Tuesday, May 17, 2011

About ordinals, brocolli, and squash

A good friend of mine, a professor of computer science with and excellent grasp of statistics, wrote me this after reviewing a learned paper I had found on the web:

All of [the author's] discussion of mean estimation assumes that you are analyzing survey results for which the responses are Low to High, or 1, 2, .. , n, e.g., a 5 point scale or a 7 point scale...not continuous scale.

Everybody calculates means, standard deviation, t tests for this type of data...and everybody is wrong. These data are ordinal, which means the distance between the points is not defined.

You can order them, but you can't legitimately do arithmetic with them. If you used very low, low, nominal, high, very high, how do you add 5 lows, 3 nominals and 6 very highs to get an average? But if you represent those values with 1,2,3,4,5, then you can do arithmetic, but without a distance measure the results are meaningless.

As an example, in my case, when it comes to vegetables, green beans are a 3 (not bad, not good), brocolli is a 2 (don't really like it, but I eat it), yellow squash on the other hand is -100000 even though 1 is the lowest I'm allowed to go.

The reason for this is that although the distance between n and n+1 is 1 for every point on the scale, the distance (in perception) between very low and low would probably be much greater than the distance between low and nominal. End of sermon.
Dr. Walter P. Bond

A similar, and supporting theme, is the backdrop for one of the more quantitative books on risk management for project managers, entitled: "Effective Risk Management: Some Keys to Success" by Edmund H. Conrow.

If you have access to a university library, you'll probably find it on the shelf. As Glen Alleman says: a difficult read in some respects, but very insightful.

Photo credit: 5 vegetables

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