Statistical Methods for Psychology

from the full model and the other sums of squares are as calculated before. Notice

also that there is one degree of freedom for the covariate, since there is one covariate; there

are (k 2 1) 5 (5 2 1) 54 dffor the adjusted treatment effect; and there are N – k – c 541 df

for error (where krepresents the number of groups and crepresents the number of

covariates).

From the summary table we see that On 4 dfthis gives us

. Dividing that term by 5 0.4909 we have F 5 4.698 on (4, 41)
df, which is significant at p ,.05. Thus we can conclude that after we control for individual
preinjection differences in activity, the treatment groups do differ on postinjection activity.

Adjusted Means

Since , we have rejected

and conclude that there were significant differences among

the treatment means after the effect of the covariate has been partialled out of the analysis.

To interpret these differences, it would be useful, if not essential, to obtain the treatment

means adjusted for the effects of the covariate. We are basically asking for an estimate of

what the postinjection treatment means would have been had the groups not differed on the

preinjection means. The adjusted means are readily obtained from the regression solution

using the covariate and treatments as predictors.

From the analysis of the revised full model, we obtained (see Table 16.8)

1 0.0738(T 4 ) 1 0.2183

YNij=0.4347(Pre) 2 0.5922(T 1 ) 1 0.0262(T 2 ) 1 0.8644(T 3 )

m 3 (adj)=m 4 (adj)=m 5 (adj)

F.05(4, 41)=2.61,Fobt=4.698 H 0 : m 1 (adj)=m 2 (adj) 5

MStreat(adj)=2.3060 MSerror

SStreat(adj)=9.2239.

SSresidual

Section 16.5 The One-Way Analysis of Covariance 605

Table 16.9 Summary tables for analysis of covariance

General Summary Table for One-Way Analysis

of Covariance

Source df SS

Covariate c

Treat (adj)

Residual

Total

Summary Table for Data in Table 16.7

Source df SS MS F

Covariate 1 38.3407 38.3407 78.108*

Treat (adj) 4 9.2239 2.3060 4.698*

Residual 41 20.1254 0.4909

Total 46 102.7689

Full Model:

*p,.05

YNij=0.4347(Pre) 2 0.5922(T 1 ) 1 0.0262(T 2 ) 1 0.8644(T 3 ) 1 0.0738(T 4 ) 1 0.2183

N 21

N 2 k 21 SSresidual(t,c)

k 21 SSregression(t,c) 2 SSregression(c)

SSregression(t,c) 2 SSregression(t)