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

Author:
Donald W. Zimmerman, dwzimm@telus.net

Editor: Richard Graf,rgraf@sunstroke.sdsu.edu

READING THE ARTICLE: You can read the article in portable document (.pdf) format (101989 bytes.)

NOTE: The content of this article is the intellectual property of the authors, who retains all rights to future publication.

This page has been accessed 3485 times since July 24, 2006.


Return to the InterStat Home Page.