The probability of making a Type II error is the same, regardless of sample size, for the HSD test.

Name: The probability of making a Type II error is the same, regardless of sample size, for the HSD test.
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The probability of making a Type II error (failing to reject a false null hypothesis) generally decreases as the sample size increases, because larger sample sizes provide more information and thus a greater ability to detect a true effect if one exists.

The Probability of Making a Type II Error Is the Same