Increasing the Power of Tests of Location and Correlation by Transforming Scores to Ranks and Indicators

Abstract

For various nonnormal distributions, the power of the Student t test can be increased if continuous measures are transformed to ranks before the test is performed. The power of the test can also be increased almost as much and, even more for some distributions, if measures are replaced by dichotomous variables with the values 0 and 1, instead of ranks. Similarly, the power of a significance test of correlation can be increased if scores are transformed to ranks, that is, with the use of the Spearman rank correlation method. Power can also be increased almost as much and in some cases even more if dichotomous variables are introduced, that is, if the phi coefficient is used as a measure of correlation.