What is a Type I error and a Type II error?

What is a Type I error and a Type II error?

• A. Type I error is a false positive (rejecting a true H0); Type II error is a false negative (failing to reject a false H0).
• B. Type I error is a false negative; Type II error is a false positive.
• C. Type I error is a p-value; Type II error is a confidence interval.
• D. Type I error occurs only with small samples.

Answer: (A)

In hypothesis testing, the key ideas are about decisions you make about the null hypothesis. A Type I error happens when you reject the null hypothesis even though it is true—a false positive. A Type II error happens when you fail to reject the null hypothesis even though it is false—a false negative. So the first describes detecting an effect that isn’t really there, while the second describes missing a real effect. The other statements mix up these concepts or bring in related ideas: a false negative is not what Type I does, a false positive is what Type I does, a p-value or a confidence interval are different concepts related to evidence and estimation, and Type I error isn’t limited to small samples—its rate is set by the chosen significance level, though smaller samples can reduce power and affect your ability to detect true effects.

In hypothesis testing, the key ideas are about decisions you make about the null hypothesis. A Type I error happens when you reject the null hypothesis even though it is true—a false positive. A Type II error happens when you fail to reject the null hypothesis even though it is false—a false negative. So the first describes detecting an effect that isn’t really there, while the second describes missing a real effect. The other statements mix up these concepts or bring in related ideas: a false negative is not what Type I does, a false positive is what Type I does, a p-value or a confidence interval are different concepts related to evidence and estimation, and Type I error isn’t limited to small samples—its rate is set by the chosen significance level, though smaller samples can reduce power and affect your ability to detect true effects.