Recent Developments In The Statistical Analysis Of Ranked Data Adapted To Educational Research
The analysis of variance technique is grad ually gaining recognition among workers in the field of educational research. There are, however, certain conditions under which this powerful statistical tool cannot be used, either because the variate is not normally distributed or because the data are qualitative and there fore cannot be measured but only indicated in terms of ranks. Furthermore, the analysis of variance technique involves calculations which become rather laborious when the data is extensive, so that more convenient methods of analysis are in order even though they may be somewhat less efficient from the standpoint of statistical analysis. Fortunately two recent developments in statistical theory make possible the rigorous analysis of ranked data by methods very similar to the analysis of variance technique. The first which is reported by Friedman1 and which is referred to by him as the "method of ranks" is essentially an analysis of variance of ranks. The second tool is an extension of the "method of ranks" and results in what Wallis2 calls the rank correlation ratio. Wallis