Increasing Power in Paired-Samples Designs by Correcting the Student t Statistic for Correlation

by Donald W. Zimmerman.

Abstract: In order to circumvent the influence of correlation in paired-samples and repeated measures experimental designs, researchers typically perform a one-sample Student t test on difference scores. This procedure entails some loss of power, because it employs n 1 degrees of freedom instead of the 2n 2 degrees of freedom of the independent-samples t test. In the case of non-normal distributions, researchers typically substitute the Wilcoxon signed-ranks test for the one-sample t test. The present study explored an alternate strategy, using a modified two-samples t test with a correction for correlation. For non-normal distributions, the same modified t test was performed on rank-transformed data. Simulations disclosed that this procedure, which retains 2n 2 degrees of freedom, protects the Type I error rate for moderate and large sample sizes, maintains power for normal distributions, and substantially increases power for many non-normal distributions.

Key Words: t test, Wilcoxon signed-ranks test, rank transformation, paired samples, repeated measures

Donald W. Zimmerman,

Editor: Richard Graf,

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