Teacher’s Corner: A Note on Interpretation of the Paired-Samples t Test

Explanations of advantages and disadvantages of paired-samples experimental designs in textbooks in education and psychology frequently overlook the change in the Type I error probability which occurs when an independent-samples t test is performed on correlated observations. This alteration of the significance level can be extreme even if the correlation is small. By comparison, the loss of power of the paired-samples t test on difference scores due to reduction of degrees of freedom, which typically is emphasized, is relatively slight. Although paired-samples designs are appropriate and widely used when there is a natural correspondence or pairing of scores, researchers have not often considered the implications of undetected correlation between supposedly independent samples in the absence of explicit pairing.