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

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

Published on January 18, 2021 by Pritha Bhandari . Revised on June 22, 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, other interesting articles, 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.

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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 .

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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.

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
• Null hypothesis

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

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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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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Statistics By Jim

Making statistics intuitive

Types I & Type II Errors in Hypothesis Testing

By Jim Frost 8 Comments

In hypothesis testing, a Type I error is a false positive while a Type II error is a false negative. In this blog post, you will learn about these two types of errors, their causes, and how to manage them.

Hypothesis tests use sample data to make inferences about the properties of a population . You gain tremendous benefits by working with random samples because it is usually impossible to measure the entire population.

However, there are tradeoffs when you use samples. The samples we use are typically a minuscule percentage of the entire population. Consequently, they occasionally misrepresent the population severely enough to cause hypothesis tests to make Type I and Type II errors.

Potential Outcomes in Hypothesis Testing

Hypothesis testing  is a procedure in inferential statistics that assesses two mutually exclusive theories about the properties of a population. For a generic hypothesis test, the two hypotheses are as follows:

• Null hypothesis : There is no effect
• Alternative hypothesis : There is an effect.

The sample data must provide sufficient evidence to reject the null hypothesis and conclude that the effect exists in the population. Ideally, a hypothesis test fails to reject the null hypothesis when the effect is not present in the population, and it rejects the null hypothesis when the effect exists.

Statisticians define two types of errors in hypothesis testing. Creatively, they call these errors Type I and Type II errors. Both types of error relate to incorrect conclusions about the null hypothesis.

The table summarizes the four possible outcomes for a hypothesis test.

Related post : How Hypothesis Tests Work: P-values and the Significance Level

Fire alarm analogy for the types of errors

Using hypothesis tests correctly improves your chances of drawing trustworthy conclusions. However, errors are bound to occur.

Unlike the fire alarm analogy, there is no sure way to determine whether an error occurred after you perform a hypothesis test. Typically, a clearer picture develops over time as other researchers conduct similar studies and an overall pattern of results appears. Seeing how your results fit in with similar studies is a crucial step in assessing your study’s findings.

Now, let’s take a look at each type of error in more depth.

Type I Error: False Positives

When you see a p-value that is less than your significance level , you get excited because your results are statistically significant. However, it could be a type I error . The supposed effect might not exist in the population. Again, there is usually no warning when this occurs.

Why do these errors occur? It comes down to sample error. Your random sample has overestimated the effect by chance. It was the luck of the draw. This type of error doesn’t indicate that the researchers did anything wrong. The experimental design, data collection, data validity , and statistical analysis can all be correct, and yet this type of error still occurs.

Even though we don’t know for sure which studies have false positive results, we do know their rate of occurrence. The rate of occurrence for Type I errors equals the significance level of the hypothesis test, which is also known as alpha (α).

The significance level is an evidentiary standard that you set to determine whether your sample data are strong enough to reject the null hypothesis. Hypothesis tests define that standard using the probability of rejecting a null hypothesis that is actually true. You set this value based on your willingness to risk a false positive.

Related post : How to Interpret P-values Correctly

Using the significance level to set the Type I error rate

When the significance level is 0.05 and the null hypothesis is true, there is a 5% chance that the test will reject the null hypothesis incorrectly. If you set alpha to 0.01, there is a 1% of a false positive. If 5% is good, then 1% seems even better, right? As you’ll see, there is a tradeoff between Type I and Type II errors. If you hold everything else constant, as you reduce the chance for a false positive, you increase the opportunity for a false negative.

Type I errors are relatively straightforward. The math is beyond the scope of this article, but statisticians designed hypothesis tests to incorporate everything that affects this error rate so that you can specify it for your studies. As long as your experimental design is sound, you collect valid data, and the data satisfy the assumptions of the hypothesis test, the Type I error rate equals the significance level that you specify. However, if there is a problem in one of those areas, it can affect the false positive rate.

Warning about a potential misinterpretation of Type I errors and the Significance Level

When the null hypothesis is correct for the population, the probability that a test produces a false positive equals the significance level. However, when you look at a statistically significant test result, you cannot state that there is a 5% chance that it represents a false positive.

Why is that the case? Imagine that we perform 100 studies on a population where the null hypothesis is true. If we use a significance level of 0.05, we’d expect that five of the studies will produce statistically significant results—false positives. Afterward, when we go to look at those significant studies, what is the probability that each one is a false positive? Not 5 percent but 100%!

That scenario also illustrates a point that I made earlier. The true picture becomes more evident after repeated experimentation. Given the pattern of results that are predominantly not significant, it is unlikely that an effect exists in the population.

Type II Error: False Negatives

When you perform a hypothesis test and your p-value is greater than your significance level, your results are not statistically significant. That’s disappointing because your sample provides insufficient evidence for concluding that the effect you’re studying exists in the population. However, there is a chance that the effect is present in the population even though the test results don’t support it. If that’s the case, you’ve just experienced a Type II error . The probability of making a Type II error is known as beta (β).

What causes Type II errors? Whereas Type I errors are caused by one thing, sample error, there are a host of possible reasons for Type II errors—small effect sizes, small sample sizes, and high data variability. Furthermore, unlike Type I errors, you can’t set the Type II error rate for your analysis. Instead, the best that you can do is estimate it before you begin your study by approximating properties of the alternative hypothesis that you’re studying. When you do this type of estimation, it’s called power analysis.

To estimate the Type II error rate, you create a hypothetical probability distribution that represents the properties of a true alternative hypothesis. However, when you’re performing a hypothesis test, you typically don’t know which hypothesis is true, much less the specific properties of the distribution for the alternative hypothesis. Consequently, the true Type II error rate is usually unknown!

Type II errors and the power of the analysis

The Type II error rate (beta) is the probability of a false negative. Therefore, the inverse of Type II errors is the probability of correctly detecting an effect. Statisticians refer to this concept as the power of a hypothesis test. Consequently, 1 – β = the statistical power. Analysts typically estimate power rather than beta directly.

If you read my post about power and sample size analysis , you know that the three factors that affect power are sample size, variability in the population, and the effect size. As you design your experiment, you can enter estimates of these three factors into statistical software and it calculates the estimated power for your test.

Suppose you perform a power analysis for an upcoming study and calculate an estimated power of 90%. For this study, the estimated Type II error rate is 10% (1 – 0.9). Keep in mind that variability and effect size are based on estimates and guesses. Consequently, power and the Type II error rate are just estimates rather than something you set directly. These estimates are only as good as the inputs into your power analysis.

Low variability and larger effect sizes decrease the Type II error rate, which increases the statistical power. However, researchers usually have less control over those aspects of a hypothesis test. Typically, researchers have the most control over sample size, making it the critical way to manage your Type II error rate. Holding everything else constant, increasing the sample size reduces the Type II error rate and increases power.

Learn more about Power in Statistics .

Graphing Type I and Type II Errors

The graph below illustrates the two types of errors using two sampling distributions. The critical region line represents the point at which you reject or fail to reject the null hypothesis. Of course, when you perform the hypothesis test, you don’t know which hypothesis is correct. And, the properties of the distribution for the alternative hypothesis are usually unknown. However, use this graph to understand the general nature of these errors and how they are related.

The distribution on the left represents the null hypothesis. If the null hypothesis is true, you only need to worry about Type I errors, which is the shaded portion of the null hypothesis distribution. The rest of the null distribution represents the correct decision of failing to reject the null.

On the other hand, if the alternative hypothesis is true, you need to worry about Type II errors. The shaded region on the alternative hypothesis distribution represents the Type II error rate. The rest of the alternative distribution represents the probability of correctly detecting an effect—power.

Moving the critical value line is equivalent to changing the significance level. If you move the line to the left, you’re increasing the significance level (e.g., α 0.05 to 0.10). Holding everything else constant, this adjustment increases the Type I error rate while reducing the Type II error rate. Moving the line to the right reduces the significance level (e.g., α 0.05 to 0.01), which decreases the Type I error rate but increases the type II error rate.

Is One Error Worse Than the Other?

As you’ve seen, the nature of the two types of error, their causes, and the certainty of their rates of occurrence are all very different.

A common question is whether one type of error is worse than the other? Statisticians designed hypothesis tests to control Type I errors while Type II errors are much less defined. Consequently, many statisticians state that it is better to fail to detect an effect when it exists than it is to conclude an effect exists when it doesn’t. That is to say, there is a tendency to assume that Type I errors are worse.

However, reality is more complex than that. You should carefully consider the consequences of each type of error for your specific test.

Suppose you are assessing the strength of a new jet engine part that is under consideration. Peoples lives are riding on the part’s strength. A false negative in this scenario merely means that the part is strong enough but the test fails to detect it. This situation does not put anyone’s life at risk. On the other hand, Type I errors are worse in this situation because they indicate the part is strong enough when it is not.

Now suppose that the jet engine part is already in use but there are concerns about it failing. In this case, you want the test to be more sensitive to detecting problems even at the risk of false positives. Type II errors are worse in this scenario because the test fails to recognize the problem and leaves these problematic parts in use for longer.

Using hypothesis tests effectively requires that you understand their error rates. By setting the significance level and estimating your test’s power, you can manage both error rates so they meet your requirements.

The error rates in this post are all for individual tests. If you need to perform multiple comparisons, such as comparing group means in ANOVA, you’ll need to use post hoc tests to control the experiment-wise error rate  or use the Bonferroni correction .

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Reader Interactions

June 4, 2024 at 2:04 pm

Very informative.

June 9, 2023 at 9:54 am

Hi Jim- I just signed up for your newsletter and this is my first question to you. I am not a statistician but work with them in my professional life as a QC consultant in biopharmaceutical development. I have a question about Type I and Type II errors in the realm of equivalence testing using two one sided difference testing (TOST). In a recent 2020 publication that I co-authored with a statistician, we stated that the probability of concluding non-equivalence when that is the truth, (which is the opposite of power, the probability of concluding equivalence when it is correct) is 1-2*alpha. This made sense to me because one uses a 90% confidence interval on a mean to evaluate whether the result is within established equivalence bounds with an alpha set to 0.05. However, it appears that specificity (1-alpha) is always the case as is power always being 1-beta. For equivalence testing the latter is 1-2*beta/2 but for specificity it stays as 1-alpha because only one of the null hypotheses in a two-sided test can fail at one time. I still see 1-2*alpha as making more sense as we show in Figure 3 of our paper which shows the white space under the distribution of the alternative hypothesis as 1-2 alpha. The paper can be downloaded as open access here if that would make my question more clear. https://bioprocessingjournal.com/index.php/article-downloads/890-vol-19-open-access-2020-defining-therapeutic-window-for-viral-vectors-a-statistical-framework-to-improve-consistency-in-assigning-product-dose-values I have consulted with other statistical colleagues and cannot get consensus so I would love your opinion and explanation! Thanks in advance!

June 10, 2023 at 1:00 am

Let me preface my response by saying that I’m not an expert in equivalence testing. But here’s my best guess about your question.

The alpha is for each of the hypothesis tests. Each one has a type I error rate of 0.05. Or, as you say, a specificity of 1-alpha. However, there are two tests so we need to consider the family-wise error rate. The formula is the following:

FWER = 1 – (1 – α)^N

Where N is the number of hypothesis tests.

For two tests, there’s a family-wise error rate of 0.0975. Or a family-wise specificity of 0.9025.

However, I believe they use 90% CI for a different reason (although it’s a very close match to the family-wise error rate). The 90% CI provides consistent results with the two one-side 95% tests. In other words, if the 90% CI is within the equivalency bounds, then the two tests will be significant. If the CI extends above the upper bound, the corresponding test won’t be significant. Etc.

However, using either rational, I’d say the overall type I error rate is about 0.1.

I hope that answers your question. And, again, I’m not an expert in this particular test.

July 18, 2022 at 5:15 am

Thank you for your valuable content. I have a question regarding correcting for multiple tests. My question is: for exactly how many tests should I correct in the scenario below?

Background: I’m testing for differences between groups A (patient group) and B (control group) in variable X. Variable X is a biological variable present in the body’s left and right side. Variable Y is a questionnaire for group A.

Step 1. Is there a significant difference within groups in the weight of left and right variable X? (I will conduct two paired sample t-tests)


If I find a significant difference in step 1, then I will conduct steps 2A and 2B. However, if I don’t find a significant difference in step 1, then I will only conduct step 2C.

Step 2A. Is there a significant difference between groups in left variable X? (I will conduct one independent sample t-test) Step 2B. Is there a significant difference between groups in right variable X? (I will conduct one independent sample t-test)

Step 2C. Is there a significant difference between groups in total variable X (left + right variable X)? (I will conduct one independent sample t-test)

If I find a significant difference in step 1, then I will conduct with steps 3A and 3B. However, if I don’t find a significant difference in step 1, then I will only conduct step 3C.

Step 3A. Is there a significant correlation between left variable X in group A and variable Y? (I will conduct Pearson correlation) Step 3B. Is there a significant correlation between right variable X in group A and variable Y? (I will conduct Pearson correlation)

Step 3C. Is there a significant correlation between total variable X in group A and variable Y? (I will conduct a Pearson correlation)

Regards, De

January 2, 2021 at 1:57 pm

I should say that being a budding statistician, this site seems to be pretty reliable. I have few doubts in here. It would be great if you can clarify it:

“A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. ”

My understanding : When we say that the significance level is 0.05 then it means we are taking 5% risk to support alternate hypothesis even though there is no difference ?( I think i am not allowed to say Null is true, because null is assumed to be true/ Right)

January 2, 2021 at 6:48 pm

The sentence as I write it is correct. Here’s a simple way to understand it. Imagine you’re conducting a computer simulation where you control the population parameters and have the computer draw random samples from the populations that you define. Now, imagine you draw samples from two populations where the means and standard deviations are equal. You know this for a fact because you set the parameters yourself. Then you conduct a series of 2-sample t-tests.

In this example, you know the null hypothesis is correct. However, thanks to random sampling error, some proportion of the t-tests will have statistically significant results (i.e., false positives or Type I errors). The proportion of false positives will equal your significance level over the long run.

Of course, in real-world experiments, you never know for sure whether the null is true or not. However, given the properties of the hypothesis, you do know what proportion of tests will give you a false positive IF the null is true–and that’s the significance level.

I’m thinking through the wording of how you wrote it and I believe it is equivalent to what I wrote. If there is no difference (the null is true), then you have a 5% chance of incorrectly supporting the alternative. And, again, you’re correct that in the real world you don’t know for sure whether the null is true. But, you can still know the false positive (Type I) error rate. For more information about that property, read my post about how hypothesis tests work .

July 9, 2018 at 11:43 am

I like to use the analogy of a trial. The null hypothesis is that the defendant is innocent. A type I error would be convicting an innocent person and a type II error would be acquitting a guilty one. I like to think that our system makes a type I error very unlikely with the trade off being that a type II error is greater.

July 9, 2018 at 12:03 pm

Hi Doug, I think that is an excellent analogy on multiple levels. As you mention, a trial would set a high bar for the significance level by choosing a very low value for alpha. This helps prevent innocent people from being convicted (Type I error) but does increase the probability of allowing the guilty to go free (Type II error). I often refer to the significant level as a evidentiary standard with this legalistic analogy in mind.

Additionally, in the justice system in the U.S., there is a presumption of innocence and the prosecutor must present sufficient evidence to prove that the defendant is guilty. That’s just like in a hypothesis test where the assumption is that the null hypothesis is true and your sample must contain sufficient evidence to be able to reject the null hypothesis and suggest that the effect exists in the population.

This analogy even works for the similarities behind the phrases “Not guilty” and “Fail to reject the null hypothesis.” In both cases, you aren’t proving innocence or that the null hypothesis is true. When a defendant is “not guilty” it might be that the evidence was insufficient to convince the jury. In a hypothesis test, when you fail to reject the null hypothesis, it’s possible that an effect exists in the population but you have insufficient evidence to detect it. Perhaps the effect exists but the sample size or effect size is too small, or the variability might be too high.

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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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• v.18(2); Jul-Dec 2009

Hypothesis testing, type I and type II errors

Amitav banerjee.

Department of Community Medicine, D. Y. Patil Medical College, Pune, India

U. B. Chitnis

S. l. jadhav, j. s. bhawalkar, s. chaudhury.

1 Department of Psychiatry, RINPAS, Kanke, Ranchi, India

Hypothesis testing is an important activity of empirical research and evidence-based medicine. A well worked up hypothesis is half the answer to the research question. For this, both knowledge of the subject derived from extensive review of the literature and working knowledge of basic statistical concepts are desirable. The present paper discusses the methods of working up a good hypothesis and statistical concepts of hypothesis testing.

Karl Popper is probably the most influential philosopher of science in the 20 th century (Wulff et al ., 1986). Many scientists, even those who do not usually read books on philosophy, are acquainted with the basic principles of his views on science. The popularity of Popper’s philosophy is due partly to the fact that it has been well explained in simple terms by, among others, the Nobel Prize winner Peter Medawar (Medawar, 1969). Popper makes the very important point that empirical scientists (those who stress on observations only as the starting point of research) put the cart in front of the horse when they claim that science proceeds from observation to theory, since there is no such thing as a pure observation which does not depend on theory. Popper states, “… the belief that we can start with pure observation alone, without anything in the nature of a theory, is absurd: As may be illustrated by the story of the man who dedicated his life to natural science, wrote down everything he could observe, and bequeathed his ‘priceless’ collection of observations to the Royal Society to be used as inductive (empirical) evidence.

STARTING POINT OF RESEARCH: HYPOTHESIS OR OBSERVATION?

The first step in the scientific process is not observation but the generation of a hypothesis which may then be tested critically by observations and experiments. Popper also makes the important claim that the goal of the scientist’s efforts is not the verification but the falsification of the initial hypothesis. It is logically impossible to verify the truth of a general law by repeated observations, but, at least in principle, it is possible to falsify such a law by a single observation. Repeated observations of white swans did not prove that all swans are white, but the observation of a single black swan sufficed to falsify that general statement (Popper, 1976).

CHARACTERISTICS OF A GOOD HYPOTHESIS

A good hypothesis must be based on a good research question. It should be simple, specific and stated in advance (Hulley et al ., 2001).

Hypothesis should be simple

A simple hypothesis contains one predictor and one outcome variable, e.g. positive family history of schizophrenia increases the risk of developing the condition in first-degree relatives. Here the single predictor variable is positive family history of schizophrenia and the outcome variable is schizophrenia. A complex hypothesis contains more than one predictor variable or more than one outcome variable, e.g., a positive family history and stressful life events are associated with an increased incidence of Alzheimer’s disease. Here there are 2 predictor variables, i.e., positive family history and stressful life events, while one outcome variable, i.e., Alzheimer’s disease. Complex hypothesis like this cannot be easily tested with a single statistical test and should always be separated into 2 or more simple hypotheses.

Hypothesis should be specific

A specific hypothesis leaves no ambiguity about the subjects and variables, or about how the test of statistical significance will be applied. It uses concise operational definitions that summarize the nature and source of the subjects and the approach to measuring variables (History of medication with tranquilizers, as measured by review of medical store records and physicians’ prescriptions in the past year, is more common in patients who attempted suicides than in controls hospitalized for other conditions). This is a long-winded sentence, but it explicitly states the nature of predictor and outcome variables, how they will be measured and the research hypothesis. Often these details may be included in the study proposal and may not be stated in the research hypothesis. However, they should be clear in the mind of the investigator while conceptualizing the study.

Hypothesis should be stated in advance

The hypothesis must be stated in writing during the proposal state. This will help to keep the research effort focused on the primary objective and create a stronger basis for interpreting the study’s results as compared to a hypothesis that emerges as a result of inspecting the data. The habit of post hoc hypothesis testing (common among researchers) is nothing but using third-degree methods on the data (data dredging), to yield at least something significant. This leads to overrating the occasional chance associations in the study.

TYPES OF HYPOTHESES

For the purpose of testing statistical significance, hypotheses are classified by the way they describe the expected difference between the study groups.

Null and alternative hypotheses

The null hypothesis states that there is no association between the predictor and outcome variables in the population (There is no difference between tranquilizer habits of patients with attempted suicides and those of age- and sex- matched “control” patients hospitalized for other diagnoses). The null hypothesis is the formal basis for testing statistical significance. By starting with the proposition that there is no association, statistical tests can estimate the probability that an observed association could be due to chance.

The proposition that there is an association — that patients with attempted suicides will report different tranquilizer habits from those of the controls — is called the alternative hypothesis. The alternative hypothesis cannot be tested directly; it is accepted by exclusion if the test of statistical significance rejects the null hypothesis.

One- and two-tailed alternative hypotheses

A one-tailed (or one-sided) hypothesis specifies the direction of the association between the predictor and outcome variables. The prediction that patients of attempted suicides will have a higher rate of use of tranquilizers than control patients is a one-tailed hypothesis. A two-tailed hypothesis states only that an association exists; it does not specify the direction. The prediction that patients with attempted suicides will have a different rate of tranquilizer use — either higher or lower than control patients — is a two-tailed hypothesis. (The word tails refers to the tail ends of the statistical distribution such as the familiar bell-shaped normal curve that is used to test a hypothesis. One tail represents a positive effect or association; the other, a negative effect.) A one-tailed hypothesis has the statistical advantage of permitting a smaller sample size as compared to that permissible by a two-tailed hypothesis. Unfortunately, one-tailed hypotheses are not always appropriate; in fact, some investigators believe that they should never be used. However, they are appropriate when only one direction for the association is important or biologically meaningful. An example is the one-sided hypothesis that a drug has a greater frequency of side effects than a placebo; the possibility that the drug has fewer side effects than the placebo is not worth testing. Whatever strategy is used, it should be stated in advance; otherwise, it would lack statistical rigor. Data dredging after it has been collected and post hoc deciding to change over to one-tailed hypothesis testing to reduce the sample size and P value are indicative of lack of scientific integrity.

STATISTICAL PRINCIPLES OF HYPOTHESIS TESTING

A hypothesis (for example, Tamiflu [oseltamivir], drug of choice in H1N1 influenza, is associated with an increased incidence of acute psychotic manifestations) is either true or false in the real world. Because the investigator cannot study all people who are at risk, he must test the hypothesis in a sample of that target population. No matter how many data a researcher collects, he can never absolutely prove (or disprove) his hypothesis. There will always be a need to draw inferences about phenomena in the population from events observed in the sample (Hulley et al ., 2001). In some ways, the investigator’s problem is similar to that faced by a judge judging a defendant [ Table 1 ]. The absolute truth whether the defendant committed the crime cannot be determined. Instead, the judge begins by presuming innocence — the defendant did not commit the crime. The judge must decide whether there is sufficient evidence to reject the presumed innocence of the defendant; the standard is known as beyond a reasonable doubt. A judge can err, however, by convicting a defendant who is innocent, or by failing to convict one who is actually guilty. In similar fashion, the investigator starts by presuming the null hypothesis, or no association between the predictor and outcome variables in the population. Based on the data collected in his sample, the investigator uses statistical tests to determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis that there is an association in the population. The standard for these tests is shown as the level of statistical significance.

The analogy between judge’s decisions and statistical tests

TYPE I (ALSO KNOWN AS ‘α’) AND TYPE II (ALSO KNOWN AS ‘β’)ERRORS

Just like a judge’s conclusion, an investigator’s conclusion may be wrong. Sometimes, by chance alone, a sample is not representative of the population. Thus the results in the sample do not reflect reality in the population, and the random error leads to an erroneous inference. A type I error (false-positive) occurs if an investigator rejects a null hypothesis that is actually true in the population; a type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is actually false in the population. Although type I and type II errors can never be avoided entirely, the investigator can reduce their likelihood by increasing the sample size (the larger the sample, the lesser is the likelihood that it will differ substantially from the population).

False-positive and false-negative results can also occur because of bias (observer, instrument, recall, etc.). (Errors due to bias, however, are not referred to as type I and type II errors.) Such errors are troublesome, since they may be difficult to detect and cannot usually be quantified.

EFFECT SIZE

The likelihood that a study will be able to detect an association between a predictor variable and an outcome variable depends, of course, on the actual magnitude of that association in the target population. If it is large (such as 90% increase in the incidence of psychosis in people who are on Tamiflu), it will be easy to detect in the sample. Conversely, if the size of the association is small (such as 2% increase in psychosis), it will be difficult to detect in the sample. Unfortunately, the investigator often does not know the actual magnitude of the association — one of the purposes of the study is to estimate it. Instead, the investigator must choose the size of the association that he would like to be able to detect in the sample. This quantity is known as the effect size. Selecting an appropriate effect size is the most difficult aspect of sample size planning. Sometimes, the investigator can use data from other studies or pilot tests to make an informed guess about a reasonable effect size. When there are no data with which to estimate it, he can choose the smallest effect size that would be clinically meaningful, for example, a 10% increase in the incidence of psychosis. Of course, from the public health point of view, even a 1% increase in psychosis incidence would be important. Thus the choice of the effect size is always somewhat arbitrary, and considerations of feasibility are often paramount. When the number of available subjects is limited, the investigator may have to work backward to determine whether the effect size that his study will be able to detect with that number of subjects is reasonable.

α,β,AND POWER

After a study is completed, the investigator uses statistical tests to try to reject the null hypothesis in favor of its alternative (much in the same way that a prosecuting attorney tries to convince a judge to reject innocence in favor of guilt). Depending on whether the null hypothesis is true or false in the target population, and assuming that the study is free of bias, 4 situations are possible, as shown in Table 2 below. In 2 of these, the findings in the sample and reality in the population are concordant, and the investigator’s inference will be correct. In the other 2 situations, either a type I (α) or a type II (β) error has been made, and the inference will be incorrect.

Truth in the population versus the results in the study sample: The four possibilities

The investigator establishes the maximum chance of making type I and type II errors in advance of the study. The probability of committing a type I error (rejecting the null hypothesis when it is actually true) is called α (alpha) the other name for this is the level of statistical significance.

If a study of Tamiflu and psychosis is designed with α = 0.05, for example, then the investigator has set 5% as the maximum chance of incorrectly rejecting the null hypothesis (and erroneously inferring that use of Tamiflu and psychosis incidence are associated in the population). This is the level of reasonable doubt that the investigator is willing to accept when he uses statistical tests to analyze the data after the study is completed.

The probability of making a type II error (failing to reject the null hypothesis when it is actually false) is called β (beta). The quantity (1 - β) is called power, the probability of observing an effect in the sample (if one), of a specified effect size or greater exists in the population.

If β is set at 0.10, then the investigator has decided that he is willing to accept a 10% chance of missing an association of a given effect size between Tamiflu and psychosis. This represents a power of 0.90, i.e., a 90% chance of finding an association of that size. For example, suppose that there really would be a 30% increase in psychosis incidence if the entire population took Tamiflu. Then 90 times out of 100, the investigator would observe an effect of that size or larger in his study. This does not mean, however, that the investigator will be absolutely unable to detect a smaller effect; just that he will have less than 90% likelihood of doing so.

Ideally alpha and beta errors would be set at zero, eliminating the possibility of false-positive and false-negative results. In practice they are made as small as possible. Reducing them, however, usually requires increasing the sample size. Sample size planning aims at choosing a sufficient number of subjects to keep alpha and beta at acceptably low levels without making the study unnecessarily expensive or difficult.

Many studies s et al pha at 0.05 and beta at 0.20 (a power of 0.80). These are somewhat arbitrary values, and others are sometimes used; the conventional range for alpha is between 0.01 and 0.10; and for beta, between 0.05 and 0.20. In general the investigator should choose a low value of alpha when the research question makes it particularly important to avoid a type I (false-positive) error, and he should choose a low value of beta when it is especially important to avoid a type II error.

The null hypothesis acts like a punching bag: It is assumed to be true in order to shadowbox it into false with a statistical test. When the data are analyzed, such tests determine the P value, the probability of obtaining the study results by chance if the null hypothesis is true. The null hypothesis is rejected in favor of the alternative hypothesis if the P value is less than alpha, the predetermined level of statistical significance (Daniel, 2000). “Nonsignificant” results — those with P value greater than alpha — do not imply that there is no association in the population; they only mean that the association observed in the sample is small compared with what could have occurred by chance alone. For example, an investigator might find that men with family history of mental illness were twice as likely to develop schizophrenia as those with no family history, but with a P value of 0.09. This means that even if family history and schizophrenia were not associated in the population, there was a 9% chance of finding such an association due to random error in the sample. If the investigator had set the significance level at 0.05, he would have to conclude that the association in the sample was “not statistically significant.” It might be tempting for the investigator to change his mind about the level of statistical significance ex post facto and report the results “showed statistical significance at P < 10”. A better choice would be to report that the “results, although suggestive of an association, did not achieve statistical significance ( P = .09)”. This solution acknowledges that statistical significance is not an “all or none” situation.

Hypothesis testing is the sheet anchor of empirical research and in the rapidly emerging practice of evidence-based medicine. However, empirical research and, ipso facto, hypothesis testing have their limits. The empirical approach to research cannot eliminate uncertainty completely. At the best, it can quantify uncertainty. This uncertainty can be of 2 types: Type I error (falsely rejecting a null hypothesis) and type II error (falsely accepting a null hypothesis). The acceptable magnitudes of type I and type II errors are set in advance and are important for sample size calculations. Another important point to remember is that we cannot ‘prove’ or ‘disprove’ anything by hypothesis testing and statistical tests. We can only knock down or reject the null hypothesis and by default accept the alternative hypothesis. If we fail to reject the null hypothesis, we accept it by default.

Source of Support: Nil

Conflict of Interest: None declared.

• Daniel W. W. In: Biostatistics. 7th ed. New York: John Wiley and Sons, Inc; 2002. Hypothesis testing; pp. 204–294. [ Google Scholar ]
• Hulley S. B, Cummings S. R, Browner W. S, Grady D, Hearst N, Newman T. B. 2nd ed. Philadelphia: Lippincott Williams and Wilkins; 2001. Getting ready to estimate sample size: Hypothesis and underlying principles In: Designing Clinical Research-An epidemiologic approach; pp. 51–63. [ Google Scholar ]
• Medawar P. B. Philadelphia: American Philosophical Society; 1969. Induction and intuition in scientific thought. [ Google Scholar ]
• Popper K. Unended Quest. An Intellectual Autobiography. Fontana Collins; p. 42. [ Google Scholar ]
• Wulff H. R, Pedersen S. A, Rosenberg R. Oxford: Blackwell Scientific Publicatons; Empirism and Realism: A philosophical problem. In: Philosophy of Medicine. [ Google Scholar ]

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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 type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one fails to reject a null hypothesis that is actually false. A type II error produces a false negative, also known as an error of omission.

For example, a test for a disease may report a negative result when the patient is infected. This is a type II error because we accept the conclusion of the test as negative, even though it is incorrect.

A type II error can be contrasted with a type I error , where researchers incorrectly reject a true null hypothesis. A type II error happens when one fails to reject a null hypothesis that is actually false. A type I error produces a false positive.

Key Takeaways

• A type II error is defined as the probability of incorrectly failing to reject the null hypothesis, when in fact it is not applicable to the entire population.
• A type II error is essentially a false negative.
• A type II error can be made less likely by making more stringent criteria for rejecting a null hypothesis, although this increases the chances of a false positive.
• The sample size, the true population size, and the preset alpha level influence the magnitude of risk of an error.
• Analysts need to weigh the likelihood and impact of type II errors with type I errors.

Understanding a Type II Error

A type II error, also known as an error of the second kind or a beta error, confirms an idea that should have been rejected—for instance, claiming that two observances are the same, despite them being different. A type II error does not reject the null hypothesis, even though the alternative hypothesis is actually correct. In other words, a false finding is accepted as true.

The likelihood of a type II error can be reduced by making more stringent criteria for rejecting a null hypothesis (H 0 ). For example, if an analyst is considering anything that falls within the +/- bounds of a 95% confidence interval as statistically insignificant (a negative result), then by decreasing that tolerance to +/- 90%, and subsequently narrowing the bounds, you will get fewer negative results, and thus reduce the chances of a false negative.

Taking these steps, however, tends to increase the chances of encountering a type I error—a false-positive result. When conducting a hypothesis test, the probability or risk of making a type I error or type II error should be considered.

The steps taken to reduce the chances of encountering a type II error tend to increase the probability of a type I error.

Type I Errors vs. Type II Errors

The difference between a type II error and a type I error is that a type I error rejects the null hypothesis when it is true (i.e., a false positive). The probability of committing a type I error is equal to the level of significance that was set for the hypothesis test. Therefore, if the level of significance is 0.05, there is a 5% chance that a type I error may occur.

The probability of committing a type II error is equal to one minus the power of the test, also known as beta. The power of the test could be increased by increasing the sample size, which decreases the risk of committing a type II error.

Some statistical literature will include overall significance level and type II error risk as part of the report’s analysis. For example, a 2021 meta-analysis of exosome in the treatment of spinal cord injury recorded an overall significance level of 0.05 and a type II error risk of 0.1.

Example of a Type II Error

Assume a biotechnology company wants to compare how effective two of its drugs are for treating diabetes. The null hypothesis states the two medications are equally effective. A null hypothesis, H 0 , is the claim that the company hopes to reject using the one-tailed test . The alternative hypothesis, H a , states that the two drugs are not equally effective. The alternative hypothesis, H a , is the state of nature that is supported by rejecting the null hypothesis.

The biotech company implements a large clinical trial of 3,000 patients with diabetes to compare the treatments. The company randomly divides the 3,000 patients into two equally sized groups, giving one group one of the treatments and the other group the other treatment. It selects a significance level of 0.05, which indicates it is willing to accept a 5% chance it may reject the null hypothesis when it is true or a 5% chance of committing a type I error.

Assume the beta is calculated to be 0.025, or 2.5%. Therefore, the probability of committing a type II error is 97.5%. If the two medications are not equal, the null hypothesis should be rejected. However, if the biotech company does not reject the null hypothesis when the drugs are not equally effective, then a type II error occurs.

What Is the Difference Between Type I and Type II Errors?

A type I error occurs if a null hypothesis is rejected that is actually true in the population. This type of error is representative of a false positive. Alternatively, a type II error occurs if a null hypothesis is not rejected that is actually false in the population. This type of error is representative of a false negative.

What Causes Type II Errors?

A type II error is commonly caused if the statistical power of a test is too low. The higher the statistical power, the greater the chance of avoiding an error. It’s often recommended that the statistical power should be set to at least 80% prior to conducting any testing.

What Factors Influence the Magnitude of Risk for Type II Errors?

As the sample size of a study increases, the risk of type II errors should decrease. As the true population effect size increases, the probability of a type II error should also decrease. Finally, the preset alpha level set by the research influences the magnitude of risk. As the alpha level set decreases, the risk of a type II error increases.

How Can a Type II Error Be Minimized?

It is not possible to fully prevent committing a type II error, but the risk can be minimized by increasing the sample size. However, doing so will also increase the risk of committing a type I error instead.

In statistics, a type II error results in a false negative—meaning that there is a finding, but it has been missed in the analysis (or that the null hypothesis is not rejected when it ought to have been). A type II error can occur if there is not enough power in statistical tests, often resulting from sample sizes that are too small. Increasing the sample size can help reduce the chances of committing a type II error.

Type II errors can be contrasted with type I errors, which are false positives.

Europe PMC. “ A Meta-Analysis of Exosome in the Treatment of Spinal Cord Injury .”

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Type II Error

"False negative" error

What is a Type II Error?

In statistical hypothesis testing, a type II error is a situation wherein a hypothesis test fails to reject the null hypothesis that is false. In other words, it causes the user to erroneously not reject the false null hypothesis because the test lacks the statistical power to detect sufficient evidence for the alternative hypothesis. The type II error is also known as a false negative.

The type II error has an inverse relationship with the power of a statistical test. This means that the higher power of a statistical test, the lower the probability of committing a type II error. The rate of a type II error (i.e., the probability of a type II error) is measured by beta (β) while the statistical power is measured by 1- β.

How to Avoid the Type II Error?

Similar to the type I error, it is not possible to completely eliminate the type II error from a hypothesis test . The only available option is to minimize the probability of committing this type of statistical error. Since a type II error is closely related to the power of a statistical test, the probability of the occurrence of the error can be minimized by increasing the power of the test.

1. Increase the sample size

One of the simplest methods to increase the power of the test is to increase the sample size used in a test. The sample size primarily determines the amount of sampling error, which translates into the ability to detect the differences in a hypothesis test. A larger sample size increases the chances to capture the differences in the statistical tests, as well as raises the power of a test.

2. Increase the significance level

Another method is to choose a higher level of significance . For instance, a researcher may choose a significance level of 0.10 instead of the commonly acceptable 0.05 level. The higher significance level implies a higher probability of rejecting the null hypothesis when it is true.

The larger probability of rejecting the null hypothesis decreases the probability of committing a type II error while the probability of committing a type I error increases. Thus, the user should always assess the impact of type I and type II errors on their decision and determine the appropriate level of statistical significance.

Practical Example

Sam is a financial analyst . He runs a hypothesis test to discover whether there is a difference in the average price changes for large-cap and small-cap stocks .

In the test, Sam assumes as the null hypothesis that there is no difference in the average price changes between large-cap and small-cap stocks. Thus, his alternative hypothesis states that a difference between the average price changes does exist.

For the significance level, Sam chooses 5%. This means that there is a 5% probability that his test will reject the null hypothesis when it is actually true.

If Sam’s test incurs a type II error, then the results of the test will indicate that there is no difference in the average price changes between large-cap and small-cap stocks. However, in reality, a difference in the average price changes does exist.

More Resources

CFI is the official provider of the global Business Intelligence & Data Analyst (BIDA)®  certification program, designed to help anyone become a world-class financial analyst. To keep learning and advancing your career, the additional CFI resources below will be useful:

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The Difference Between Type I and Type II Errors in Hypothesis Testing

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The statistical practice of hypothesis testing is widespread not only in statistics but also throughout the natural and social sciences. When we conduct a hypothesis test there a couple of things that could go wrong. There are two kinds of errors, which by design cannot be avoided, and we must be aware that these errors exist. The errors are given the quite pedestrian names of type I and type II errors. What are type I and type II errors, and how we distinguish between them? Briefly:

• Type I errors happen when we reject a true null hypothesis
• Type II errors happen when we fail to reject a false null hypothesis

We will explore more background behind these types of errors with the goal of understanding these statements.

Hypothesis Testing

The process of hypothesis testing can seem to be quite varied with a multitude of test statistics. But the general process is the same. Hypothesis testing involves the statement of a null hypothesis and the selection of a level of significance . The null hypothesis is either true or false and represents the default claim for a treatment or procedure. For example, when examining the effectiveness of a drug, the null hypothesis would be that the drug has no effect on a disease.

After formulating the null hypothesis and choosing a level of significance, we acquire data through observation. Statistical calculations tell us whether or not we should reject the null hypothesis.

In an ideal world, we would always reject the null hypothesis when it is false, and we would not reject the null hypothesis when it is indeed true. But there are two other scenarios that are possible, each of which will result in an error.

Type I Error

The first kind of error that is possible involves the rejection of a null hypothesis that is actually true. This kind of error is called a type I error and is sometimes called an error of the first kind.

Type I errors are equivalent to false positives. Let’s go back to the example of a drug being used to treat a disease. If we reject the null hypothesis in this situation, then our claim is that the drug does, in fact, have some effect on a disease. But if the null hypothesis is true, then, in reality, the drug does not combat the disease at all. The drug is falsely claimed to have a positive effect on a disease.

Type I errors can be controlled. The value of alpha, which is related to the level of significance that we selected has a direct bearing on type I errors. Alpha is the maximum probability that we have a type I error. For a 95% confidence level, the value of alpha is 0.05. This means that there is a 5% probability that we will reject a true null hypothesis. In the long run, one out of every twenty hypothesis tests that we perform at this level will result in a type I error.

Type II Error

The other kind of error that is possible occurs when we do not reject a null hypothesis that is false. This sort of error is called a type II error and is also referred to as an error of the second kind.

Type II errors are equivalent to false negatives. If we think back again to the scenario in which we are testing a drug, what would a type II error look like? A type II error would occur if we accepted that the drug had no effect on a disease, but in reality, it did.

The probability of a type II error is given by the Greek letter beta. This number is related to the power or sensitivity of the hypothesis test, denoted by 1 – beta.

How to Avoid Errors

Type I and type II errors are part of the process of hypothesis testing. Although the errors cannot be completely eliminated, we can minimize one type of error.

Typically when we try to decrease the probability one type of error, the probability for the other type increases. We could decrease the value of alpha from 0.05 to 0.01, corresponding to a 99% level of confidence . However, if everything else remains the same, then the probability of a type II error will nearly always increase.

Many times the real world application of our hypothesis test will determine if we are more accepting of type I or type II errors. This will then be used when we design our statistical experiment.

• Type I and Type II Errors in Statistics
• What Level of Alpha Determines Statistical Significance?
• What Is the Difference Between Alpha and P-Values?
• The Runs Test for Random Sequences
• What 'Fail to Reject' Means in a Hypothesis Test
• How to Construct a Confidence Interval for a Population Proportion
• How to Find Critical Values with a Chi-Square Table
• Null Hypothesis and Alternative Hypothesis
• An Example of a Hypothesis Test
• What Is ANOVA?
• Degrees of Freedom for Independence of Variables in Two-Way Table
• How to Find Degrees of Freedom in Statistics
• Confidence Interval for the Difference of Two Population Proportions
• An Example of Chi-Square Test for a Multinomial Experiment
• Example of a Permutation Test
• How to Calculate the Margin of Error

5. Differences between means: type I and type II errors and power

Large sample standard error of difference between means.

• 3 $\begingroup$ See xkcd.com/882 for an illustrated example of Type I errors in a "real time scenario." Perhaps after reading that you could come up with an analogous example of Type II errors. $\endgroup$ –  whuber ♦ Commented Aug 3, 2014 at 15:26
• 1 $\begingroup$ It is not obvious to me what "real time scenarios" means. Do you mean "real world" perhaps? $\endgroup$ –  Thomas Commented Aug 3, 2014 at 19:36
• 1 $\begingroup$ Yeah Thomas,I meant real world.I have been reading few examples as given below,but what I wanted to know is that the reason why that happens.Does it have to do something with the sample size or kind of sample we take? $\endgroup$ –  maddy Commented Aug 9, 2014 at 15:22
• $\begingroup$ Wikipedia makes this sound way way more complicated than it is, so thanks all answerers for the simpler explanation :) en.wikipedia.org/wiki/Type_I_and_type_II_errors#Example $\endgroup$ –  Nathan majicvr.com Commented Aug 2, 2022 at 2:08

5 Answers 5

A picture is worth a thousand words. Null hypothesis: patient is not pregnant .

Image via Paul Ellis .

• $\begingroup$ ...and a word generates a thousand images. For the benefit of all readers, of all levels of knowledge and understanding, perhaps it would be useful after the picture, to explain how and why it represents examples of type I and type II errors. $\endgroup$ –  Alecos Papadopoulos Commented Aug 3, 2014 at 18:36
• 1 $\begingroup$ @AlecosPapadopoulos And yet explaining humor carries its own problems. The OP has already indicated a familiarity with textbook explanation. $\endgroup$ –  Alexis Commented Aug 3, 2014 at 20:03
• $\begingroup$ So, I guess the null hypothesis in the left picture is "Pregnant" and the doctor falsely asserts it ("false positive"), while in the right picture the null hypothesis is also "Pregnant" and the doctor falsely negates it (false negative)? $\endgroup$ –  Alecos Papadopoulos Commented Aug 3, 2014 at 20:43
• 1 $\begingroup$ Not sure how you get that. The null hypothesis on the left is "not pregnant", and the error is Type I. Har har. The null hypothesis on the right is also "not pregnant" and the error is Type II. Har har. $\endgroup$ –  Alexis Commented Aug 3, 2014 at 21:44
• $\begingroup$ You seem to have mistakenly edited your post to mention that the null hypothesis is "pregnant", whereas it is of course "not pregnant". $\endgroup$ –  amoeba Commented Aug 3, 2014 at 21:55

Let's say you are testing a new drug for some disease. In a test of its effectiveness, a type I error would be to say it has an effect when it does not; a type II error would be to say it has no effect when it does.

Type I error /false positive: is same as rejecting the null when it is true.

Few Examples:

• (With the null hypothesis that the person is innocent), convicting an innocent person
• (With the null hypothesis that e-mail is non-spam), non-spam mail is sent to spam box
• (With the null hypothesis that there is no metal present in passenger's bag), metal detector beeps (detects metal) for a bag with no metal

Type II error /false negative: is similar to accepting the null when it is false.

(With the null hypothesis that the person is innocent), letting a guilty person go free.

(With the null hypothesis that e-mail is non-spam), Spam mail is sent to Inbox

(With the null hypothesis that there is no metal present in passenger's bag), metal detector fails to beep (does not detect metal) for a bag with metal in it

Other beautiful examples in layman's terms are give here:

Is there a way to remember the definitions of Type I and Type II Errors?

• $\begingroup$ In Type II (false negative), shouldn't it be "spam email is sent to inbox"? $\endgroup$ –  Celdor Commented Dec 18, 2017 at 13:01

The boy who cried wolf.

I am not sure who is who in the fable but the basic idea is that the two types of errors (Type I and Type II) are timely ordered in the famous fable.

Type I : villagers ( scientists ) believe there is a wolf ( effect in population ), since the boy cried wolf, but in reality there is not any.

Type II : villagers ( scientists ) believe there is not any wolf ( effect in population ), although the boy cries wolf, and in reality there is a wolf.

Never been a fan of a examples that taught which one is "worse" as (in my opinion) it is dependent on a problem at hand.

Null hypothesis is: "Today is not my friends birthday."

• Type I error: My friend does not have birthday today but I will wish her happy birthday.
• Type II error: My friend has birthday today but I don't wish her happy birthday.

• 1 $\begingroup$ These are not serious answers. $\endgroup$ –  Michael R. Chernick Commented Feb 14, 2018 at 17:35

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Type I Error and Type II Error

Experimental errors in research.

While you might not have heard of Type I error or Type II error, you’re probably familiar with the terms “false positive” and “false negative.”

This article is a part of the guide:

• Null Hypothesis
• Research Hypothesis
• Defining a Research Problem
• Selecting Method

Browse Full Outline

• 1 Scientific Method
• 2.1.1 Null Hypothesis
• 2.1.2 Research Hypothesis
• 2.2 Prediction
• 2.3 Conceptual Variable
• 3.1 Operationalization
• 3.2 Selecting Method
• 3.3 Measurements
• 3.4 Scientific Observation
• 4.1 Empirical Evidence
• 5.1 Generalization
• 5.2 Errors in Conclusion

A common medical example is a patient who takes an HIV test which promises a 99.9% accuracy rate. This means that in 0.1% of cases, or 1 in every 1000, the test gives a 'false positive,' informing a patient that they have the virus when they do not.

On the other hand, the test could also show a false negative reading, giving a person who is actually HIV positive the all-clear. This is why most medical tests require duplicate samples, to stack the odds in our favor. A 1 in 1000 chance of a false positive becomes a 1 in 1 000 000 chance of two false positives, if two tests are taken.

With any scientific process , there is no such thing as total proof or total rejection, whether of test results or of a null hypothesis . Researchers must work instead with probabilities. So even if the probabilities are lowered to 1 in 1000 000, there is still the chance that the results may be wrong.

How Does This Translate to Science?

Type i error.

A Type I error is often referred to as a “false positive” and is the incorrect rejection of the true null hypothesis in favor of the alternative.

In the example above, the null hypothesis refers to the natural state of things or the absence of the tested effect or phenomenon, i.e. stating that the patient is HIV negative. The alternative hypothesis states that the patient is HIV positive. Many medical tests will have the disease they are testing for as the alternative hypothesis and the lack of that disease as the null hypothesis.

A Type I error would thus occur when the patient doesn’t have the virus but the test shows that they do. In other words, the test incorrectly rejects the true null hypothesis that the patient is HIV negative.

Type II Error

A Type II error is the inverse of a Type I error and is the false acceptance of a null hypothesis that is not actually true, i.e. a false negative. A Type II error would entail the test telling the patient they are free of HIV when they are not.

Considering this HIV example, which error type do you think is more acceptable? In other words, would you rather have a test that was more prone to Type I or Type II error? With HIV, it’s likely that the momentary stress of a false positive is better than feeling relieved at a false negative and then failing to take steps to treat the disease. Pregnancy tests, blood tests and any diagnostic tool that has serious consequences for the health of a patient are usually overly sensitive for this reason – it is much better for them to err on the side of a false positive.

But in most fields of science, Type II errors are seen as less serious than Type I errors. With the Type II error, a chance to reject the null hypothesis was lost, and no conclusion is inferred from a non-rejected null. But the Type I error is more serious, because you have wrongly rejected the null hypothesis and ultimately made a claim that is not true. In science, finding a phenomenon where there is none is more egregious than failing to find a phenomenon where there is. Therefore in most research designs, effort is made to err on the side of a false negative.

Replication

This is the key reason why scientific experiments must be replicable.

Even if the highest level of proof is reached, where P < 0.01 ( probability is less than 1%), out of every 100 experiments, there will still be one false result. To a certain extent, duplicate or triplicate samples reduce the chance of error , but may still mask chance if the error -causing variable is present in all samples.

But if other researchers, using the same equipment, replicate the experiment and find that the results are the same, the chances of 5 or 10 experiments giving false results is unbelievably small. This is how science regulates and minimizes the potential for both Type I and Type II errors.

Of course, in certain experiments and medical diagnoses, replication is not always possible, so the possibility of Type I and II errors is always a factor.

One area that is guilty of forgetting about Type I and II errors is in the legal system, where a jury is seldom told that fingerprint and DNA tests may produce false results. There have been many documented failures of justice involving such tests. Today courts will no longer accept these tests alone as proof of guilt, and require other evidence to reduce the possibility of error to acceptable levels.

Type III Errors

Some statisticians are now adopting a third type of error, Type III, which is where the null hypothesis was correctly rejected …but for the wrong reason.

In an experiment, a researcher might postulate a hypothesis and perform research. After analyzing the results statistically, the null hypothesis is rejected.

The problem is that there may indeed be some relationship between the variables , but it’s not the one stated in the hypothesis. There is no error in rejecting the null here, but the error lies in accepting an incorrect alternative hypothesis. Hence a still unknown process may underlie the relationship, and the researchers are none the wiser.

As an example, researchers may be interested to see if there is any difference in two group means, and find that there is one. So they reject the null hypothesis but don’t notice that the difference is actually in the opposite direction to what their results found. Perhaps random chance led them to collect low scores from the group that is in reality higher and high scores from the group that is in reality lower. This is a curious way of being both correct and incorrect at the same time! As you can imagine, Type III errors are rare.

Economist Howard Raiffa gives a different definition for Type III error, one that others have called Type 0: getting the correct answer to an incorrect question.

Additionally, a Type IV error has been defined as incorrectly interpreting a null hypothesis that has been correctly rejected. Type IV error comes down to faulty analysis, bias or fumbling with the data to arrive at incorrect conclusions.

Errors of all types should be taken into account by scientists when conducting research.

Whilst replication can minimize the chances of an inaccurate result, it is no substitute for clear and logical research design, and careful analysis of results.

Many scientists do not accept quasi-experiments , because they are difficult to replicate and analyze, and therefore have a higher risk of being affected by error.

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Type 2 error

What is a type 2 (type ii ) error.

A type 2 error is a statistics term used to refer to a type of error that is made when no conclusive winner is declared between a control and a variation when there actually should be one.

What are the differences between type I and type II errors?

When you’re performing statistical hypothesis testing, there are two types of errors that can occur: type I errors and type II errors .

Type I errors are like “false positives” and happen when you conclude that the variation you’re experimenting with is a “winner” when it’s actually not. Scientifically, this means that you are incorrectly rejecting the true null hypothesis and believe a relationship exists when it actually doesn’t. The chance that you commit type I errors is known as the type I error rate or significance level (p-value)--this number is conventionally and arbitrarily set to 0.05 (5%).

Type II errors are like “false negatives,” an incorrect rejection that a variation in a test has made no statistically significant difference. Statistically speaking, this means you’re mistakenly believing the false null hypothesis and think a relationship doesn’t exist when it actually does. You commit a type 2 error when you don’t believe something that is in fact true.

Why do type 2 errors occur?

Statistical power is the probability that a test will detect a real difference in conversion rate between two or more variations.

The most important factor determinant of the power of a given test is its sample size. The statistical power also depends on the magnitude of the difference in conversion rate you are looking to test.

The smaller the difference you want to detect, the larger the sample size (and the longer the length of time) you require.

Marketers can easily underpower their tests by using a sample size that is too small.

That means that they have a slim chance of detecting true positives, even when a substantial difference in conversion rate actually exists.

In A/B testing , there is a balance to strike between speed of test data and certainty in results accuracy. One way to solve this problem is to run a test for a longer period of time to increase its sample size and hopefully reduce the probability of a type 2 error.

Why is it important to watch out for type 2 errors?

One reason to watch out for type 2 errors is that they can hinder your customer conversion optimization cost in the long run.

If you fail to see the effects of variations in your alternative hypotheses where they actually exist, you may be wasting your time and not taking advantage of opportunities to improve your conversion rate .

Type 2 error example

Let’s consider a hypothetical situation. You are in charge of an ecommerce site and you are testing variations of a landing page. We’ll examine how a type 2 error could negatively impact your company’s revenue.

Your hypothesis test involves changing the “Buy Now” CTA button from green to red will significantly increase conversions compared to your original landing page. You launch your A/B test and wait for the random sample of data to trickle in.

Within 48 hours, you discover that the conversion rate for the green button is identical to the conversion rate for the red button (4.8%) with a 95% level of significance.

Disappointed, you declare the green button a failure and keep the landing page as it is.

The following week, you read an article about how green buttons are boosting conversion rates. You decide to try out your hypothesis again. This time, you wait two weeks before checking your results.

Eureka! You discover that the green button has a 5% conversion rate compared with the 4.8% of the red button and has statistical significance. It turns out that you committed a type 2 error because your sample size was too small.

How to avoid type 2 errors

While it is impossible to completely avoid type 2 errors, it is possible to reduce the chance that they will occur by increasing your sample size. This means running an experiment for longer and gathering more data to help you make the correct decision with your test results. This will help avoid reaching the false conclusion that an experiment does not have any impact, when it actually does.

Another way to help prevent type 2 errors is to make big and bold changes to your webpages and apps during experiments. The larger the effect of a change, the smaller sample size you will require and the smaller the chance that you will not notice a change. A 25% increase in conversion rate is much easier to notice than a 0.001% increase.

• Key Differences

Know the Differences & Comparisons

Difference Between Type I and Type II Errors

The testing of hypothesis is a common procedure; that researcher use to prove the validity, that determines whether a specific hypothesis is correct or not. The result of testing is a cornerstone for accepting or rejecting the null hypothesis (H 0 ). The null hypothesis is a proposition; that does not expect any difference or effect. An alternative hypothesis (H 1 ) is a premise that expects some difference or effect.

There are slight and subtle differences between type I and type II errors, that we are going to discuss in this article.

Content: Type I Error Vs Type II Error

Comparison chart, possible outcomes.

Definition of Type I Error

In statistics, type I error is defined as an error that occurs when the sample results cause the rejection of the null hypothesis, in spite of the fact that it is true. In simple terms, the error of agreeing to the alternative hypothesis, when the results can be ascribed to chance.

Also known as the alpha error, it leads the researcher to infer that there is a variation between two observances when they are identical. The likelihood of type I error, is equal to the level of significance, that the researcher sets for his test. Here the level of significance refers to the chances of making type I error.

E.g. Suppose on the basis of data, the research team of a firm concluded that more than 50% of the total customers like the new service started by the company, which is, in fact, less than 50%.

Definition of Type II Error

When on the basis of data, the null hypothesis is accepted, when it is actually false, then this kind of error is known as Type II Error. It arises when the researcher fails to deny the false null hypothesis. It is denoted by Greek letter ‘beta (β)’ and often known as beta error.

Type II error is the failure of the researcher in agreeing to an alternative hypothesis, although it is true. It validates a proposition; that ought to be refused. The researcher concludes that the two observances are identical when in fact they are not.

The likelihood of making such error is analogous to the power of the test. Here, the power of test alludes to the probability of rejecting of the null hypothesis, which is false and needs to be rejected. As the sample size increases, the power of test also increases, that results in the reduction in risk of making type II error.

E.g. Suppose on the basis of sample results, the research team of an organisation claims that less than 50% of the total customers like the new service started by the company, which is, in fact, greater than 50%.

Key Differences Between Type I and Type II Error

The points given below are substantial so far as the differences between type I and type II error is concerned:

• Type I error is an error that takes place when the outcome is a rejection of null hypothesis which is, in fact, true. Type II error occurs when the sample results in the acceptance of null hypothesis, which is actually false.
• Type I error or otherwise known as false positives, in essence, the positive result is equivalent to the refusal of the null hypothesis. In contrast, Type II error is also known as false negatives, i.e. negative result, leads to the acceptance of the null hypothesis.
• When the null hypothesis is true but mistakenly rejected, it is type I error. As against this, when the null hypothesis is false but erroneously accepted, it is type II error.
• Type I error tends to assert something that is not really present, i.e. it is a false hit. On the contrary, type II error fails in identifying something, that is present, i.e. it is a miss.
• The probability of committing type I error is the sample as the level of significance. Conversely, the likelihood of committing type II error is same as the power of the test.
• Greek letter ‘α’ indicates type I error. Unlike, type II error which is denoted by Greek letter ‘β’.

By and large, Type I error crops up when the researcher notice some difference, when in fact, there is none, whereas type II error arises when the researcher does not discover any difference when in truth there is one. The occurrence of the two kinds of errors is very common as they are a part of testing process. These two errors cannot be removed completely but can be reduced to a certain level.

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Sajib banik says

January 19, 2017 at 11:00 pm

useful information

Tomisi says

May 10, 2018 at 11:48 pm

Thanks, the simplicity of your illusrations in essay and tables is great contribution to the demystification of statistics.

Tika Ram Khatiwada says

January 9, 2019 at 1:39 pm

Very simply and clearly defined.

sanjaya says

January 9, 2019 at 3:56 pm

Good article..

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Type I and Type II Errors

Type I and Type II Errors are central for hypothesis testing in general, which subsequently impacts various aspects of science including but not limited to statistical analysis. False discovery refers to a Type I error where a true Null Hypothesis is incorrectly rejected. On the other end of the spectrum, Type II errors occur when a true null hypothesis fails to get rejected.

In this article, we will discuss Type I and Type II Errors in detail, including examples and differences.

Table of Content

Type I and Type II Error in Statistics

What is error, what is type i error (false positive), what is type ii error (false negative), type i and type ii errors – table, type i and type ii errors examples, examples of type i error, examples of type ii error, factors affecting type i and type ii errors, how to minimize type i and type ii errors, difference between type i and type ii errors.

In statistics , Type I and Type II errors represent two kinds of errors that can occur when making a decision about a hypothesis based on sample data. Understanding these errors is crucial for interpreting the results of hypothesis tests.

In the statistics and hypothesis testing , an error refers to the emergence of discrepancies between the result value based on observation or calculation and the actual value or expected value.

The failures may happen in different factors, such as turbulent sampling, unclear implementation, or faulty assumptions. Errors can be of many types, such as

• Measurement Error
• Calculation Error
• Human Error
• Systematic Error
• Random Error

In hypothesis testing, it is often clear which kind of error is the problem, either a Type I error or a Type II one.

Type I error, also known as a false positive , occurs in statistical hypothesis testing when a null hypothesis that is actually true is rejected. In other words, it’s the error of incorrectly concluding that there is a significant effect or difference when there isn’t one in reality.

In hypothesis testing, there are two competing hypotheses:

• Null Hypothesis (H 0 ): This hypothesis represents a default assumption that there is no effect, no difference, or no relationship in the population being studied.
• Alternative Hypothesis (H 1 ): This hypothesis represents the opposite of the null hypothesis. It suggests that there is a significant effect, difference, or relationship in the population.

A Type I error occurs when the null hypothesis is rejected based on the sample data, even though it is actually true in the population.

Type II error, also known as a false negative , occurs in statistical hypothesis testing when a null hypothesis that is actually false is not rejected. In other words, it’s the error of failing to detect a significant effect or difference when one exists in reality.

A Type II error occurs when the null hypothesis is not rejected based on the sample data, even though it is actually false in the population. In other words, it’s a failure to recognize a real effect or difference.

Suppose a medical researcher is testing a new drug to see if it’s effective in treating a certain condition. The null hypothesis (H 0 ) states that the drug has no effect, while the alternative hypothesis (H 1 ) suggests that the drug is effective. If the researcher conducts a statistical test and fails to reject the null hypothesis (H 0 ), concluding that the drug is not effective, when in fact it does have an effect, this would be a Type II error.

The table given below shows the relationship between True and False:

Some of examples of type I error include:

• Medical Testing : Suppose a medical test is designed to diagnose a particular disease. The null hypothesis ( H 0 ) is that the person does not have the disease, and the alternative hypothesis ( H 1 ) is that the person does have the disease. A Type I error occurs if the test incorrectly indicates that a person has the disease (rejects the null hypothesis) when they do not actually have it.
• Legal System : In a criminal trial, the null hypothesis ( H 0 ) is that the defendant is innocent, while the alternative hypothesis ( H 1 ) is that the defendant is guilty. A Type I error occurs if the jury convicts the defendant (rejects the null hypothesis) when they are actually innocent.
• Quality Control : In manufacturing, quality control inspectors may test products to ensure they meet certain specifications. The null hypothesis ( H 0 ) is that the product meets the required standard, while the alternative hypothesis ( H 1 ) is that the product does not meet the standard. A Type I error occurs if a product is rejected (null hypothesis is rejected) as defective when it actually meets the required standard.

Using the same H 0 and H 1 , some examples of type II error include:

• Medical Testing : In a medical test designed to diagnose a disease, a Type II error occurs if the test incorrectly indicates that a person does not have the disease (fails to reject the null hypothesis) when they actually do have it.
• Legal System : In a criminal trial, a Type II error occurs if the jury acquits the defendant (fails to reject the null hypothesis) when they are actually guilty.
• Quality Control : In manufacturing, a Type II error occurs if a defective product is accepted (fails to reject the null hypothesis) as meeting the required standard.

Some of the common factors affecting errors are:

• Sample Size: In statistical hypothesis testing, larger sample sizes generally reduce the probability of both Type I and Type II errors. With larger samples, the estimates tend to be more precise, resulting in more accurate conclusions.
• Significance Level: The significance level (α) in hypothesis testing determines the probability of committing a Type I error. Choosing a lower significance level reduces the risk of Type I error but increases the risk of Type II error, and vice versa.
• Effect Size: The magnitude of the effect or difference being tested influences the probability of Type II error. Smaller effect sizes are more challenging to detect, increasing the likelihood of failing to reject the null hypothesis when it’s false.
• Statistical Power: The power of Statistics (1 – β) dictates that the opportunity for rejecting a wrong null hypothesis is based on the inverse of the chance of committing a Type II error. The power level of the test rises, thus a chance of the Type II error dropping.

To minimize Type I and Type II errors in hypothesis testing, there are several strategies that can be employed based on the information from the sources provided:

• By setting a lower significance level, the chances of incorrectly rejecting the null hypothesis decrease, thus minimizing Type I errors.
• Increasing the sample size reduces the variability of the statistic, making it less likely to fall in the non-rejection region when it should be rejected, thus minimizing Type II errors.

Some of the key differences between Type I and Type II Errors are listed in the following table:

Conclusion – Type I and Type II Errors

In conclusion, type I errors occur when we mistakenly reject a true null hypothesis, while Type II errors happen when we fail to reject a false null hypothesis. Being aware of these errors helps us make more informed decisions, minimizing the risks of false conclusions.

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Difference between Null and Alternate Hypothesis Z-Score Table

Type I and Type II Errors – FAQs

What is type i error.

Type I Error occurs when a null hypothesis is incorrectly rejected, indicating a false positive result, concluding that there is an effect or difference when there isn’t one.

What is an Example of a Type 1 Error?

An example of Type I Error is that convicting an innocent person (null hypothesis: innocence) based on insufficient evidence, incorrectly rejecting the null hypothesis of innocence.

What is Type II Error?

Type II Error happens when a null hypothesis is incorrectly accepted, failing to detect a true effect or difference when one actually exists.

What is an Example of a Type 2 Error?

An example of type 2 error is that failing to diagnose a disease in a patient (null hypothesis: absence of disease) despite them actually having the disease, incorrectly failing to reject the null hypothesis.

What is the difference between Type 1 and Type 2 Errors?

Type I error involves incorrectly rejecting a true null hypothesis, while Type II error involves failing to reject a false null hypothesis. In simpler terms, Type I error is a false positive, while Type II error is a false negative.

What is Type 3 Error?

Type 3 Error is not a standard statistical term. It’s sometimes informally used to describe situations where the researcher correctly rejects the null hypothesis but for the wrong reason, often due to a flaw in the experimental design or analysis.

How are Type I and Type II Errors related to hypothesis testing?

In hypothesis testing, Type I Error relates to the significance level (α), which represents the probability of rejecting a true null hypothesis. Type II Error relates to the power of the test (β), which represents the probability of failing to reject a false null hypothesis.

What are some examples of Type I and Type II Errors?

Type I Error: Rejecting a null hypothesis that a new drug has no side effects when it actually does (false positive). Type II Error: Failing to reject a null hypothesis that a new drug has no effect when it actually does (false negative).

How can one minimize Type I and Type II Errors?

Type I Error can be minimized by choosing a lower significance level (α) for hypothesis testing. Type II Error can be minimized by increasing the sample size or improving the sensitivity of the test.

What is the relationship between Type I and Type II Errors?

There is often a trade-off between Type I and Type II Errors. Decreasing the probability of one type of error typically increases the probability of the other.

How do Type I and Type II Errors impact decision-making?

Type I Errors can lead to false conclusions, such as mistakenly believing a treatment is effective when it’s not. Type II Errors can result in missed opportunities, such as failing to identify an effective treatment.

In which fields are Type I and Type II Errors commonly encountered?

Type I and Type II Errors are encountered in various fields, including medical research, quality control, criminal justice, and market research.

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Type 1 and Type 2 Errors Explained - Differences and Examples

Understanding type 1 and type 2 errors is essential. Knowing what and how to manage them can help improve your testing and minimize future mistakes.

Types of errors in statistics

Probability in error types, type 1 error examples, type 2 error examples, how to manage and minimize type 1 and 2 errors, using amplitude to reduce errors.

In product and web testing, we generally categorize statistical errors into two main types—type 1 and type 2 errors. These are closely related to the ideas of hypothesis testing and significance levels.

Researchers often develop a null (H0) and an alternate hypothesis (H1) when conducting experiments or analyzing data . The null hypothesis usually represents the status quo or the baseline assumption, while the alternative hypothesis represents the claim or effect being investigated.

The goal is to determine whether the observed data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

With this in mind, let’s explore each type and the main differences between type 1 errors vs type 2 errors.

Type 1 Error

A type 1 error occurs when you reject the null hypothesis when it is actually true. In other words, you conclude there is a notable effect or difference when there isn’t one—such as a problem or bug that doesn’t exist.

This error is also known as a “false positive” because you’re falsely detecting something insignificant. Say your testing flags an issue with a feature that’s working correctly—this is a type 1 error.

The problem has not resulted from a bug in your code or product but has come about purely by chance or through unrelated factors. This doesn’t mean your testing was completely incorrect, but there isn’t enough weighting to confidently say the flag is genuine and significant enough to make changes.

Type 1 errors can lead to unnecessary reworks, wasted resources, and delays in your development cycle. You might alter something or add new features that don’t benefit the application.

Type 2 Error

A type 2 error, or “false negative,” happens when you fail to reject the null hypothesis when the alternative hypothesis is actually true. In this case, you’re failing to detect an effect or difference (like a problem or bug) that does exist.

It’s called a “false negative,” as you’re falsely concluding there’s no effect when there is one. For example, if your test suite gives the green light to a broken feature or one not functioning as intended, it’s a type 2 error.

Type 2 errors don’t mean you fully accept the null hypothesis—the testing only indicates whether to reject it. In fact, your testing might not have enough statistical power to detect an effect.

A type 2 error can result in you launching faulty products or features. This can massively harm your user experience and damage your brand’s reputation, ultimately impacting sales and revenue.

Understanding and managing type 1 and type 2 errors means understanding some math, specifically probability and statistics.

Let’s unpack the probabilities associated with each type of error and how they relate to statistical significance and power.

Type 1 Error Probability

The probability of getting a type 1 error is represented by alpha (α).

In testing, researchers typically set a desired significance level (α) to control the risk of type 1 errors. This is the statistical probability of getting those results ( p value). You get the p value by doing a t-test, comparing the means of two groups.

Common significance levels (α) are 0.05 (5%) or 0.01 (1%)—this means there’s a 5% or 1% chance of incorrectly rejecting the null hypothesis when it’s true.

If the p value is lower than α, it suggests your results are unlikely to have occurred by chance alone. Therefore, you can reject the null hypothesis and conclude that the alternative hypothesis is supported by your data.

However, the results are not statistically significant if the p value is higher than α. As they could have occurred by chance, you fail to reject the null hypothesis, and there isn’t enough evidence to support the alternative hypothesis.

You can set a lower significance level to reduce the probability of a type 1 error. For example, reducing the level from 0.05 to 0.01 effectively means you’re willing to accept a 1% chance of a type 1 error instead of 5%.

Type 2 Error Probability

The probability of having a type 2 error is denoted by beta (β). It’s inversely related to the statistical power of the test—this is the extent to which a test can correctly detect a real effect when there is one.

Statistical power is calculated as 1 - β. For example, if your risk of committing a type 2 error is 20%, your power level is 80% (1.0 - 0.02 = 0.8). A higher power indicates a lower probability of a type 2 error, meaning you’re less likely to have a false negative. Levels of 80% or more are generally considered acceptable.

Several factors can influence statistical power, including the sample size, effect size, and the chosen significance level. Increasing the sample size and significance level increases the test's power, indirectly reducing the probability of a type 2 error.

Balancing Type 1 and Type 2 Errors

There’s often a trade-off between type 1 and type 2 errors. For instance, lowering the significance level (a) reduces the probability of a type 1 error but increases the likelihood of a Type 2 error (and vice versa).

Researchers and product teams must carefully consider the relative consequences of each type of error in their specific context.

Take medical testing—a type 1 error (false positive) in this field might lead to unnecessary treatment, while a type 2 error (false negative) could result in a missed diagnosis.

It all depends on your product and context. If the cost of a false positive is high, you might want to set a lower significance level (to lower the probability of type 1 error). However, if the impact of missing a genuine issue is more severe (type 2 error), you might choose a higher level to increase the statistical power of your tests.

Knowing the probabilities associated with type 1 and type 2 errors helps teams make better decisions about their testing processes, balance each type's risks, and ensure their products meet proper quality standards.

To help you better understand type 1 errors or false positives in product software and web testing, here are some examples.

In each case, the Type 1 error could lead to unnecessary actions or investigations based on inaccurate or false positive results despite the absence of an actual issue or effect.

Mistaken A/B test result

Your team runs an A/B test to see if a new feature improves user engagement metrics, such as time spent on the platform or click-through rates.

The results show a statistically significant difference between the control and experiment groups, leading you to conclude the new feature is successful and should be rolled out to all users.

However, after further investigation and analysis, you realize the observed difference was not due to the feature itself but an unrelated factor, such as a marketing campaign or a seasonal trend.

You committed a Type 1 error by incorrectly rejecting the null hypothesis (no difference between the groups) when the new feature had no real effect.

Usability testing false positive

Imagine you’re testing that same new feature for usability. Your testing finds that people are struggling to use it—your team puts this down to a design flaw and decides to redesign the element.

However, after getting the same results, you realize that the users’ difficulty using the feature isn’t due to its design but rather their unfamiliarity with it.

After more exposure, they’re able to navigate the feature more easily. Your misattribution led to unnecessary design efforts and a prolonged launch.

This is a classic example of a Type 1 error, where the usability test incorrectly rejected the null hypothesis (the feature is usable).

Inaccurate performance issue detection

Your team uses performance testing to spot your app’s bottlenecks, slowdowns, or other performance issues.

A routine test reports a performance issue with a specific component, such as slow response times or high resource utilization. You allocate resources and efforts to investigate and confront the problem.

However, after in-depth profiling, load testing, and analysis, you find the issue was a false positive, and the component is working normally.

This is another example of a Type 1 error: testing incorrectly flagged a non-existent performance problem, leading to pointless troubleshooting efforts and potential resource waste.

In these examples, the type 2 error resulted in missed opportunities for improvement, the sending out of faulty products or features, or the failure to tackle existing issues or problems.

Missed bug detection

Your team has implemented a new feature in your web application, and you have designed test cases to catch each bug.

However, one of the tests fails to detect a critical bug, leading to the release of a faulty feature with unexpected behavior and functionality issues.

This is a type 2 error—your testing failed to reject the null hypothesis (no bug) when the alternative (bug present) was true.

Overlooked performance issues

Your product relies on a third-party API for data retrieval, and you regularly conduct performance testing to ensure optimal response times.

However, during a particular testing cycle, your team didn’t identify a significant slowdown in the API response times. This results in performance issues and a poor user experience for your customers, with slow page loads or delayed data updates.

As your performance testing failed to spot an existing performance problem, this is a type 2 error.

Undetected security vulnerability

Your security team carries out frequent penetration testing, code reviews, and security audits to highlight potential vulnerabilities in your web application.

However, a critical cross-site scripting (XSS) vulnerability goes undetected, enabling malicious actors to inject client-side scripts and potentially gain access to sensitive data or perform unauthorized actions. This puts your users’ data and security at risk.

It’s also another type 2 error, as your testing didn’t reject the null hypothesis (no vulnerability) when the alternative hypothesis (vulnerability present) was true.

Although it’s impossible to eliminate type 1 and type 2 errors, there are several strategies your product teams can apply to manage and minimize their risks.

Implementing these can improve the accuracy and reliability of your testing process, ultimately leading to you delivering better products and user experiences.

Adjust significance levels

We’ve already discussed adjusting significance levels—this is one of the most straightforward strategies.

Suppose the consequences of getting a false positive (type 1 error) are more severe. In that case, you may wish to set a lower significance level to reduce the probability of rejecting a true null hypothesis.

On the other hand, if overlooking an actual effect (type 2 error) is more costly, you can increase the significance level to improve the statistical power of your tests.

Increase sample size

Increasing the sample size of your tests can help minimize the probability of both type 1 and type 2 errors.

A larger sample size gives you more statistical power, making it easier to spot genuine effects and reducing the likelihood of false positives or negatives.

Implement more thorough testing methodologies

Adopting more thorough and accurate testing methods, such as comprehensive test case design, code coverage analysis, and exploratory testing, can help minimize the risk of missed issues or bugs (type 2 errors).

Regularly reviewing and updating your testing suite to meet changing product requirements can also make it more effective.

Use multiple testing techniques

Combining different testing techniques, including unit, integration, performance, and usability tests, can give you a more complete view of your product’s quality. This reduces the chances of overlooking important issues, which could later affect your bottom line.

Continuously monitor and feedback

Continuous monitoring and feedback loops enable you to identify and deal with any issues missed during the initial testing phases.

This might include monitoring your production systems, gathering user feedback, and conducting post-release testing.

Conduct root cause analysis

When errors are flagged, you must do a root cause analysis to find the underlying reasons for this false positive or negative.

This can help you refine your testing process, improve test case design, and prevent similar errors from occurring in the future.

Foster a culture of quality

Promoting a culture of quality within your organization can help ensure that everyone is invested in minimizing errors and delivering high-quality products.

To achieve this, ask your company to offer more training, encourage collaboration, and foster an environment where team members feel empowered to raise concerns or suggest improvements.

Encountering type 1 and type 2 errors can be disheartening for product teams. Here’s where Ampltide Experiment can help.

The A/B testing platform features help compensate for and correct the presence of type 1 and type 2 errors. By managing and minimizing their risk, you’re able to run more confident product experiments and tests.

Some of Amplitude’s main experimental features include its:

• Sample size calculator : This helps you determine the minimum sample size needed to detect significant effects.
• Experiment duration estimator : The platform’s estimator gives you an idea of how long your experiment needs to run to reach statistical significance.
• Bonferroni correction application : Amplitude uses the Bonferroni correction to adjust the finance level when testing multiple hypotheses.
• Minimum sample size threshold : The platform sets a minimum threshold that experiments must meet before declaring significance.

Use Amplitude to help you design more robust testing, ensure sufficient statistical power, control for multiple tests, and oversee your results. Get increased confidence in your experiment results and make more informed decisions about product changes and feature releases.

Ready to place more trust in your product testing? Sign up for Amplitude now .

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