Normal probability plots and the "fat pencil test"

An informal approximation of a normality test, called "the fat pencil test", is often applied to a probability plot. Imagine a "fat pencil" lying on top of the fitted line:
  • If it covers all the data points on the plot, the data are probably normal.
  • If points are far enough from the fitted line that they are visible beyond the edges of the fat pencil, the data are probably nonnormal.

This informal approach is not a substitute for the statistical inference of the normality test itself, but it is useful as a quick visual assessment. The fat pencil test is applied to the following probability plots. The bands represent a fat pencil on top of the fitted line.

The "fat pencil test" with normal data
The "fat pencil test" with nonnormal data
By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy