StATS: What is a Type II Error?

In your research, you specify a null hypothesis (typically labeled H0) and an alternative hypothesis (typically labeled Ha, or sometimes H1). By tradition, the null hypothesis corresponds to no change.

When you are using Statistics to decide between these two hypothesis, you have to allow for the possibility of error. Actually, if you are using any other procedure, you should still allow for the possibility of error, but we statisticians are the only ones honest enough to admit this.

• A Type II error is accepting the null hypothesis when the null hypothesis is false.

Many studies have small sample sizes that make it difficult to reject the null hypothesis, even when there is a big change in the data. In these situations, a Type II error might be a possible explanation for the negative study results.

Example

Consider a new drug that we will put on the market if we can show that it is better than a placebo. In this context, H0 would represent the hypothesis that the average improvement (or perhaps the probability of improvement) among all patients taking the new drug is equal to the average improvement (probability of improvement) among all patients taking the placebo.

• A Type II error would be keeping an effective drug off the market.

Suppose we are comparing two groups of patients, one with a possibly dangerous exposure (e.g., non-ionizing radiation), and the other unexposed. In this context, H0 would represent the hypothesis that the average level of harm (or perhaps the probability of harm) among those with exposure is equal to the average level (probability) of harm among those without the exposure.

• A Type II error would be absolving an exposure that actually does harm.

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Definitions, Category: Definitions, Category: Hypothesis testing.