The analysis of data from experimental designs is often hampered by the lack of more than one procedure available for the analysis, especially when that procedure is based on assumptions which do not apply in the situation at hand. In this paper two classes of alternative procedures are discussed and compared. One is the aligned ranks procedure which first standardizes the data by subtracting an appropriate estimate of location, then replaces the data with ranks, and finally uses an appropriate test statistic which has asymptotically a chi-square distribution. The second procedure is the rank transform which first replaces all of the data with the ranks, and then employs the usual parametric methods, but computed on the ranks instead of the data. Some Monte Carlo simulations for a test of interaction in a two way layout with replication enable the robustness and power of these two methods to be compared with the usual analysis of variance.
- aligned ranks analysis of variance on ranks
- rank transforms