Statistical Methods for Psychology

If we drop the interaction terms representing the interaction of the covariate (Distract) with

the Task 3 Group interaction, we have

5 36389.60175

The difference between these two sums of squares 5 338.82097. The most complete model

had 13 degrees of freedom, while the second had 9 df, meaning that the above sum of

squares is based on 13 29 54 df. Converting to mean squares we have

We can test the difference between these two models by using from the more

complete model and computing

This is an Fon [(f 2 r), (N 2 f 2 1)] 5 4 and 121 df. The critical value is

, so we will not reject the null hypothesis of homogeneity of regression.

We will conclude that we have no reason to doubt that the regression lines relating Errors

to Distract have the same slope in the nine cells. This will allow us to adopt a much

F.05(4, 121)=2.45

F=

MSdifference

MSresidual

=

84.70524

71.10333

=1.19

MSresidual

MSdifference=338.82097> 4 =84.70524.

SSregressionc,a,b,ab

Section 16.9 The Factorial Analysis of Covariance 615

Table 16.12 Design matrix for the analysis of covariance for smoking data

CT 1 T 2 G 1 G 2 TG 11 TG 12 TG 21 TG 22 cTG 11 cTG 12 cTG 21 cTG 22

107101 01000107 0 0 0 9

97101 0100097 0 0 0 10

101100 10100 0101 0 0 12

118100 10100 0118 0 0 16

641021 21 21 2100264 26400 8

1231021 21 21 21002123 2123 0 0 10

126011 00010 0 0126 0 27

143011 00010 0 0143 0 49

113010 10001 0 0 0113 48

X 5 Y 5

96010 10001 0 0 0 96 49

1080121 210021 21002108 2108 34

1320121 210021 21002132 2132 47

110 21 2110210102110 0 2110 0 15

116 21 2110210102116 0 2116 0 13

93 21 2 101 0 210210293 0 293 7

102 21 2 101 0 2102102102 0 2102 11

130 21 21 21 211111130130130130 3

114 21 21 21 211111114114114114 3