Multiple Comparisons Test

Multiple Comparisons Tests

• Only used if the results of an ANOVA yield significant difference
• ANOVA results only indicate that a difference exits among means, not where the difference is
• Referred to as ad hoc or a posteriori test 
• Used after you know there is a significant difference from the ANOVA
• Several types of multiple comparisons tests
• Three broad categories
• Generic multiple comparisons test
• Control group test
• Multiple contrasts tests
• Generic Multiple comparisons test
• evaluate all possible pairs/combinations of means
• Tukey's HSD test
• Student-Newman-Keels (SNK) test
• Control Group test
• Evaluate differences between experimental group versus the control group
• Dunnett's test
• Multiple Contrats tests
• can be used like the traditional tests mentioned above to evaluate differences among pairs of mean but is better used to evaluate homogeneous groups of means against other such groups or individual means 
• Scheme Test
• Basic mechanics of Multiple Comparisons Test
• Observed Test Statistic
• SE=standard error
• Statistical Hypotheses
• A and B represent any pairs of means
• Pairwise comparisons 
• arranged in order from largest to smallest
• Calculate observed test statistic for each comparison
• Enclosure Rule
• If two mean are not different from each other then all means in between them are also not different from each other
• Similarities among different Multiple Comparisons Test
• All test involve pairwise comparisons of means
• Rank order the means for comparisons 
• Calculate an observed q value similar to the t test and z scores
• Compare with a critical value and reject or do not reject the null hypothesis for each pairwise comparison 
• Use the enclosure rule in all tests
• Differences among different Multiple Comparisons test
• how the means are rank order
• most test are two-tailed but control group tests can be one tailed test
• the SE term differs among tests 
• Mechanics 
• Arrange statistical hypotheses 
• Calculate test statistics= observed q
• Decisions rules and critical values
• Test 
• Tukey's HSD
• SNK
• Dunnett
• Scheme