Non-central t distribution and the power of the t test: A rejoinder

The Power of Replicated Measures to Increase Statistical Power

When running statistical tests, researchers can commit a Type II error, that is, fail to reject the null hypothesis when it is false. To diminish the probability of committing a Type II error (β), statistical power must be augmented. Typically, this is done by increasing sample size, as more participants provide more power. When the estimated effect size is small, however, the sample size required to achieve sufficient statistical power can be prohibitive. To alleviate this lack of power, a common practice is to measure participants multiple times under the same condition. Here, we show how to estimate statistical power by taking into account the benefit of such replicated measures. To that end, two additional parameters are required: the correlation between the multiple measures within a given condition and the number of times the measure is replicated. An analysis of a sample of 15 studies (total of 298 participants and 38,404 measurements) suggests that in simple cognitive tasks, the correlation between multiple measures is approximately .14. Although multiple measurements increase statistical power, this effect is not linear, but reaches a plateau past 20 to 50 replications (depending on the correlation). Hence, multiple measurements do not replace the added population representativeness provided by additional participants.