Statistical Methods for Psychology

never had morphine (Condition S-M) or because they had received morphine in a different

context (Mc-M), with the mean of the other three groups (M-M, S-S, and M-S). We also

planned to compare group Mc-M with group M-M, and group M-S with group S-S, for the

same reasons given in the discussion of individual t tests. Finally, we planned to compare

group M-M with group S-S to see whether morphine tolerance developed to such an extent

that animals that always received morphine were no different after only four trials from an-

imals that always received saline. (As we will see shortly, these four contrasts are not inde-

pendent, but they answer substantive questions.) The analysis is shown in Table 12.2.

Each of these Fvalues can be evaluated against. As expected, the

first three contrasts are significant. The fourth contrast, comparing M-M with S-S, is not

significant, indicating that complete morphine tolerance seems to develop in as few as four

trials. (Be careful here, as I am acting as if I can prove the null hypothesis, when we know

that such is not possible.) Note that contrasts 2 and 3 test the same hypotheses that we

F.05(1, 35)=4.12

374 Chapter 12 Multiple Comparisons Among Treatment Means

Table 12.2 A set of a priori comparisons on morphine data

Groups: M-S M-M S-S S-M Mc-M

Means: 4.00 10.00 11.00 24.00 29.00

Coefficient

aj 213 2 1 3 1 3 1 2 1 2 0.833 18.167

bj 0 2 1 0012 19

cj 2 1 0 1002 7

dj 0121002 21

F=

MScontrast

MSerror

=

4.00

32.00

=0.125

SScontrast 4 =

nAadjXjB^2

ad

(^2) j =

8( 2 1)^2

2

=

8

2

=4.00

F=

MScontrast

MSerror

=

196.00

32.00

=6.125

SScontrast 3 =

nAacjXjB^2

ac

2

j

=

8(7)^2

2

=

392

2

=196.00

F=

MScontrast

MSerror

=

1444.00

32.00

=45.125

SScontrast 2 =

nAabjXjB^2

ab

2

j

=

8(19)^2

2

=

2888

2

=1444.00

F=

MScontrast

MSerror

=

3169.42

32.00

=99.04

SScontrast 1 =

nAaajXjB^2

aa

2

j

=

8(18.17)^2

0.8333

=

2641.19

0.8333

=3169.42

> > > > >

aaj^2 c= aajXj