What is the Type II error in hypothesis testing?

What is the Type II error in hypothesis testing?

• A. The probability of detecting a false effect
• B. The probability of missing a true effect
• C. The probability of obtaining a significant result by chance
• D. The probability of making a Type I error

Answer: (B)

Type II error occurs when there is a real effect but the test does not detect it, so you fail to reject the null hypothesis. In plain terms, you miss a true effect. This is also called a false negative, and its probability is beta. The test’s power, which is 1 minus beta, reflects how likely you are to detect a real effect; higher power means fewer Type II errors. Factors that influence this include the true effect size, sample size, data variability, and the chosen significance level. To reduce Type II error, you can increase sample size, improve measurement precision, or sometimes accept a higher alpha level (at the cost of more false positives). Why the other ideas don’t fit: detecting a false effect relates to the test’s power as well but describes a true positive vs. false negative distinction, not Type II error per se. obtaining a significant result by chance points to a false positive (Type I error) rather than failing to detect a real effect. making a Type I error is the mistaken rejection of a true null hypothesis, again a Type I error.

Type II error occurs when there is a real effect but the test does not detect it, so you fail to reject the null hypothesis. In plain terms, you miss a true effect. This is also called a false negative, and its probability is beta. The test’s power, which is 1 minus beta, reflects how likely you are to detect a real effect; higher power means fewer Type II errors. Factors that influence this include the true effect size, sample size, data variability, and the chosen significance level. To reduce Type II error, you can increase sample size, improve measurement precision, or sometimes accept a higher alpha level (at the cost of more false positives).

Why the other ideas don’t fit: detecting a false effect relates to the test’s power as well but describes a true positive vs. false negative distinction, not Type II error per se. obtaining a significant result by chance points to a false positive (Type I error) rather than failing to detect a real effect. making a Type I error is the mistaken rejection of a true null hypothesis, again a Type I error.