A confidence interval allows a measurement of both effect size and precision, the two aspects of study data that are conflated in a P -value. A properly interpreted confidence interval allows these two aspects of the results to be inferred separately and quantitatively. The effect size is measured directly by the point estimate, which, if not given explicitly, can be calculated from the two confidence limits. For a difference measure, the point estimate is the arithmetic mean of the two limits, and for a ratio measure, it is the geometric mean. Precision is measured by the narrowness of the confidence interval. Thus, the two limits of a confidence interval convey information on both effect size and precision. The single number that is the P -value, even without degrading it into categories of “significant” and “not significant”, cannot measure two distinct things. Instead the P -value mixes effect size and precision in a way that by itself reveals little about either.

Scientists who wish to avoid type I or type II errors at all costs may have chosen the wrong profession, because making and correcting mistakes are inherent to science. There is a way, however, to minimize both type I and type II errors. All that is needed is simply to abandon significance testing. If one does not impose an artificial and potentially misleading dichotomous interpretation upon the data, one can reduce all type I and type II errors to zero. Instead of significance testing, one can rely on confidence intervals, interpreted quantitatively, not simply as surrogate significance tests. Only then would the analyses be truly quantitative.

Finally, here is a gratuitous bit of advice for testers and estimators alike: both P -values and confidence intervals are calculated and all too often interpreted as if the study they came from were free of bias. In reality, every study is biased to some extent. Even those who wisely eschew significance testing should keep in mind that if any study were increased in size, its precision would improve and thus all its confidence intervals would shrink, but as they do, they would eventually converge around incorrect values as a result of bias. The final interpretation should measure effect size and precision separately, while considering bias and even correcting for it [ 7 ].

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Home > Finance > Type 1 Error: Definition, False Positives, And Examples

Type 1 Error: Definition, False Positives, And Examples

Published: February 12, 2024

Learn about type 1 errors in finance, including their definition, false positives, and examples. Gain insights into the significance of avoiding these errors in financial decision-making.

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Understanding Type 1 Error: The Sneaky False Positives

Imagine this scenario: You’re conducting a critical experiment to test a new drug that could potentially save lives. The results are in, and it appears that the drug is effective in treating the targeted condition. The excitement kicks in as you imagine the life-changing impact this discovery could have. But wait! Is the drug really effective, or is it just a Type 1 error?

Key Takeaways

• A Type 1 error occurs when a null hypothesis is mistakenly rejected.
• It leads to false positives, where a positive result is observed, but no effect or relationship exists.

In the field of statistics, a Type 1 error occurs when a null hypothesis is mistakenly rejected, meaning that there is a positive result when, in reality, no effect or relationship exists. In simple terms, it’s a false positive.

Let’s explore this concept further and understand why Type 1 errors can wreak havoc on scientific and statistical analysis.

Anatomy of a Type 1 Error

When conducting any experiment or test, researchers work with two opposing hypotheses:

• The null hypothesis (H0): This hypothesis suggests that there is no effect or relationship between variables. It assumes that any observed differences or correlations are due to random chance alone.
• The alternative hypothesis (Ha): This hypothesis suggests that there is an effect or relationship between variables. It proposes that the observed differences or correlations are not due to random chance but rather a genuine effect.

When analyzing the data obtained from an experiment, researchers set a critical value or threshold, known as the significance level (α). This threshold determines what level of evidence is required to reject the null hypothesis and accept the alternative hypothesis.

A Type 1 error occurs when the null hypothesis is rejected, even though it is true. In other words, it wrongly concludes that there is an effect or relationship when, in reality, there is none.

Real-World Examples of Type 1 Errors

To give you a clearer understanding of Type 1 errors, let’s explore a couple of real-life examples:

• A medical test for a rare disease: Imagine a medical test designed to detect a rare disease that only affects 0.1% of the population. The test is 99% accurate, meaning that it correctly identifies positive cases 99% of the time. However, it also has a 5% chance of producing a false positive result. Now, let’s assume that out of 1000 people, only one actually has the disease. If all 1000 people take the test, we would expect approximately 10 false positives (5% of the 999 healthy people). This shows how Type 1 errors can occur even when using seemingly reliable tests.
• Legal decisions: In a court of law, the presumption is that an individual is innocent until proven guilty. However, a Type 1 error, in this case, would occur if an innocent person is wrongly convicted. The Justice system acknowledges this risk and establishes strict protocols and standards of evidence to minimize the chances of a Type 1 error in criminal cases.

Type 1 errors can have significant consequences, leading to wasted resources, misinterpretation of data, and even disastrous medical or legal outcomes. Therefore, it is crucial for researchers, statisticians, and decision-makers to understand the concept of Type 1 errors and take appropriate measures to minimize their occurrence.

In Conclusion

Understanding the concept of Type 1 error is essential when analyzing data and test results. It serves as a reminder of the importance of applying critical thinking and statistical measures to avoid drawing false conclusions.

So, the next time you come across a positive result that seems too good to be true, remember the lurking presence of Type 1 errors and be cautious before accepting it at face value.

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