How does high variability within groups affect a study's power?

How does high variability within groups affect a study's power?

• A. It increases the power
• B. It decreases the power
• C. It has no effect on power
• D. It increases the risk of Type I error

Answer: (B)

Power reflects how likely a study is to detect a real difference between groups. When there is high variability within groups, that extra noise makes the true difference harder to distinguish from random fluctuations. In practical terms, the standard error of the difference in means grows with within-group variability, so the test statistic (which compares the observed difference to this noise) shrinks and the chance of rejecting the null when a real difference exists goes down. So, with the same sample size and the same true effect, high within-group variability lowers power. This variability doesn’t inherently raise the risk of a false positive (Type I error) when the test’s alpha level is held steady; it mainly raises the chance of a false negative (failing to detect a real effect). To restore power, you can either increase the sample size, reduce measurement noise, or look for a larger true difference.

Power reflects how likely a study is to detect a real difference between groups. When there is high variability within groups, that extra noise makes the true difference harder to distinguish from random fluctuations. In practical terms, the standard error of the difference in means grows with within-group variability, so the test statistic (which compares the observed difference to this noise) shrinks and the chance of rejecting the null when a real difference exists goes down. So, with the same sample size and the same true effect, high within-group variability lowers power.

This variability doesn’t inherently raise the risk of a false positive (Type I error) when the test’s alpha level is held steady; it mainly raises the chance of a false negative (failing to detect a real effect). To restore power, you can either increase the sample size, reduce measurement noise, or look for a larger true difference.