Title: Some Misconceptions about the Normal Distribution
Author: Keith M. Bower
Publication Source: American Society for Quality, Six Sigma Forum, May 2003
Abstract
This article discusses three misconceptions regarding the use of the normal distribution in theory and practice, namely:
(1) Something is “wrong” if the distribution is non-normal.
(2) The larger the sample size, the closer it approximates a normal distribution.
(3) Capability estimates do not depend on normality.
Notes
I considered it very important to address misconception (1) first as many organizations I came across were teaching the “if the distribution isn’t Normal, something must be wrong” for processes where a Normal distribution couldn’t feasibly make sense. My feeling was that people were not looking clearly at the process. Instead, they looked to “chop off” datapoints merely to get a p-value for a test for normality to exceed 0.05. Obviously that is very poor practice.
Misconception (2) is somewhat trivial, but probably clarified an issue for some people, whereas misconception (3) has a direct impact of process evaluations. I was keen to point people towards the paper by Somerville and Montgomery as it should be a real eye-opener to those not familiar with just how large an impact non-normality can be on capability estimates.
An audio version of the paper is available by clicking the play button below.
To download Adobe Acrobat (for free) click here.