A review of normal distributions and how to test their normality using a normality test.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Distributions: Normal
Six Sigma-Measure – Lesson 9
A review of normal distributions and how to test their normality using a
normality test.
Six Sigma-Measure #08 – Distributions: Overview
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted by any means
(electronic, mechanical, photographic, photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.

2. Normal Distributions (bell curve)
o Why is it called a “normal” distribution?
• “Normal” implies the typical randomness that we expect to occur in life.
• If there was no randomness, then we can presume there is some influence (bias or skewness).
• We want the data that we analyze to be unbiased, therefore we need to ensure it reflects the
“normal” randomness we would expect.
 Otherwise if the data is biased, then why analyze it if we can’t be confident we’ll find the right root cause?
o A normal distribution is bell-shaped.
• The bell shape is created because most
of the data points fall in the middle.
• The shape of the bell is influenced by
the mean and standard deviation.
o Characteristics of a normal distribution.
• Completely described by its mean and standard deviation.
• The tails on either end of the curve extend +/- infinity.
• The area under the curve represents 100% of possible observations.
• The curve is symmetrical where 50% of the data points fall on either side of the mean.
• The mean (average) will be relatively equal to the median (50th percentile).
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.

3. Normality Testing
o A distribution with a bell curve doesn’t necessarily mean it’s “normal”.
• It’s not uncommon for a distribution to appear normal, but it really isn’t.
• The normality of the distribution should be statistically tested.
o Use the Anderson-Darling test of a Normality Test or Probability Plot.
• A normality test or probability plot will plot the data on a logarithmic scale.
 In Minitab, go to Stat > Basic Statistics > Normality Test or go to Graph > Probability Plot
• Normal data will appear like a straight line; Minitab will try to fit a line along the data points.
 A “fat pencil” test is if a fat pencil can lay
across and cover all the data points, then
it’s probably a normal distribution.
• A better test is to examine the p-value
of the Anderson-Darling (AD) test.
 If p-value > 0.05, then it’s normal.
 If p-value < 0.05, then it’s not normal.
– In these examples, 0.05 is referring to the
alpha risk which is the % chance of being
right when concluding the data is normal.
5% is a commonly acceptable threshold.
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
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This p-value is > 0.05
which means it’s a
normal distribution

4. Practical Application
o Open the “Minitab Sample Data.MPJ” file and try to do the following:
• Run a normality test on each continuous metric.
• Which metrics are normally distributed? How can you prove it?
o Next, pull some historical data for at least 2 continuous metrics used by your
organization and try following the same steps described above.
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
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