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. That 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-sample t test with a correction for correlation, analogous to the “z test for correlated samples” used at one time for paired observations. For non-normal distributions, the same modified t test was performed on rank-transformed data. Simulations disclosed that this procedure protects the Type I error rate for moderate and large sample sizes, maintains power for normal distributions and several symmetric non-normal distributions, and substantially increases power for various skewed nonnormal distributions.