Tuesday, November 10, 2009

Normal Calculus Scores

6DZU26SW93B5 A few weeks ago I was reading the post Double Calculus on the Learning Curves blog and the histogram of the grade distribution of the calculus scores really what caught my attention. For starters, the histogram was generated using JMP and I'm always glad to see other users of JMP, but most of all, the distribution looked quite normal. Quoting from the blog: "Can you believe this grade distribution? Way more normal than anything that comes out of my class. Skewness of 0.03."

Images of grading by the "curve", as well as "normal scores", came to mind, and this made me think of my favorite tool for assessing normality: the normal probability plot. The normal probability plot is a plot of the ordered data against the expected normal scores (Z scores) such that, if the normal distribution is a good approximation for the data, the points follow an aproximate straight line.
A normal probability plot is easily generated in JMP using the distribution platform by clicking the contextual menu to the right of the histogram title.

In a normal probability plot the points do not have to fall exactly on a straight line, just hover around it so that a "fat pen" will cover them (the "fat pen" test). JMP also provides confidence bands around the line to facilitate interpretation.

We can clearly see that the calculus scores follow closely the straight line, indicating that the data can be well approximated by a normal distribution. These calculus scores are in fact normal scores!

No comments:

Post a Comment