Matthew DeBell wrote: > What would be an appropriate way to compare two sets of ranked data? For > example, suppose I have a class of students with class rank calculated by > two different methods. (Say, one ranking is based on GPA reported by the > student in a survey and one is based on GPA from school records.) I want to > compare the rankings in a systematic way and be able to say whether the two > methods yield more or less the same results. > > Should I use Spearman's rank correlation coefficient? Kendall's tau? > Something else? > > Or should I just, say, compute the absolute value of the rank difference for > each student and find the mean and median difference between the two ranking > methods? > > Thanks. > > MD
If you must use ranks then the obvious statistic is the Spearman correlation, which is just another name for the Pearson correlation of the ranks. If you want to think in terms of differences rather than correlation, recognize that the correlation is a negative linear function of the mean square difference between the two rankings. Stay away from the absolute differences -- they work well only if the differences are small (i.e., when the correlation is large and positive).