I.     A Priori Comparisons

A. Planned in Advance

B. Derived from Theory and Hypotheses

C.Use t test for independent groups

1.              Formula:

2.              Recall that the bottom part of the formula is:

3.              Since there are 3 groups, there is a better estimate of the population variance, _________. So, if all ns are equal, formula becomes:

D.Example:

E. Appropriate when:

1.               

2.               

3.              If not,

II.  Post Hoc - A Posteriori Comparisons

A. Overview

1.              2 Situations

a)              Do experiment and see which groups are furthest apart

b)             Do all possible comparisons

2.              Either way, must correct for inflated probability values that occur when doing multiple tests

3.              Q or Studentized range Distributions

a)              Another frequency distribution

b)             Taking k samples of equal n from the same population (not just 2 like t test)

c)              Table G

4.              2 sources of Type I error

a)              Experiment-wise error - probability of making 1 or more type I errors for all comparisons within an experiment

b)             Comparison-wise error - probability of making a type I error in any given comparison

5.              Groups have equal ns

B. Tukey's Honestly Significant Difference (HSD) Test

1.              Calculate Qobt formula:

2.              Note: same as t test above, but it's Q because using Q distribution

3.              This maintains the experiment-wise error rate at alpha set for the ANOVA

4.              Must calculate Qobt for each possible comparison

5.              Compare Qobt to Qcrit from Table G

6.              Need alpha: set in advance, for the preceding ANOVA

7.              Df for MSw

8.              K = number of groups

9.              Example

C.Newman-Keuls Test

1.              Recall that Tukey's HSD maintains experiment-wise error

2.              Newman-Keuls maintains comparison-wise error

3.              Steps

a)              Rank order group means

b)             Calculate Qobt - same as Tukey's HSD

c)              Calculate r = number of means encompassed by the comparison

d)             Use df for MSw

e)              Determine Qcrit from Table G using df and r

D.Comparing A Priori, Tukey's HSD, and Newman-Keuls

1.              A Priori - most powerful because best chance of rejecting Ho

2.              Tukey's HSD - most conservative - least chance of rejecting Ho because controlling for experiment-wise error

3.              This leaves Newman-Keuls in the middle