Nonparametric Test Flowcharts

In general, the power of parametric tests are greater than the power of the alternative nonparametric test. As the sample size increases and becomes larger, the power of the nonparametric test approaches it parametric alternative.

Nonparametric test also assume that the underlying distributions are symmetric by not necessarily normal. When the choice exist on whether to use the parametric or nonparametric test, if the distribution is fairly symmetric, the standard parametric test are better choices than the nonparametric alternatives.

For example, if you are not sure if two data sets are normally distributed it may be safer to substitute the Mann-Whitney test to reduce the risk of drawing a wrong conclusion when testing two means. 


When to use

  • Data can not be assumed to meet normality assumptions and can not be practically transformed to approximate normality.
  • With qualitative data of nominal scale or ranked data of ordinal scale.
  • When comparing Median values for skewed data (such as right or left skewed data). See Histograms for more insight on skewed data.
  • When there are very few, if any, assumptions regarding the shape of the distribution. However, if there is a bi-modal distribution, the data should be reviewed and separated to correctly analyze the true process performance. Don't be forceful or careless and rush into a nonparametric test when there is clearly two (or more) unique situations in within the data. Use the Runs Test to verify the nonnormality is related to random causes and not a results of special causes.  

Comparables to Parametric Tests

A sample and a target (or given value) 

Parametric - One Sample t test (testing means)

Nonparametric - One Sample Wilcoxon or One Sample Sign (testing medians)

Two independent samples 

Parametric - Two Sample t test (testing means)

NonParametric - Mann-Whitney (testing medians)

>2 independent samples

Parametric - ANOVA (testing means)

NonParametric - Mood's-Median or Kruskal-Wallis Test (testing medians)


Use the Runs Test to examine the randomness of the data


Refresher

Follow these steps when you believe the data does not meet normality assumptions:

  • Attempt to transform the data such as through a Box-Cox transformation.
  • Use the Runs Test to verify the data the is random (void of special causes)
  • If the transformation doesn't work, the apply the nonparametric test

 




Return to BASIC STATISTICS

Return to Hypothesis Testing

Templates and Calculators

Search Six Sigma related job openings

Return the Six-Sigma-Material.com Home Page


 Site Membership
CLICK HERE


Six Sigma Green Belt Certification
Black Belt Certification

Six Sigma

Templates & Calculators


Six Sigma Modules

The following presentations are available to download.

Click Here

Green Belt Program (1,000+ Slides)

Basic Statistics

SPC

Process Mapping

Capability Studies

MSA

Cause & Effect Matrix

FMEA

Multivariate Analysis

Central Limit Theorem

Confidence Intervals

Hypothesis Testing

T Tests

1-Way Anova Test

Chi-Square Test

Correlation and Regression

SMED

Control Plan

Kaizen

Error Proofing


Advanced Statistics
in Excel

Advanced Statistics in Excel

Six Sigma & Lean Courses

Agile & Scrum Online Course