Analysis of covariance using the rank transformation.

The rank transformation refers to the replacement of data by their ranks, with a subsequent analysis using the usual normal theory procedure, but calculated on the ranks rather than on the data. Rank transformation procedures have previously been shown by the authors to have properties of robustness and power in both regression and analysis of variance. It seems natural to consider the use of the rank transformation in analysis of covariance, which is a combination of regression and analysis of variance. In this paper the rank transformation approach to analysis of covariance is presented and examined. Comparisons are made with the rank transformation procedure given by Quade (1967, Journal of the American Statistical Association 62, 1187-1200), and some 'standard' data sets are used to compare the results of these two procedures. A Monte Carlo simulation study examines the behavior of these methods under the null hypothesis and under alternative hypotheses, with both normal and nonnormal distributions. All results are compared with the usual analysis of covariance procedure on the basis of robustness and power.