null hypothesis type 1 error

Type 1 and Type 2 Errors in Statistics

Saul Mcleod, PhD

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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

Exploratory Data Analysis

Research Methodology , Statistics

What Is Face Validity In Research? Importance & How To Measure

Criterion Validity: Definition & Examples

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What Is a Type I Error?

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Type 1 Error: Definition, False Positives, and Examples

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

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

Key Takeaways

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

How a Type I Error Works

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

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

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

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

False Positive Type I Error

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

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

Examples of Type I Errors

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

Criminal Trials

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

Medical Testing

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

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

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

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

How Does a Type I Error Occur?

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

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

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

What Is a Null Hypothesis?

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

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

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

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

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

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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.

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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9.2 Outcomes and the Type I and Type II Errors

When you perform a hypothesis test, there are four possible outcomes depending on the actual truth, or falseness, of the null hypothesis H 0 and the decision to reject or not. The outcomes are summarized in the following table:

The four possible outcomes in the table are as follows:

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

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

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

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

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

The Power of the Test is 1 – β . Ideally, we want a high power that is as close to one as possible. Increasing the sample size can increase the Power of the Test.

The following are examples of Type I and Type II errors.

Example 9.5

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

Type I error: Frank does not go rock climbing because he considers that the equipment is not safe, when in fact, the equipment is really safe. Frank is making the mistake of rejecting the null hypothesis, when the equipment is actually safe!

Type II error: Frank goes climbing, thinking that his equipment is safe, but this is a mistake, and he painfully realizes that his equipment is not as safe as it should have been. Frank assumed that the null hypothesis was true, when it was not.

α = probability that Frank thinks his rock climbing equipment may not be safe when, in fact, it really is safe. β = probability that Frank thinks his rock climbing equipment may be safe when, in fact, it is not safe.

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

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

Example 9.6

Suppose the null hypothesis, H 0 , is: a tomato plant is alive when a class visits the school garden.

Type I error: The null hypothesis claims that the tomato plant is alive, and it is true, but the students make the mistake of thinking that the plant is already dead.

Type II error: The tomato plant is already dead (the null hypothesis is false), but the students do not notice it, and believe that the tomato plant is alive.

α = probability that the class thinks the tomato plant is dead when, in fact, it is alive = P (Type I error). β = probability that the class thinks the tomato plant is alive when, in fact, it is dead = P (Type II error).

The error with the greater consequence is the Type I error. (If the class thinks the plant is dead, they will not water it.)

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

Example 9.7

It’s a Boy Genetic Labs, a genetics company, claims to be able to increase the likelihood that a pregnancy will result in a boy being born. Statisticians want to test the claim. Suppose that the null hypothesis, H 0 , is: It’s a Boy Genetic Labs has no effect on gender outcome.

Type I error : This error results when a true null hypothesis is rejected. In the context of this scenario, we would state that we believe that It’s a Boy Genetic Labs influences the gender outcome, when in fact it has no effect. The probability of this error occurring is denoted by the Greek letter alpha, α .

Type II error : This error results when we fail to reject a false null hypothesis. In context, we would state that It’s a Boy Genetic Labs does not influence the gender outcome of a pregnancy when, in fact, it does. The probability of this error occurring is denoted by the Greek letter beta, β .

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

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

Example 9.8

A certain experimental drug claims a cure rate of at least 75 percent for males with a disease. Describe both the Type I and Type II errors in context. Which error is the more serious?

Type I : A patient believes the cure rate for the drug is less than 75 percent when it actually is at least 75 percent.

Type II : A patient believes the experimental drug has at least a 75 percent cure rate when it has a cure rate that is less than 75 percent.

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

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

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

Identify the Type I and Type II errors from these four possible choices.

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

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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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Ind Psychiatry J
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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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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Introduction types of mistakes suggestions resources table of contents about, type i and ii errors and significance levels.

Setting a significance level ( before doing inference) has the advantage that the analyst is not tempted to chose a cut-off on the basis of what he or she hopes is true.
It has the disadvantage that it neglects that some p-values might best be considered borderline. This is one reason 2 why it is important to report p-values when reporting results of hypothesis tests. It is also good practice to include confidence intervals corresponding to the hypothesis test. (For example, if a hypothesis test for the difference of two means is performed, also give a confidence interval for the difference of those means. If the significance level for the hypothesis test is .05, then use confidence level 95% for the confidence interval.)
The blue (leftmost) curve is the sampling distribution assuming the null hypothesis " " µ = 0."
The green (rightmost) curve is the sampling distribution assuming the specific alternate hypothesis " µ =1".
The vertical red line shows the cut-off for rejection of the null hypothesis: the null hypothesis is rejected for values of the test statistic to the right of the red line (and not rejected for values to the left of the red line)>
The area of the diagonally hatched region to the right of the red line and under the blue curve is the probability of type I error ( α )
The area of the horizontally hatched region to the left of the red line and under the green curve is the probability of Type II error ( β )
If the consequences of a type I error are serious or expensive, then a very small significance level is appropriate.
If the consequences of a Type I error are not very serious (and especially if a Type II error has serious consequences), then a larger significance level is appropriate.
Sometimes there may be serious consequences of each alternative, so some compromises or weighing priorities may be necessary. The trial analogy illustrates this well: Which is better or worse, imprisoning an innocent person or letting a guilty person go free? 6 This is a value judgment; value judgments are often involved in deciding on significance levels. Trying to avoid the issue by always choosing the same significance level is itself a value judgment.
Sometimes different stakeholders have different interests that compete (e.g., in the second example above, the developers of Drug 2 might prefer to have a smaller significance level.)
See http://core.ecu.edu/psyc/wuenschk/StatHelp/Type-I-II-Errors.htm for more discussion of the considerations involved in deciding what are reasonable levels for Type I and Type II errors.
See the discussion of Power for more on deciding on a significance level.
Similar considerations hold for setting confidence levels for confidence intervals .
This is an instance of the common mistake of expecting too much certainty .
There is always a possibility of a Type I error; the sample in the study might have been one of the small percentage of samples giving an unusually extreme test statistic.
This is why replicating experiments (i.e., repeating the experiment with another sample) is important. The more experiments that give the same result, the stronger the evidence.
There is also the possibility that the sample is biased or the method of analysis was inappropriate ; either of these could lead to a misleading result.

Math Article
Type I And Type Ii Errors

Type I and Type II Errors

Type I and Type II errors are subjected to the result of the null hypothesis. In case of type I or type-1 error, the null hypothesis is rejected though it is true whereas type II or type-2 error, the null hypothesis is not rejected even when the alternative hypothesis is true. Both the error type-i and type-ii are also known as “ false negative ”. A lot of statistical theory rotates around the reduction of one or both of these errors, still, the total elimination of both is explained as a statistical impossibility.

Type I Error

A type I error appears when the null hypothesis (H 0 ) of an experiment is true, but still, it is rejected. It is stating something which is not present or a false hit. A type I error is often called a false positive (an event that shows that a given condition is present when it is absent). In words of community tales, a person may see the bear when there is none (raising a false alarm) where the null hypothesis (H 0 ) contains the statement: “There is no bear”.

The type I error significance level or rate level is the probability of refusing the null hypothesis given that it is true. It is represented by Greek letter α (alpha) and is also known as alpha level. Usually, the significance level or the probability of type i error is set to 0.05 (5%), assuming that it is satisfactory to have a 5% probability of inaccurately rejecting the null hypothesis.

Type II Error

A type II error appears when the null hypothesis is false but mistakenly fails to be refused. It is losing to state what is present and a miss. A type II error is also known as false negative (where a real hit was rejected by the test and is observed as a miss), in an experiment checking for a condition with a final outcome of true or false.

A type II error is assigned when a true alternative hypothesis is not acknowledged. In other words, an examiner may miss discovering the bear when in fact a bear is present (hence fails in raising the alarm). Again, H0, the null hypothesis, consists of the statement that, “There is no bear”, wherein, if a wolf is indeed present, is a type II error on the part of the investigator. Here, the bear either exists or does not exist within given circumstances, the question arises here is if it is correctly identified or not, either missing detecting it when it is present, or identifying it when it is not present.

The rate level of the type II error is represented by the Greek letter β (beta) and linked to the power of a test (which equals 1−β).

Also, read:

Table of Type I and Type II Error

The relationship between truth or false of the null hypothesis and outcomes or result of the test is given in the tabular form:

Type I and Type II Errors Example

Check out some real-life examples to understand the type-i and type-ii error in the null hypothesis.

Example 1 : Let us consider a null hypothesis – A man is not guilty of a crime.

Then in this case:

Example 2: Null hypothesis- A patient’s signs after treatment A, are the same from a placebo.

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8.2: Type I and II Errors

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Rachel Webb
Portland State University

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How do you quantify really small? Is 5% or 10% or 15% really small? How do you decide? That depends on your field of study and the importance of the situation. Is this a pilot study? Is someone’s life at risk? Would you lose your job? Most industry standards use 5% as the cutoff point for how small is small enough, but 1%, 5% and 10% are frequently used depending on what the situation calls for.

Now, how small is small enough? To answer that, you really want to know the types of errors you can make in hypothesis testing.

The first error is if you say that H 0 is false, when in fact it is true. This means you reject H 0 when H 0 was true. The second error is if you say that H 0 is true, when in fact it is false. This means you fail to reject H 0 when H 0 is false.

Figure 8-4 shows that if we “Reject H 0 ” when H 0 is actually true, we are committing a type I error. The probability of committing a type I error is the Greek letter $\alpha$, pronounced alpha. This can be controlled by the researcher by choosing a specific level of significance $\alpha$.

Figure 8-4 shows that if we “Do Not Reject H 0 ” when H 0 is actually false, we are committing a type II error. The probability of committing a type II error is denoted with the Greek letter β, pronounced beta. When we increase the sample size this will reduce β. The power of a test is 1 – β.

A jury trial is about to take place to decide if a person is guilty of committing murder. The hypotheses for this situation would be:

$H_0$: The defendant is innocent
$H_1$: The defendant is not innocent

The jury has two possible decisions to make, either acquit or convict the person on trial, based on the evidence that is presented. There are two possible ways that the jury could make a mistake. They could convict an innocent person or they could let a guilty person go free. Both are bad news, but if the death penalty was sentenced to the convicted person, the justice system could be killing an innocent person. If a murderer is let go without enough evidence to convict them then they could possibly murder again. In statistics we call these two types of mistakes a type I and II error.

Figure 8-5 is a diagram to see the four possible jury decisions and two errors.

Type I Error is rejecting H 0 when H 0 is true, and Type II Error is failing to reject H 0 when H 0 is false.

Since these are the only two possible errors, one can define the probabilities attached to each error.

$\alpha$ = P(Type I Error) = P(Rejecting H 0 | H 0 is true)

β = P(Type II Error) = P(Failing to reject H 0 | H 0 is false)

An investment company wants to build a new food cart. They know from experience that food carts are successful if they have on average more than 100 people a day walk by the location. They have a potential site to build on, but before they begin, they want to see if they have enough foot traffic. They observe how many people walk by the site every day over a month. They will build if there is more than an average of 100 people who walk by the site each day. In simple terms, explain what the type I & II errors would be using context from the problem.

The hypotheses are: H 0 : μ = 100 and H 1 : μ > 100.

Sometimes it is helpful to use words next to your hypotheses instead of the formal symbols

H 0 : μ ≤ 100 (Do not build)
H 1 : μ > 100 (Build).

A type I error would be to reject the null when in fact it is true. Take your finger and cover up the null hypothesis (our decision is to reject the null), then what is showing? The alternative hypothesis is what action we take.

If we reject H 0 then we would build the new food cart. However, H 0 was actually true, which means that the mean was less than or equal to 100 people walking by.

In more simple terms, this would mean that our evidence showed that we have enough foot traffic to support the food cart. Once we build, though, there was not on average more than 100 people that walk by and the food cart may fail.

A type II error would be to fail to reject the null when in fact the null is false. Evidence shows that we should not build on the site, but this actually would have been a prime location to build on.

The missed opportunity of a type II error is not as bad as possibly losing thousands of dollars on a bad investment.

What is more severe of an error is dependent on what side of the desk you are sitting on. For instance, if a hypothesis is about miles per gallon for a new car the hypotheses may be set up differently depending on if you are buying the car or selling the car. For this course, the claim will be stated in the problem and always set up the hypotheses to match the stated claim. In general, the research question should be set up as some type of change in the alternative hypothesis.

Controlling for Type I Error

The significance level used by the researcher should be picked prior to collection and analyzing data. This is called “a priori,” versus picking α after you have done your analysis which is called “post hoc.” When deciding on what significance level to pick, one needs to look at the severity of the consequences of the type I and type II errors. For example, if the type I error may cause the loss of life or large amounts of money the researcher would want to set $\alpha$ low.

Controlling for Type II Error

The power of a test is the complement of a type II error or correctly rejecting a false null hypothesis. You can increase the power of the test and hence decrease the type II error by increasing the sample size. Similar to confidence intervals, where we can reduce our margin of error when we increase the sample size. In general, we would like to have a high confidence level and a high power for our hypothesis tests. When you increase your confidence level, then in turn the power of the test will decrease. Calculating the probability of a type II error is a little more difficult and it is a conditional probability based on the researcher’s hypotheses and is not discussed in this course.

“‘That's right!’ shouted Vroomfondel, ‘we demand rigidly defined areas of doubt and uncertainty!’” (Adams, 2002)

Visualizing $\alpha$ and β

If $\alpha$ increases that means the chances of making a type I error will increase. It is more likely that a type I error will occur. It makes sense that you are less likely to make type II errors, only because you will be rejecting H 0 more often. You will be failing to reject H 0 less, and therefore, the chance of making a type II error will decrease. Thus, as α increases, β will decrease, and vice versa. That makes them seem like complements, but they are not complements. Consider one more factor – sample size.

Consider if you have a larger sample that is representative of the population, then it makes sense that you have more accuracy than with a smaller sample. Think of it this way, which would you trust more, a sample mean of 890 if you had a sample size of 35 or sample size of 350 (assuming a representative sample)? Of course, the 350 because there are more data points and so more accuracy. If you are more accurate, then there is less chance that you will make any error.

By increasing the sample size of a representative sample, you decrease β.

For a constant sample size, n , if $\alpha$ increases, β decreases.
For a constant significance level, $\alpha$, if n increases, β decreases.

When the sample size becomes large, point estimates become more precise and any real differences in the mean and null value become easier to detect and recognize. Even a very small difference would likely be detected if we took a large enough sample size. Sometimes researchers will take such a large sample size that even the slightest difference is detected. While we still say that difference is statistically significant, it might not be practically significant. Statistically significant differences are sometimes so minor that they are not practically relevant. This is especially important to research: if we conduct a study, we want to focus on finding a meaningful result. We do not want to spend lots of money finding results that hold no practical value.

The role of a statistician in conducting a study often includes planning the size of the study. The statistician might first consult experts or scientific literature to learn what would be the smallest meaningful difference from the null value. They also would obtain some reasonable estimate for the standard deviation. With these important pieces of information, they would choose a sufficiently large sample size so that the power for the meaningful difference is perhaps 80% or 90%. While larger sample sizes may still be used, the statistician might advise against using them in some cases, especially in sensitive areas of research.

If we look at the following two sampling distributions in Figure 8-6, the one on the left represents the sampling distribution for the true unknown mean. The curve on the right represents the sampling distribution based on the hypotheses the researcher is making. Do you remember the difference between a sampling distribution, the distribution of a sample, and the distribution of the population? Revisit the Central Limit Theorem in Chapter 6 if needed.

If we start with $\alpha$ = 0.05, the critical value is represented by the vertical green line at $z_{\alpha}$ = 1.96. Then the blue shaded area to the right of this line represents $\alpha$. The area under the curve to the left of $z_{\alpha / 2}$ = 1.96 based on the researcher’s claim would represent β.

If we were to change $\alpha$ from 0.05 to 0.01 then we get a critical value of $z_{\alpha / 2}$ = 2.576. Note that when $\alpha$ decreases, then β increases which means your power 1 – β decreases. See Figure 8-7.

This text does not go over how to calculate β. You will need to be able to write out a sentence interpreting either the type I or II errors given a set of hypotheses. You also need to know the relationship between $\alpha$, β, confidence level, and power.

Hypothesis tests are not flawless, since we can make a wrong decision in statistical hypothesis tests based on the data. For example, in the court system, innocent people are sometimes wrongly convicted and the guilty sometimes walk free, or diagnostic tests that have false negatives or false positives. However, the difference is that in statistical hypothesis tests, we have the tools necessary to quantify how often we make such errors. A type I Error is rejecting the null hypothesis when H 0 is actually true. A type II Error is failing to reject the null hypothesis when the alternative is actually true (H 0 is false).

We use the symbols $\alpha$ = P(Type I Error) and β = P(Type II Error). The critical value is a cutoff point on the horizontal axis of the sampling distribution that you can compare your test statistic to see if you should reject the null hypothesis. For a left-tailed test the critical value will always be on the left side of the sampling distribution, the right-tailed test will always be on the right side, and a two-tailed test will be on both tails. Use technology to find the critical values. Most of the time in this course the shortcut menus that we use will give you the critical values as part of the output.

8.2.1 Finding Critical Values

A researcher decides they want to have a 5% chance of making a type I error so they set α = 0.05. What z-score would represent that 5% area? It would depend on if the hypotheses were a left-tailed, two-tailed or right-tailed test. This zscore is called a critical value. Figure 8-8 shows examples of critical values for the three possible sets of hypotheses.

Two-tailed Test

If we are doing a two-tailed test then the $\alpha$ = 5% area gets divided into both tails. We denote these critical values $z_{\alpha / 2}$ and $z_{1-\alpha / 2}$. When the sample data finds a z-score ( test statistic ) that is either less than or equal to $z_{\alpha / 2}$ or greater than or equal to $z_{1-\alpha / 2}$ then we would reject H 0 . The area to the left of the critical value $z_{\alpha / 2}$ and to the right of the critical value $z_{1-\alpha / 2}$ is called the critical or rejection region. See Figure 8-9.

When $\alpha$ = 0.05 then the critical values $z_{\alpha / 2}$ and $z_{1-\alpha / 2}$ are found using the following technology.

Excel: $z_{\alpha / 2}$ =NORM.S.INV(0.025) = –1.96 and $z_{1-\alpha / 2}$ =NORM.S.INV(0.975) = 1.96

TI-Calculator: $z_{\alpha / 2}$ = invNorm(0.025,0,1) = –1.96 and $z_{1-\alpha / 2}$ = invNorm(0.975,0,1) = 1.96

Since the normal distribution is symmetric, you only need to find one side’s z-score and we usually represent the critical values as ± $z_{\alpha / 2}$.

Most of the time we will be finding a probability (p-value) instead of the critical values. The p-value and critical values are related and tell the same information so it is important to know what a critical value represents.

Right-tailed Test

If we are doing a right-tailed test then the $\alpha$ = 5% area goes into the right tail. We denote this critical value $z_{1-\alpha}$. When the sample data finds a z-score more than $z_{1-\alpha}$ then we would reject H 0 , reject H 0 if the test statistic is ≥ $z_{1-\alpha}$. The area to the right of the critical value $z_{1-\alpha}$ is called the critical region. See Figure 8-10.

Figure 8-10

When $\alpha$ = 0.05 then the critical value $z_{1-\alpha}$ is found using the following technology.

Excel: $z_{1-\alpha}$ =NORM.S.INV(0.95) = 1.645 Figure 8-10

TI-Calculator: $z_{1-\alpha}$ = invNorm(0.95,0,1) = 1.645

Left-tailed Test

If we are doing a left-tailed test then the $\alpha$ = 5% area goes into the left tail. If the sampling distribution is a normal distribution then we can use the inverse normal function in Excel or calculator to find the corresponding z-score. We denote this critical value $z_{\alpha}$.

When the sample data finds a z-score less than $z_{\alpha}$ then we would reject H0, reject Ho if the test statistic is ≤ $z_{\alpha}$. The area to the left of the critical value $z_{\alpha}$ is called the critical region. See Figure 8-11.

Figure 8-11

When $\alpha$ = 0.05 then the critical value $z_{\alpha}$ is found using the following technology.

Excel: $z_{\alpha}$ =NORM.S.INV(0.05) = –1.645

TI-Calculator: $z_{\alpha}$ = invNorm(0.05,0,1) = –1.645

The Claim and Summary

The wording on the summary statement changes depending on which hypothesis the researcher claims to be true. We really should always be setting up the claim in the alternative hypothesis since most of the time we are collecting evidence to show that a change has occurred, but occasionally a textbook will have the claim in the null hypothesis. Do not use the phrase “accept H 0 ” since this implies that H0 is true. The lack of evidence is not evidence of nothing.

There were only two possible correct answers for the decision step.

i. Reject H 0

ii. Fail to reject H 0

Caution! If we fail to reject the null this does not mean that there was no change, we just do not have any evidence that change has occurred. The absence of evidence is not evidence of absence. On the other hand, we need to be careful when we reject the null hypothesis we have not proved that there is change.

When we reject the null hypothesis, there is only evidence that a change has occurred. Our evidence could have been false and lead to an incorrect decision. If we use the phrase, “accept H 0 ” this implies that H 0 was true, but we just do not have evidence that it is false. Hence you will be marked incorrect for your decision if you use accept H 0 , use instead “fail to reject H 0 ” or “do not reject H 0 .”

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Type I and Type II Errors

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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, 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:

Examples of Type I Error

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.

Examples of Type II Error

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.

FAQs on Type I and Type II Errors

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.

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Type I & Type II Errors
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 ...
Type 1 Error Overview & Example
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.
Type 1 and Type 2 Errors in Statistics
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).
Types I & Type II Errors in Hypothesis Testing
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.
Type I and type II errors
Type I and type II errors. In statistical hypothesis testing, a type I error, or a false positive, is the rejection of the null hypothesis when it is actually true. For example, an innocent person may be convicted. A type II error, or a false negative, is the failure to reject a null hypothesis that is actually false.
Type 1 Error: Definition, False Positives, and Examples
Type I Error: A Type I error is a type of error that occurs when a null hypothesis is rejected although it is true. The error accepts the alternative hypothesis ...
9.2: Type I and Type II Errors
9.2: Type I and Type II Errors. When you perform a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis H0 and the decision to reject or not. The outcomes are summarized in the following table: The four possible outcomes in the table are: is true (correct decision).
Type I & Type II Errors
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 ...
Introduction to Type I and Type II errors (video)
And the null hypothesis tends to be kind of what was always assumed or the status quo while the alternative hypothesis, hey, there's news here, there's something alternative here. And to test it, and we're really testing the null hypothesis. We're gonna decide whether we want to reject or fail to reject the null hypothesis, we take a sample.
Type 1 errors (video)
So the power of a test tells us something about how strong the test is, that is how well the test can differentiate between H0 and H1. To improve the power of a test one can lower the variance or one can increase alfa (type 1 error). Power curves shows the power of the test given different values of H1. The longer H1 is from H0 the easier it is ...
9.2 Outcomes and the Type I and Type II Errors
Suppose the null hypothesis, H 0, is: Frank's rock climbing equipment is safe. Type I error: Frank does not go rock climbing because he considers that the equipment is not safe, when in fact, the equipment is really safe. Frank is making the mistake of rejecting the null hypothesis, when the equipment is actually safe!
9.3: Outcomes and the Type I and Type II Errors
Example 9.3.1 9.3. 1: Type I vs. Type II errors. Suppose the null hypothesis, H0 H 0, is: Frank's rock climbing equipment is safe. Type I error: Frank thinks that his rock climbing equipment may not be safe when, in fact, it really is safe. Type II error: Frank thinks that his rock climbing equipment may be safe when, in fact, it is not safe.
6.1
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 ...
9.2: Outcomes, Type I and Type II Errors
9.2: Outcomes, Type I and Type II Errors. When you perform a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis H0 and the decision to reject or not. The outcomes are summarized in the following table: The four possible outcomes in the table are:
Type I and Type II Errors and Statistical Power
This article will help providers determine the likelihood of type I or type II errors and judge adequacy of statistical power. Then one can decide whether or not the evidence provided should be implemented in practice or used to guide future studies. ... Power is the ability to correctly reject a null hypothesis that is indeed false ...
PDF Type I and Type II errors
The q-value of H(k) controlling the pFDR then can be estimated by (1 ) ( ) k k P W m W P λ − −λ. It is also the estimated pFDR if we reject all the null hypotheses with p-values ≤ P( )k. Maximum Likelihood Estimation
Hypothesis testing, type I and type II errors
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).
A guide to type 1 errors: Examples and best practices
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 ...
Type I and II Errors
A significance level α corresponds to a certain value of the test statistic, say t α, represented by the orange line in the picture of a sampling distribution below (the picture illustrates a hypothesis test with alternate hypothesis "µ > 0")
Hypothesis Testing: Type 1 and Type 2 Errors
In some cases, however, researchers will reject or accept the null hypothesis when they shouldn't have. Data Scientists refer to these errors as Type I (False Positive) and Type II (False ...
Type I and Type II Error
Type I and Type II errors are subjected to the result of the null hypothesis. In case of type I or type-1 error, the null hypothesis is rejected though it is true whereas type II or type-2 error, the null hypothesis is not rejected even when the alternative hypothesis is true. ... (5%), assuming that it is satisfactory to have a 5% probability ...
8.2: Type I and II Errors
We use the symbols $\alpha$ = P(Type I Error) and β = P(Type II Error). The critical value is a cutoff point on the horizontal axis of the sampling distribution that you can compare your test statistic to see if you should reject the null hypothesis.
Type I and Type II Errors in Statistics
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.
Unveiling Test Power's Role in BI Hypothesis Testing
1 Test Power. The power of a test in hypothesis testing is the probability that the test correctly rejects a false null hypothesis. In simpler terms, it measures a test's ability to identify a ...
‎Hypothesis Test
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Type 1 and Type 2 Errors in Statistics

Type I error

Implications

Type II error

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

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

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

Further Information

What Is a Type I Error?

The Bottom Line

Type 1 Error: Definition, False Positives, and Examples

Key Takeaways

How a Type I Error Works

False Positive Type I Error

Examples of Type I Errors

Criminal Trials

Medical Testing

How Does a Type I Error Occur?

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

What Is a Null Hypothesis?

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

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

Table of contents

Type I error rate

Type II error rate

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Pritha Bhandari

9.2 Outcomes and the Type I and Type II Errors

Example 9.5

Example 9.6

Example 9.7

Example 9.8

User Preferences

Keyboard Shortcuts

Example: Trial Section

Example: Culinary Arts Study Section

Hypothesis testing, type I and type II errors

U. B. Chitnis

STARTING POINT OF RESEARCH: HYPOTHESIS OR OBSERVATION?

CHARACTERISTICS OF A GOOD HYPOTHESIS

Hypothesis should be simple

Hypothesis should be specific

Hypothesis should be stated in advance

TYPES OF HYPOTHESES

Null and alternative hypotheses

One- and two-tailed alternative hypotheses

STATISTICAL PRINCIPLES OF HYPOTHESIS TESTING

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

EFFECT SIZE

α,β,AND POWER

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A guide to type 1 errors: Examples and best practices

What is a type 1 error?

Type 1 vs. type 2 errors

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Factors that contribute to type 1 errors

Insufficient sample size

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COMMON MISTEAKS MISTAKES IN USING STATISTICS: Spotting and Avoiding Them

Type I and Type II Errors

Type I Error

Type II Error

Table of Type I and Type II Error

Type I and Type II Errors Example

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