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.

I specialize in helping graduate students and researchers in psychology, education, economics and the social sciences with all aspects of statistical analysis. Many new and relatively uncommon statistical techniques are available, and these may widen the field of hypotheses you can investigate. Graphical techniques are often misapplied, but, done correctly, they can summarize a great deal of information in a single figure. ** I can help with writing papers, writing grant applications, and doing analysis for grants and research.**

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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!

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

Can you run ridit analysis by spss? If yes, how?

Thanks a lot

Avi fro Israel

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

Hi there, I am planing to use RII and SII to model the trend of socioeconomic inequality in obesity. Can anyone tell me how to adjust/weight the sample size in stata? Do I need to use ridit score? If I need to, how and by which variable? Many thanks!!!

Hi Jim,

It’s just me here, and I don’t know STATA, sorry

Peter

In the first equation, what’s sigma? Is a standard deviation of something?

Regards, Blaise

Blaise – it was a typo. It should have been summation. I fixed it.