Nonparametric Statistics

Biostatistics BI 45, Saint Anselm College

 

Types of Non-parametric Tests

Non-parametric Tests Summary Table

Parametric Test

Assumptions of the parametric test

Non-parametric alternatives

Two independent (unpaired) samples Student's t test

1) data from both samples are randomly selected

2) data from both samples come from normally distributed populations

3) homogeneity of variance (variances are equal)

Mann-Whitney U test

Two dependent (paired) samples Student's t test

1) the differences (di) must come from a normally distributed population of differences)

Wilcoxon signed rank (paired samples or matched pairs) test

ANOVA

1) data from all samples are randomly selected

2) data from all samples come from normally distributed populations

3) homogeneity of variance (variances are equal)

Kruskal-Wallis H test

Pearson Product Moment Correlation Coefficient Analysis

1) Y data for each X must be randomly selected from a normal distribution of Y values

2) X data for each Y must be randomly selected from a normal distribution of X values

Spearman Rank Correlation Coefficient Analysis

 

 

Non-parametric equivalent of Student's t tests

 

Mechanics of the Mann Whitney U test - analogue of the Two Independent samples t test

 

Two-tailed Statistical Hypotheses
 
 

One-tailed Statistical Hypotheses

 
 
 
 
 
Calculating Observed U
 
 
 
 
 
 
 
 
Critical Value of U
 
 
 
 
 
Decision Rules - 2-tailed tests
 
 
 
 
 
Decision Rules - 1-tailed tests
 
 
 
 
 
 
 

 

Mechanics of the Wilcoxon Matched Pairs (or Signed Ranks, Paired Samples, Rank Sum) test - analogue of the Two Dependent samples t test (calculations are based on a comparison of the sums of the absolute values of the positive rankings, R, and negative rankings, S, of differences between samples)

 

 

Non-parametric equivalent of the ANOVA

 

Kruskal-Wallis test

 

Non-parametric equivalent of Correlation Coefficient

 

Spearman Rank Correlation Coefficient

 

 

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Trademark and Disclaimers

Copyright 2001 Jay Pitocchelli. All rights reserved. The contents of this page are the intellectual property of Dr. Jay Pitocchelli for distribution to students enrolled in Biostatistics BI 45 at Saint Anselm College. These pages may not be copied, photocopied, reproduced, translated, or published in any electronic or machine-readable form in whole or in part without prior written approval of Jay Pitocchelli. Students enrolled in Biostatistics BI 45 at Saint Anselm College have permission to print this material for their lecture notes. All formulae and critical values from: Zar, J. H. 1999. Biostatistical Analysis. (4th ed.). New Jersey, Prentice Hall.