When dealing with ordinal data, many methods require you to assign a number or score to each level of a variable. For instance, if you ask people about their political orientation and whether it is very conservative, somewhat conservative, moderate, somewhat liberal or very liberal, you might assign these scores of 1, 2, 3, 4 and 5, respectively. But that is somewhat arbitrary.
One alternative was suggested by Bross (1958) and brought to my attention in reading Alan Agresti’s excellent book: Analysis of Ordinal Categorical Data . It is the average cumulative proportion, known as a ridit, and is given by
where is the proportion in the jth category
Perhaps the best use of ridits is in analyzing tables with an arbitrary number of rows and columns. You can then calculate the mean ridit per row
Then, for any two rows, A and B, the value
`estimates the probability of a better response with treatment A than treatment B’ (Agresti, p. 17)
In SAS(R) you can do ridit analysis in
PROC FREQ, by using the
scores = ridit option on the
Specialties: Regression, logistic regression, cluster analysis, statistical graphics, quantile regression.