how to avoid type 1 error in research

Type I vs Type II Errors: Causes, Examples & Prevention

There are two common types of errors, type I and type II errors you’ll likely encounter when testing a statistical hypothesis. The mistaken rejection of the finding or the null hypothesis is known as a type I error. In other words, type I error is the false-positive finding in hypothesis testing . Type II error on the other hand is the false-negative finding in hypothesis testing.

To better understand the two types of errors, here’s an example:

Let’s assume you notice some flu-like symptoms and decide to go to a hospital to get tested for the presence of malaria. There is a possibility of two errors occurring:

In type I error (False positive): The result of the test shows you have malaria but you actually don’t have it.
Type II error (false negative): The test result indicates that you don’t have malaria when you in fact do.

Type I error and Type II error are extensively used in areas such as computer science, Engineering, Statistics, and many more.

The chance of committing a type I error is known as alpha (α), while the chance of committing a type II error is known as beta (β). If you carefully plan your study design, you can minimize the probability of committing either of the errors.

Read: Survey Errors To Avoid: Types, Sources, Examples, Mitigation

What are Type I Errors?

Type I error is an omission that happens when a null hypothesis is reprobated during hypothesis testing. This is when it is indeed precise or positive and should not have been initially disapproved. So if a null hypothesis is erroneously rejected when it is positive, it is called a Type I error.

What this means is that results are concluded to be significant when in actual fact, it was obtained by chance.

When conducting hypothesis testing, a null hypothesis is determined before carrying out the actual test. The null hypothesis may presume that there is no chain of circumstances between the items being tested which may cause an outcome for the test.

When a null hypothesis is rejected, it means a chain of circumstances has been established between the items being tested even though it is a false alarm or false positive. This could lead to an error or many errors in a test, known as a Type I error.

It is worthy of note that statistical outcomes of every testing involve uncertainties, so making errors while performing these hypothesis testings is unavoidable. It is inherent that type I error may be considered as an error of commission in the sense that the producer or researcher mistakenly decides on a false outcome.

Read: Systematic Errors in Research: Definition, Examples

Causes of Type I Error

When a factor other than the variable affects the variables being tested. This factor that causes the effect produces a result that supports the decision to reject the null hypothesis.
When the result of a hypothesis testing is caused by chance, it is a Type I error.
Lastly, because a null hypothesis and the significance level are decided before conducting a hypothesis test, and also the sample size is not considered, a type I error may occur due to chance.

Read: Margin of error – Definition, Formula + Application

Risk Factor and Probability of Type I Error

The risk factor and probability of Type I error are mostly set in advance and the level of significance of the hypothesis testing is known.
The level of significance in a test is represented by α and it signifies the rate of the possibility of Type I error.
While it is possible to reduce the rate of Type I error by using a determined sample size. The consequence of this, however, is that the possibility of a Type II error occurring in a test will increase.
In a case where Type I error is decided at 5 percent, it means in the null hypothesis ( H 0), chances are there that 5 in the 100 hypotheses even if true will be rejected.
Another risk factor is that both Type I and Type II errors can not be changed simultaneously. To reduce the possibility of one error occurring means the possibility of the other error will increase. Hence changing the outcome of one test inherently affects the outcome of the other test.

Read: Sampling Bias: Definition, Types + [Examples]

Consequences of a Type I Error

A type I error will result in a false alarm. The outcome of the hypothesis testing will be a false positive. This implies that the researcher decided the result of a hypothesis testing is true when in fact, it is not.

For a sales group, the consequences of a type I error may result in losing potential market and missing out on probable sales because the findings of a test are faulty.

What are Type II Errors?

A Type II error means a researcher or producer did not disapprove of the alternate hypothesis when it is in fact negative or false. This does not mean the null hypothesis is accepted as positive as hypothesis testing only indicates if a null hypothesis should be rejected.

A Type II error means a conclusion on the effect of the test wasn’t recognized when an effect truly existed. Before a test can be said to have a real effect, it has to have a power level that is 80% or more.

This implies the statistical power of a test determines the risk of a type II error. The probability of a type II error occurring largely depends on how high the statistical power is.

Note: Null hypothesis is represented as (H0) and alternative hypothesis is represented as (H1)

Causes of Type II Error

Type II error is mainly caused by the statistical power of a test being low. A Type II error will occur if the statistical test is not powerful enough.
The size of the sample can also lead to a Type I error because the outcome of the test will be affected. A small sample size might hide the significant level of the items being tested.
Another cause of Type Ii error is the possibility that a researcher may disapprove of the actual outcome of a hypothesis even when it is correct.

Probability of Type II Error

To arrive at the possibility of a Type II error occurring, the power of the test must be deducted from type 1.
The level of significance in a test is represented by β and it shows the rate of the possibility of Type I error.
It is possible to reduce the rate of Type II error if the significance level of the test is increased.
In a case where Type II error is decided at 5 percent, it means in the null hypothesis ( H 0), chances are there that 5 in the 100 hypotheses even if it is false will be accepted.
Type I error and Type II error are connected. Hence, to reduce the possibility of one type of error from occurring means the possibility of the other error will increase.
It is important to decide which error has lesser effects on the test.

Consequences of a Type II Error

Type II errors can also result in a wrong decision that will affect the outcomes of a test and have real-life consequences.

Note that even if you proved your test hypothesis, your conversion result can invalidate the outcome unintended. This turn of events can be discouraging, hence the need to be extra careful when conducting hypothesis testing.

How to Avoid Type I and II errors

Type I error and type II errors can not be entirely avoided in hypothesis testing, but the researcher can reduce the probability of them occurring.

For Type I error, minimize the significance level to avoid making errors. This can be determined by the researcher.

To avoid type II errors, ensure the test has high statistical power. The higher the statistical power, the higher the chance of avoiding an error. Set your statistical power to 80% and above and conduct your test.

Increase the sample size of the hypothesis testing.

The Type II error can also be avoided if the significance level of the test hypothesis is chosen.

How to Detect Type I and Type II Errors in Data

After completing a study, the researcher can conduct any of the available statistical tests to reject the default hypothesis in favor of its alternative. If the study is free of bias, there are four possible outcomes. See the image below;

Image source: IPJ

If the findings in the sample and reality in the population match, the researchers’ inferences will be correct. However, if in any of the situations a type I or II error has been made, the inference will be incorrect.

Key Differences between Type I & II Errors

In statistical hypothesis testing, a type I error is caused by disapproving a null hypothesis that is otherwise correct while in contrast, Type II error occurs when the null hypothesis is not rejected even though it is not true.
Type I error is the same as a false alarm or false positive while Type II error is also referred to as false negative.
A Type I error is represented by α while a Type II error is represented by β.
The level of significance determines the possibility of a type I error while type II error is the possibility of deducting the power of the test from 1.
You can decrease the possibility of Type I error by reducing the level of significance. The same way you can reduce the probability of a Type II error by increasing the significance level of the test.
Type I error occurs when you reject the null hypothesis, in contrast, Type II error occurs when you accept an incorrect outcome of a false hypothesis

Examples of Type I & II errors

Type i error examples.

To understand the statistical significance of Type I error, let us look at this example.

In this hypothesis, a driver wants to determine the relationship between him getting a new driving wheel and the number of passengers he carries in a week.

Now, if the number of passengers he carries in a week increases after he got a new driving wheel than the number of passengers he carried in a week with the old driving wheel, this driver might assume that there is a relationship between the new wheel and the increase in the number of passengers and support the alternative hypothesis.

However, the increment in the number of passengers he carried in a week, might have been influenced by chance and not by the new wheel which results in type I error.

By this indication, the driver should have supported the null hypothesis because the increment of his passengers might have been due to chance and not fact.

Type II error examples

For Type II error and statistical power, let us assume a hypothesis where a farmer that rears birds assumes none of his birds have bird-flu. He observes his birds for four days to find out if there are symptoms of the flu.

If after four days, the farmer sees no symptoms of the flu in his birds, he might assume his birds are indeed free from bird flu whereas the bird flu might have affected his birds and the symptoms are obvious on the sixth day.

By this indication, the farmer accepts that no flu exists in his birds. This leads to a type II error where it supports the null hypothesis when it is in fact false.

Frequently Asked Questions about Type I and II Errors

Is a Type I or Type II error worse?

Both Type I and type II errors could be worse based on the type of research being conducted.

A Type I error means an incorrect assumption has been made when the assumption is in reality not true. The consequence of this is that other alternatives are disapproved of to accept this conclusion. A type II error implies that a null hypothesis was not rejected. This means that a significant outcome wouldn’t have any benefit in reality.

A Type I error however may be terrible for statisticians. It is difficult to decide which of the errors is worse than the other but both types of errors could do enough damage to your research.

Does sample size affect type 1 error?

Small or large sample size does not affect type I error . So sample size will not increase the occurrence of Type I error.

The only principle is that your test has a normal sample size. If the sample size is small in Type II errors, the level of significance will decrease.

This may cause a false assumption from the researcher and discredit the outcome of the hypothesis testing.

What is statistical power as it relates to Type I or Type II errors

Statistical power is used in type II to deduce the measurement error. This is because random errors reduce the statistical power of hypothesis testing. Not only that, the larger the size of the effect, the more detectable the errors are.

The statistical power of a hypothesis increases when the level of significance increases. The statistical power also increases when a larger sample size is being tested thereby reducing the errors. If you want the risk of Type II error to reduce, increase the level of significance of the test.

What is statistical significance as it relates to Type I or Type II errors

Statistical significance relates to Type I error. Researchers sometimes assume that the outcome of a test is statistically significant when they are not and the researcher then rejects the null hypothesis. The fact is, the outcome might have happened due to chance.

A type I error decreases when a lower significance level is set.

If your test power is lower compared to the significance level, then the alternative hypothesis is relevant to the statistical significance of your test, then the outcome is relevant.

In this article, we have extensively discussed Type I error and Type II error. We have also discussed their causes, the probabilities of their occurrence, and how to avoid them. We have seen that both Types of errors have their usefulness and limitations. The best approach as a researcher is to know which to apply and when.

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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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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.

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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Statistics By Jim

Making statistics intuitive

Type 1 Error Overview & Example

By Jim Frost Leave a Comment

What is a Type 1 Error?

A type 1 error (AKA Type I error) occurs when you reject a true null hypothesis in a hypothesis test. In other words, a statistically significant test result indicates that a population effect exists when it does not. A type 1 error is a false positive because the test detects an effect in the sample that doesn’t exist in the population.

Caution! Type 1 errors can occur in hypothesis testing.

By rejecting a true null hypothesis, you incorrectly conclude that the effect exists when it doesn’t . Of course, you don’t know that you’re committing an error at the time. You’re just following the results of your hypothesis test.

Type 1 errors can have serious consequences. When testing a new medication, a false positive could mean putting a useless drug on the market. Understanding and managing these errors is essential for reliable statistical conclusions.

Related post : Hypothesis Testing Overview

Type 1 Error Example

Let’s take that technical information and bring it to life with an example of a type 1 error in action. For the study in this example, we’ll assume we know that the effect doesn’t exist. You wouldn’t know that in the real world, which is why you conduct the study!

Suppose we’re testing a new medicine that is completely ineffective. We perform a study, collect the data, and perform the hypothesis test.

The hypotheses for this test are the following:

Null : The medicine has no effect in the population
Alternative : The medicine is effective in the population.

The analysis produces a p-value of 0.03, less than our alpha level of 0.05. Our study is statistically significant . Therefore, we reject the null and conclude the medicine is effective.

Unfortunately, these results are incorrect because the medicine is ineffective. The statistically significant results make us think the medicine is effective when it isn’t. It’s a false positive. A type 1 error has occurred and we don’t even know it!

Learn more about the Null Hypothesis .

Why Do They Occur?

Hypothesis tests use sample data to infer the properties of populations. You gain incredible benefits by using random samples because it is usually impossible to evaluate an entire population.

Unfortunately, using samples introduces potential problems, including Type 1 errors. Random samples tend to reflect the population from which they’re drawn. However, they can occasionally misrepresent the population enough to cause false positives.

Type 1 errors sneak into our analysis due to chance during random sampling. Even when we do everything right – following assumptions and using correct procedures – randomness in data collection can lead to misleading results.

Imagine rolling a die. Sometimes, purely by chance, you get more sixes than expected. Similarly, randomness can produce unusual samples that misrepresent the population.

In short, the luck of the draw can cause Type 1 errors (false positives) to occur.

Learn more about Representative Samples and Random Sampling .

Probability of a Type 1 Error

While we don’t know when studies produce false positive results, we do know their rate of occurrence. The probability of making a Type 1 error is denoted by the Greek letter alpha (α), which is the significance level of the test. By choosing your significance level, you’re setting the false positive rate.

A standard value for α is 0.05. This significance level produces a 5% chance of rejecting a true null hypothesis.

A critical benefit for hypothesis testing is that when the null hypothesis is true, the probability of a Type 1 error (false positive) is low. This fact helps you trust statistically significant results.

Related posts : Significance Level and How Hypothesis Tests Work: Alpha & P-values .

Minimizing False Positives

There’s no way to eliminate Type 1 errors entirely, but you can reduce them by lowering your significance level (e.g., from 0.05 to 0.01). However, lower alphas also lessen the probability of detecting an effect if one exists.

It’s a balancing act. Set α too high, and you risk more false positives. Set it too low, and you might miss real effects ( Type 2 errors or false negatives ). Choosing the right α depends on the context and consequences of your test.

In hypothesis testing, understanding Type 1 errors is vital. They represent a false positive, where we think we’ve found something significant when we haven’t. By carefully choosing our significance level, we can reduce the risk of these errors and make more accurate statistical decisions.

Compare and contrast Type I vs. Type II Errors .

Acosta, Griselda; Smith, Eric; and Kreinovich, Vladik, “ Why Area Under the Curve in Hypothesis Testing? ” (2019). Departmental Technical Reports (CS) . 1360.

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Which Statistical Error Is Worse: Type 1 or Type 2?

Topics: Hypothesis Testing , Statistics

People can make mistakes when they test a hypothesis with statistical analysis. Specifically, they can make either Type I or Type II errors.

As you analyze your own data and test hypotheses, understanding the difference between Type I and Type II errors is extremely important, because there's a risk of making each type of error in every analysis, and the amount of risk is in your control.

So if you're testing a hypothesis about a safety or quality issue that could affect people's lives, or a project that might save your business millions of dollars, which type of error has more serious or costly consequences? Is there one type of error that's more important to control than another?

Before we attempt to answer that question, let's review what these errors are.

The Null Hypothesis and Type 1 and 2 Errors

	) not rejected	) rejected
Null (H ) is true.	Correct conclusion.
Null (H ) is false.		Correct conclusion.

These errors relate to the statistical concepts of risk, significance, and power.

Reducing the Risk of Statistical Errors

Statisticians call the risk, or probability, of making a Type I error "alpha," aka "significance level." In other words, it's your willingness to risk rejecting the null when it's true. Alpha is commonly set at 0.05, which is a 5 percent chance of rejecting the null when it is true. The lower the alpha, the less your risk of rejecting the null incorrectly. In life-or-death situations, for example, an alpha of 0.01 reduces the chance of a Type I error to just 1 percent. A Type 2 error relates to the concept of "power," and the probability of making this error is referred to as "beta." We can reduce our risk of making a Type II error by making sure our test has enough power—which depends on whether the sample size is sufficiently large to detect a difference when it exists.

The Default Argument for "Which Error Is Worse"

Let's return to the question of which error, Type 1 or Type 2, is worse. The go-to example to help people think about this is a defendant accused of a crime that demands an extremely harsh sentence.

The null hypothesis is that the defendant is innocent. Of course you wouldn't want to let a guilty person off the hook, but most people would say that sentencing an innocent person to such punishment is a worse consequence.

Hence, many textbooks and instructors will say that the Type 1 (false positive) is worse than a Type 2 (false negative) error. The rationale boils down to the idea that if you stick to the status quo or default assumption, at least you're not making things worse .

And in many cases, that's true. But like so much in statistics, in application it's not really so black or white. The analogy of the defendant is great for teaching the concept, but when we try to make it a rule of thumb for which type of error is worse in practice, it falls apart.

So Which Type of Error Is Worse, Already?

I'm sorry to disappoint you, but as with so many things in life and statistics, the honest answer to this question has to be, "It depends."

In one instance, the Type I error may have consequences that are less acceptable than those from a Type II error. In another, the Type II error could be less costly than a Type I error. And sometimes, as Dan Smith pointed out in Significance a few years back with respect to Six Sigma and quality improvement, "neither" is the only answer to which error is worse:

Most Six Sigma students are going to use the skills they learn in the context of business. In business, whether we cost a company $3 million by suggesting an alternative process when there is nothing wrong with the current process or we fail to realize $3 million in gains when we should switch to a new process but fail to do so, the end result is the same. The company failed to capture $3 million in additional revenue.

Look at the Potential Consequences

Since there's not a clear rule of thumb about whether Type 1 or Type 2 errors are worse, our best option when using data to test a hypothesis is to look very carefully at the fallout that might follow both kinds of errors. Several experts suggest using a table like the one below to detail the consequences for a Type 1 and a Type 2 error in your particular analysis.

	true, but rejected	false, but not rejected
	Medicine A does not relieve Condition B, but is not eliminated as a treatment option.	Medicine A relieves Condition B, but is eliminated as a treatment option.
	Patients with Condition B who receive Medicine A get no relief. They may experience worsening condition and/or side effects, up to and including death. Litigation possible.	A viable treatment remains unavailable to patients with Condition B. Development costs are lost. Profit potential is eliminated.

Whatever your analysis involves, understanding the difference between Type 1 and Type 2 errors, and considering and mitigating their respective risks as appropriate, is always wise. For each type of error, make sure you've answered this question: "What's the worst that could happen?"

To explore this topic further, check out this article on using power and sample size calculations to balance your risk of a type 2 error and testing costs, or this blog post about considering the appropriate alpha for your particular test.

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Type I Error

"False positive" error

What is a Type I Error?

In statistical hypothesis testing, a Type I error is essentially the rejection of the true null hypothesis. The type I error is also known as the false positive error. In other words, it falsely infers the existence of a phenomenon that does not exist.

Note that the type I error does not imply that we erroneously accept the alternative hypothesis of an experiment.

The probability of committing the type I error is measured by the significance level (α) of a hypothesis test. The significance level indicates the probability of erroneously rejecting the true null hypothesis. For instance, a significance level of 0.05 reveals that there is a 5% probability of rejecting the true null hypothesis.

How to Avoid a Type I Error?

It is not possible to completely eliminate the probability of a type I error in hypothesis testing . However, there are opportunities to minimize the risks of obtaining results that contain a type I error.

One of the most common approaches to minimizing the probability of getting a false positive error is to minimize the significance level of a hypothesis test. Since the significance level is chosen by a researcher, the level can be changed. For example, the significance level can be minimized to 1% (0.01). This indicates that there is a 1% probability of incorrectly rejecting the null hypothesis.

However, lowering the significance level may lead to a situation wherein the results of the hypothesis test may not capture the true parameter or the true difference of the test.

Example of a Type I Error

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 that the null hypothesis is that there is no difference in the average price changes between large-cap and small-cap stocks. Thus, his alternative hypothesis states that the 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 I error, the results of the test will indicate that the difference in the average price changes between large-cap and small-cap stocks exists while there is no significant difference among the groups.

Additional 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:

Type II Error
Conditional Probability
Independent Events
Sample Selection Bias
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A guide to type 1 errors: Examples and best practices

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

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

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

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

What is a type 1 error?

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

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

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

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

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

Type 1 vs. type 2 errors

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

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

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

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

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

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

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

Factors that contribute to type 1 errors

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

Insufficient sample size

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

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

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

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

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

Type 1 error examples

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

False positive impact of a new feature

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

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

This results in a type 1 error.

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

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

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

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

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

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

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

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

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

Best practices to minimize type 1 errors

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

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

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

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