Table 8.9: Attribution scores for three religious
groups
(^) Religious Community
(^) Christian
Religion Group 1
Muslim
Religion Group 2
Jewish
Religion Group 3
17 22 18
19 19 13
18 22 18
17 19 20
18 19 12
15 14 15
16 15 17
17 14 18
TOTAL 137 144 131
Mean 17.125 18.000 16.375
Data summarizing ANOVA computations are usually presented in an ANOVA table
which identifies the sources of variance, sums of squares and degrees of freedom, means
squares and F-statistics. (See for example, Figure 8.13.)
Source of variation Degrees of Freedom
(df)
SS MS
(SS/df)F
(MSmod/MSerror)
Between groups (MODEL)k− 1
Within individuals
(ERROR)CORRECTED TOTAL N− 1
Where:
SS Is the sums of squares
MS Is the mean square, sums of squares divided by the degrees of freedom
F Is the ratio of MS effect to MS error
k Is the number of independent groups (treatments or subgroups)
N Is the total number of observations in the analysis
nj Is the number of observations in the jth group (subgroup or treatment)Figure 8.13 Layout of results table for
One-way ANOVA
Consider for example the data presented in Table 8.9. The df(between groups) is (3–1)=2. A
degree of freedom is lost because deviations from the overall mean sum to zero. The
constraint here is that the deviations of the subgroup means from the overall mean must
sum to zero hence 1 df is lost. The degrees of freedom between individuals within
groups, what is usually termed df(error), is again given by the constraint that deviations
from each subgroup mean sum to zero. Here there are three subgroup means so the df are:
(n 1 –1)+(n 2 –1)+(n 3 –1)=(8–1) +(8−l)+(8−1)=21. The error degrees of freedom can be
evaluated simply by subtraction, df(error)=df(corrected total)−df(between groups)=(24–1)−2=21. The
Inferences involving continuous data 317