# Non-Parametric Resources

## General Resources

This module, published by the Boston University School of Public Health, introduces non-parametric statistical tests and when they should be used, followed by tutorials on several tests.

Statistics Review 6: Nonparametric Methods

This paper from the Critical Care Journal includes a short applied overview of the Sign Test, the Wilcoxon Signed Rank Test, and the Wilcoxon Rank Sum Test, followed by examples.

An Overview of Non-parametric Tests in SAS: When, Why, and How

This paper from Duke Clinical Research Institute goes over when to use non-parametric tests, followed by a brief explanation and example SAS code for the Sign Test, the Wilcoxon Signed Rank Test, the Wilcoxon Rank Sum Test, the Kruskal-Wallis Test, and the Kolmogorov-Smirnov Test.

## Sign Test Resources

A detailed Minitab example from the University of New Mexico.

#### R

Documentation for the BDSA R package Sign Test. Contains a brief description of the function, followed by R code examples.

Example code for the Sign Test using both the BDSA package function 'Sign.test' and base R, with brief explanations of each. Written by Avril Coghlan.

#### SAS

SAS Univariate Procedure: Testing for Location

Brief annotated example of a one-sample Sign Test with output in SAS.

## Wilcoxon Signed Rank Test Resources

#### General

Non-parametric Tests and Confidence Intervals (pdf)

This resource from University of New Mexico covers both the theory and application of the Wilcoxon Signed Rank Test. Examples are in R.

#### Minitab

Wilcoxon Signed Rank Test Using Minitab by Laerd Statistics

This guide lays out the assumptions and Minitab procedure for the Wilcoxon Signed Rank Test and how to interpret the printed output.

#### R

Documentation for the R base Wilcoxon Signed Rank Test function. Contains a brief description, followed by R code examples.

#### SAS

Wilcoxon Signed Rank Test in SAS

Basic overview with a worked through example in SAS.

#### SPSS

Wilcoxon Signed-Rank Test using SPSS Statistics by Laerd Statistics

This guide lays out the SPSS procedure for the Wilcoxon Signed Rank Test and how to interpret the printed output.

## Wilcoxon Rank Sum Test/Mann-Whitney U Test/Wilcoxon-Mann-Whitney Test Resources

#### General

The Wilcoxon Rank Sum Test (pdf)

This resource from Chris Wild, University of Auckland, contains detailed, worked-through examples of the Wilcoxon Rank Sum Test.

#### Minitab

Minitab Example of Mann-Whitney Test

A short guide to the procedure and output interpretation for Wilcoxon Rank Sum/Mann-Whitney U Test in Minitab.

#### R

The Wilcoxon Rank Sum Test in R, by Clay Ford, University of Virginia Library

Brief overview of the Wilcoxon Rank Sum test assumptions and procedure, with a detailed example based in R.

#### SPSS

Mann-Whitney U Test in SPSS by Laerd Statistics

This guide lays out the SPSS procedure for the Wilcoxon Rank Sum/Mann-Whitney U Test and how to interpret the printed output.

SPSS: The Mann-Whitney U Test (pdf)

A brief introduction to the Wilcoxon Rank Sum/Mann-Whitney U Test procedure, followed by an SPSS tutorial.

## Kruskal-Wallis Test Resources

#### Minitab

Minitab Overview for Kruskal-Wallis

Short explanation of when to use Kruskal-Wallis with brief Minitab instructions.

Minitab Example of Kruskal-Wallis

Minitab procedure and output interpretation.

#### R

Brief Kruskal-Wallis Test example in R.

Documentation for the R base Kruskal-Wallis Test function. Contains a brief description and several R code examples.

#### SPSS

Kruskal-Wallis Test in SPSS by Laerd Statistics

This guide lays out the assumptions and SPSS procedure for the Kruskal-Wallis Test and how to interpret the printed output.

### Post-Hoc Multiple Comparisons Testing for the Kruskal-Wallis Test

#### Dunn's Test

Instructions for downloading and using the macro, interpreting the output, followed by an explanation of Dunn's Test.

Brief instructions on running Dunn's Test in SPSS.

Documentation for the dunn.test R package Dunn's Test. Contains a brief description of the function, and several R code examples.

Kruskal-Wallis Multiple Comparison Macro

Links to a Dunn's Test SAS Macro, and two examples from Alan C. Elliot and Linda S. Hynan, UT Southwestern Medical Center.

#### Conover-Iman Test

Not currently available in SAS, SPSS, or Minitab.

Documentation for the conover.test R package. Contains a brief explanation of the Conover-Iman Test, a description of the function, several R code examples, and a description of the example data included in the package.

## The Friedman Test Resources

#### R

Basic overview of the Friedman Test, with an annotated example. Written by Ellen Marshall and Basile Marquier, Sheffield University.

Documentation for the R base Friedman Test function. Contains a brief description and several R code examples.

#### SAS

Basic SAS tutorial for Chi-Squared based Friedman Test, to be used for large samples.

#### SPSS

The Friedman Test in SPSS: Laerd Statistics

This guide lays out the assumptions and SPSS procedure for the Friedman Test and how to interpret the printed output.

### Post-hoc Multiple Comparison Testing for the Friedman Test

#### Conover's Test

Not available in SPSS or Minitab.

The Pairwise Multiple Comparison of Mean Ranks Package.

R function vignette which shows the calculations used in post-hoc testing for the Friedman Test.

## Quade Test Resources

#### R

Detailed R example, with information on background, assumptions and interpretation.

Documentation for the R base Quade Test function. Contains a brief description and several R code examples.

#### SPSS

Can SPSS do a Non-parametric or Rank Analysis of Covariance (Quade's Test)?

Instructions on running the Quade Test in SPSS. This can be method can be applied to other programs.

### Post-Hoc Multiple Comparison Testing for Quade Test

Not available in SPSS, SAS, or MInitab.

The Pairwise Multiple Comparison of Mean Ranks Package.

R function vignette which shows the calculations used in post-hoc testing for the Quade Test.

## Spearman's Rank Correlation Coefficient Resources

#### General

Statstutor: Spearman's Correlation (pdf)

Excellent introduction to Spearman’s Rank Correlation, with visuals. Also goes over the interpretation of SPSS output.

A Comparison of the Pearson and Spearman Correlation Methods

Visual explanation of both Pearson and Spearman’s Correlation.

How To Do Spearman Correlation in Excel

Goes over when to use Spearman’s Rank Correlation, the procedure for calculating it, and how to calculate it in Excel.

#### Minitab

Spearman's Correlation using Minitab: Laerd Statistics

This guide lays out the procedure for calculating Spearman's Correlation in Minitab and how to interpret the printed output.

#### R

Documentation for the R base correlation function. This function can output the Spearman's correlation coefficient. Contains a brief description and R code example.

Documentation for the R base correlation test function. This function tests for significance of the Spearman's correlation coefficient. Contains a brief description and R code example.

#### SAS

SAS Example - Correlation Coefficients

Example code for calculating Pearson, Spearman, and Kendall's Correlation with Fisher transformation based confidence intervals.

#### SPSS

Spearman's Correlation using SPSS: Laerd Statistics

This guide lays out the assumptions and procedure for calculating Spearman's Correlation in SPSS and how to interpret the printed output.

## Kendall's Tau/Kendall Correlation Coefficient/Kendall's Coefficient of Concordance Resources

#### General

Kendall’s Tau Correlation: Excel

A brief explanation of the procedure for calculating Kendall's Tau, with links to tutorials on running it in Excel.

Kendall's Tau-b using SPSS: Laerd Statistics

This guide lays out the assumptions and SPSS procedure for Kendall's Tau, how to interpret the printed output and report the results.

Significance Test for Kendall's Tau-b in R

This tutorial gives a brief introduction to Kendall's Tau, followed by annotated R code for computing the correlation and testing its significance.

SAS Example - Correlation Coefficients: Penn State University

Example code for calculating Pearson, Spearman, and Kendall's Correlation with Fisher transformation based confidence intervals.