An extension on hypothesis testing, this lesson explains what nonparametric tests are and how they’re used for non-normal distributions.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Hypothesis Testing: Central Tendency –
Non-Normal (Nonparametric Tests Overview)
Six Sigma-Analyze – Lesson 19
An extension on hypothesis testing, this lesson what nonparametric tests are
and how they’re used for non-normal dist.
Six Sigma-Analyze #18 – Hypothesis Testing: Central Tendency –
Normal (Compare 2+ Factors)
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. Is the data type for both values discrete?
What are you measuring?
Is the data normal?
SpreadCentral Tendency
Compare 1:Standard
1 Proportion Test
Compare 1:1
2 Proportion Test
Compare 2+ Factors
Chi2 Test
Compare 1:Standard
1 Sample T Test
Compare 1:1
2 Sample T Test
or Paired T Test
Compare 2+ Factors
One-way ANOVA Test
Compare 1:Standard
1 Sample Wilcoxon
or 1 Sample Sign
Compare 1:1
Mann-Whitney Test
Compare 2+ Factors
Mood’s Median Test
or Kruskal-Wallis Test
Compare 1:Standard
1 Variance Test
Compare 1:1
2 Variance Test
Compare 2+ Factors
Test for Equal Variances
Yes No
Yes No
Proportions
Compare 1:1
Pearson Correlation
or Fitted Line Plot
Compare 2+ Factors
Multiple Regression or
General Linear Model
Is the data type for both values continuous?
Relationships
No Yes
Review Finding the Right Statistical Test
o Nonparametric tests are typically used for non-normal distributions.
• The type of statistical test depends on the data to be tested, as described in the chart below:
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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Lesson
Current

3. Nonparametric Tests
o What are nonparametric tests?
• They are statistical tests that don’t require the distribution to have certain
parameters such as a normal distribution with parameters μ and σ.
 Since nonparametric tests don’t require these parameters typical for normal
distributions, they can be very powerful when testing non-normal distributions.
o If non-normal distributions have bias, then why should we test them?
• For the most part, non-normal distributions may have bias or be skewed
from the collected sample. But this may not always be the case.
 It’s more ideal to run statistical tests designed for normal distributions.
• Should the process being measured have a normal distribution?
 If YES, then ask…
– Is the method used for collecting the sample data random and unbiased?
– Does the measurement extend across multiple, different processes?
– If YES to either of these questions, then fix the method for collecting the sample and re-collect it.
 If NO, then it may be appropriate to continue the hypothesis testing using nonparametric tests.
– Measurements that don’t extend below zero are more likely to be non-normally distributed. For example…
» Measurements of time that start at zero, like call duration or handle time.
» Measurements of dollars that start at zero, like salaries or home values.
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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4. Practical Application
o Refer to the critical metric (output Y) and at least 5 factors (input X’s) you identified in
a previous lesson for applying to this hypothesis testing.
• For any continuous factor that has a non-normal distribution, should the process that the metric
is measuring have a normal distribution?
 If YES, then…
– Is the method used for collecting the sample data random and unbiased?
– Does the measurement extend across multiple, different processes?
– If YES to either of these questions, then fix the method for collecting the sample and re-collect it.
 If NO, then it may be appropriate to continue the hypothesis testing using nonparametric tests.
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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