This document discusses non-normal and bimodal distributions. It explains that non-normal distributions have bias or skewness, which can be caused by non-random sampling methods or processes influencing the results. The median is a better measure of central tendency for non-normal distributions. Bimodal distributions have two central tendencies, indicating observations from multiple populations. The document provides examples and instructs the reader to analyze sample data to identify normal and non-normal distributions using normality tests.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Distributions: Non-Normal
Six Sigma-Measure – Lesson 10
A review of non-normal and bi-modal distributions and how to test them
using a normality test.
Six Sigma-Measure #09 – Distributions: Normal
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. Non-Normal Distributions
o Non-normal distributions have bias or skewness.
• Since normal distributions reflect natural randomness in life, non-normal distributions are not
random and therefore have something influencing its results.
• The bias in the data can be caused by two possible things:
 The method for getting the sampled data was not random.
 The process itself (from which the sample is pulled) has something skewing it.
• Example: Measuring the life of 1000 batteries.
 What kind of distribution would you expect? If it’s non-normal, then what may be causing it?
 What are some things you would change to try to get a normal distribution?
o Measure central tendency with the median.
• Bias in the data can cause the mean to shift.
• The median (50th percentile) never shifts.
• What type of non-normal distribution is it?
 Many types of non-normal distributions exist (e.g., weibull, lognormal, gamma, logistic, etc.).
– To find out, go to Stat > Reliability/Survival > Distribution Analysis (Right) > Distribution ID Plot… (Not avail in Minitab 14)
– Select the distribution type with the highest correlation coefficient; it can also be run for discrete factors in a variable.
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.
This distribution
is non-normal
because the
p-value is < 0.05

3. Bimodal Distribution
o What is a bimodal distribution?
• These are distributions that appear to have two central tendencies (two bell curves).
 It’s possible to have more than two bell curves (multi-modality), but it’s not as common.
• These occur when observations are taken from different populations.
 Most things we measure do not have more than one central tendency. Therefore when we see this, it’s
most likely a sign that we are measuring observations from more than one population.
• Example: Examine the graphical summary of data below.
 What can you conclude
from this result?
 Is it a normal or non-
normal distribution?
 What’s the central tendency?
Is it reliable?
 How can this be fixed?
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.

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 non-normally distributed? How can you prove it?
• Which metric (if any) has multi-modality?
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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