Multiple Comparisons Tests

 

This is a summary of the mechanics necessary for each of the Post Hoc or Multiple Comparisons test covered in this course.

 

Tukey's HSD

Statistical hypotheses

Formulae

Decision rules

Student Newman Keuls

Statistical hypotheses

Formulae

Decision rules

Dunnett's test

Statistical hypotheses

Formulae

Decision rules

Scheffe test

Statistical hypotheses

Formulae

Decision rules

SS-STP

Statistical hypotheses

Formulae

Decision rules

 

Tukey's HSD

 

Statistical Hypotheses

 

 

Formula for q statistic

 

 

 

 

Critical Values and Decisions to Reject/NotReject

 

 

Example from Zar (1999)

 

Student-Newman-Keuls Test (SNK)

 

Statistical Hypotheses

 

 

Formula for q statistic

same as Tukey test - see above

 

Critical Values and Decisions to Reject/NotReject

 

p = range of means being compared

 

Example from Zar (1999)

 

Dunnett's Test

 

Statistical Hypotheses: Two-Tailed Test

 

 

Statistical Hypotheses: One-Tailed Tests

 

 

Formula for q' statistic

 

 

 

Equal sample sizes

 

Unequal sample sizes

 

Critical Values and Decisions to Reject/NotReject

 

 

Example from Zar (1999)

 

Scheffe's Test

 

Statistical Hypotheses - Multiple Hypothesesfor various comparisons between means

 

Comparing two means

Comparing one mean against two means

Comparing three means against two means

Formula for S statistic

 

Comparing two means

 

Comparing various combinations of means

 

 

Critical Values and Decisions to Reject/NotReject

 

 

Example from Zar (1999)

 

Simultaneous Sums of Squares Test Procedure(SS-STP)

 

Statistical Hypotheses

same as Scheffe's test - see above

 

Formula

 

 

Comparing two means

 

 

Comparing one mean against a group of means

 

 

Comparing various combinations of means

 

 

 

Critical Values and Decisions to Reject/NotReject

 

 

 

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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.