Statistical Methods for Psychology

we will solve for and refer that to Dunn’s tables. Taking the pairwise tests first, the

calculations follow.

Mc-M versus M-M:

S-S versus M-S:

M-M versus S-S:

The calculations for the more complex contrast, letting the , 1 3, 1 3, 2 1 2, 212

as before, follow.

S-M and Mc-M versus M-M, S-S, and M-S:

From Appendix , with c 5 4 and 5 35, we find by interpolation. In

this case, the first and last contrasts are significant, but the other two are not.^8 Whereas we

earlier rejected the hypothesis that groups S-S and M-S were sampled from populations

with the same mean, using the more conservative Bonferroni ttest we are no longer able to

reject that hypothesis. Here we cannot conclude that prior morphine injections lead to

hypersensitivity to pain. The difference in conclusions between the two procedures is a di-

rect result of our use of the more conservative familywise error rate. If we wish to concen-

trate on per comparison error rates, ignoring FW, then we evaluate each t (or F) against the

critical value at a5.05. On the other hand, if we are primarily concerned with controlling

FW, then we evaluate each t, or F, at a more stringent level. The difference is not in the

arithmetic of the test; it is in the critical value we choose to use. The choice is up to the

experimenter.

Multistage Bonferroni Procedures

The Bonferroni multiple-comparison procedure has a number of variations. Although

these are covered here in the context of the analysis of variance, they can be applied

equally well whenever we have multiple hypothesis tests for which we wish to control

the familywise error rate. These procedures have the advantage of setting a limit on the

FWerror rate at aagainst any set of possible null hypotheses, as does the Tukey HSD

(to be discussed shortly), while at the same time being less conservative than Tukey’s test

t¿ dferror t¿.05(35)=2.64

t¿=

aajXj

B

aa

2

jMSerror

n

=

A^12 B(24) 1 Á 1 A-^13 B(4)

B

(0.833)(32.00)

8

=

18.167

1 3.3333

=9.95

aj= 1 > 3 > > > >

t¿=

Xi 2 Xj

B

2 MSerror

n

=

10.00 2 11.00

B

(2)(32.00)

8

=

- 1

18

=-0.35

t¿=

Xi 2 Xj

B

2 MSerror

n

=

11.00 2 4.00

B

(2)(32.00)

8

=

7

18

=2.47

t¿=

Xi 2 Xj

B

2 MSerror

n

=

29.00 2 10.00

B

(2)(32.00)

8

=

19

18

=6.72

t¿

12.3 A Priori Comparisons 379

(^8) The actual probabilities would be .000, .073, 1.00, and .000.