This simulation demonstrates the effect of the correlation between measures in a one-way within-subjects ANOVA with two levels. This test is equivalent to a correlated t test. The default values for this demonstration are for an experiment with \(10\) subjects each measured under two conditions. The population difference for the two conditions is \(1.85\) and the variance in each of the conditions is \(4.0\). The graph shows the power of the test as a function of the population correlation between the two scores for the \(0.10\), \(0.05\), and \(0.01\) significance levels. The power of an independent-groups \(t\) test (which assumes the correlation is \(0\)) is shown by the \(x's\).
Experiment with different combinations of the parameters. Is the correlation an important factor in power?