Wednesday, September 27, 2006

z-Scores and Other Standardization Schemes

(Updated March 14, 2015) 

As you know, I like to find real-life examples of the concepts covered in class. Standard deviations, z scores, etc., rarely come up in the public discourse. One place they do come up, however, is in the criteria for membership in Mensa, also known as the "high IQ society" (click here and then scroll down a bit). Mensa requires someone to be in the top 2% of IQ scores or 2 SD above the mean. Those of you who fly on American Eagle into and out of Lubbock, and read the American Way magazine on the plane, may have noticed that each issue includes some sample Mensa items, for your amusement and bemusement.

First, to summarize how different distributions are normed to different means and standard deviations, here's a list (each distribution's properties can be reported in the form, M +/- SD):

Mean SD
Normal (z) 0 1
McCall T 50 10
IQ Tests 100 15 or 16

Here's an informative document from Valdosta State University on standardization of variables onto different scales.

Here is a link on the "Flynn Effect" (rising population-level IQ's over the years), for those who are interested.