Wiki Page, Math 13 - Perez Sandbox : Module 20 - Introduction to Hypothesis Testing (5a of 5)

Wiki Page
2026-01-17T21:15:31-08:00

What Can Go Wrong: Two Types of Errors

Statistical investigations involve making decisions in the face of uncertainty, so there is always some chance of making a wrong decision. In hypothesis testing, two types of wrong decisions can occur.

If the null hypothesis is true, but we reject it, the error is a Type I error.

If the null hypothesis is false, but we fail to reject it, the error is a Type II error.

The following table summarizes Type I and II errors.

Type I and Type II errors

We Reject Ho
(accept Ha)

We Fail to Reject Ho
(not enough information to accept Ha)

H₀ is true. | Type I Error | Correct Decision
H₀ is false. | Correct Decision | Type II Error

Comment

Type I and Type II errors are not caused by mistakes. These errors are the result of random chance. The data provide evidence for a conclusion that is false. It’s no one’s fault!

EXAMPLE Data use on Smartphones

In a previous example, we looked at a hypothesis test about data usage on smartphones. The researcher investigated the claim that the mean data usage for all teens is greater than 62 MBs. The sample mean was 75 MBs. The P-value was approximately 0.023. In this situation, the P-value is the probability that we will get a sample mean of 75 MBs or higher if the true mean is 62 MBs.

Notice that the result (75 MBs) isn’t impossible, only very unusual. The result is rare enough that we question whether the null hypothesis is true. This is why we reject the null hypothesis. But it is possible that the null hypothesis hypothesis is true and the researcher happened to get a very unusual sample mean. In this case, the result is just due to chance, and the data have led to a Type I error: rejecting the null hypothesis when it is actually true.

EXAMPLE White male support for Obama in 2012

In a previous example, we conducted a hypothesis test using poll results to determine if white male support for Obama in 2012 will be less than 40%. Our poll of white males showed 35% planning to vote for Obama in 2012. Based on the sampling distribution, we estimated the P-value as 0.078. In this situation, the P-value is the probability that we will get a sample proportion of 0.35 or less if 0.40 of the population of white males support Obama.

At the 5% level, the poll did not give strong enough evidence for us to conclude that less than 40% of white males will vote for Obama in 2012.

Which type of error is possible in this situation? If, in fact, it is true that less than 40% of this population support Obama, then the data led to a Type II error: failing to reject a null hypothesis that is false. In other words, we failed to accept an alternative hypothesis that is true.

We definitely did not make a Type I error here because a Type I error requires that we reject the null hypothesis.

Mark this page as done, then click the "Next" or > button to continue.

Content by the Open Learning Initiative and licensed under CC BY.