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 table statement.

4 Responses to “Using ridits to assign scores to categories of ordinal scales”

1. Rick Wicklin says:

   July 30, 2010 at 8:04 am

   Agresti is giving a one-day short course on the Analysis of Ordinal Categorical Data next week at JSM 2010 in Vancouver:
   http://www.amstat.org/meetings/jsm/2010/index.cfm?fuseaction=courses
   I’ll be there!
2. Peter Flom says:

   July 30, 2010 at 8:14 am

   I won’t be at JSM, but Agresti is a great author, he’s probably a great speaker too.
3. Avi says:

   February 13, 2013 at 12:14 pm

   Can you run ridit analysis by spss? If yes, how?
   Thanks a lot
   Avi fro Israel
4. Peter Flom says:

   February 13, 2013 at 1:06 pm

   I don’t know SPSS at all, but you probably can do it somehow.