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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 that if the distribution is not Normal, something must be wrong... for processes where a Normal distribution could not feasibly make sense. My feeling was that people were not looking clearly at the process. Instead, they looked to remove 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.

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