Statistical Analysis for Education and Psychology Researchers

The mean square for between conditions (over the three occasions): MS(bet) is
SS(bet)/df(bet)=107.2000/2=53.6. Mean square error is calculated in exactly the same way
for MS(subj) and MS(error): MS(subj)=SS(subj)/df(subj)=33.733/4= 8.433;
MS(error)=SS(error)/df(error)=29.467/8=3.6834.

Step 4: Calculate F-ratios

The main hypothesis of interest is whether there are any differences in reading accuracy
over the period in which pupils were in the reading recovery programme, that is whether
mean scores differ over time. A test of this hypothesis is given by the F-test statistic
which is MS(bet)/MS(error) =53.6/3.6834=14.5518. If we assume no interaction between
subjects and measurement occasions, the hypothesis of overall differences among
subjects is tested by the F-statistic which is MS(subj)/MS(error)=8.433/3.6834 =2.2895.

Interpretation

The F-statistics are interpreted as usual (see previous worked example). For the between
conditions effect, the critical value of F at the 5 per cent level with 2 and 8 df is 4.46.
Since the obtained F of 14.55 (rounded) is larger than this we can reject the null
hypothesis and conclude that there are significant differences in reading accuracy over
the three measurement occasions; F=14.55; df 2,8; p< 0.05. For subjects, the critical F-
value is 3.84, since the observed value of 2.29 is less than this we can conclude that
overall, differences among subjects are not statistically significant. Results of these tests
can be presented in a summary table as follows:

Table 8.12: Summary table for One-way repeated

measures ANOVA

Source of variation Degrees of freedom SS MS F

Between occasions 2 107.200 53.60F=14.55; df 2, 8

Subjects 4 33.733 8.433F=2.29; df 4, 8

Error 8 29.467 3.6834

Corrected total 14 170.400

Computer Analysis

The following SAS code performs a One-way repeated measures ANOVA on the data
presented in Table 8.11.

data a;

input subj t1 t2 t3;

cards;

1 8 7 4

2 7 8 5

3 9 5 3

4 5 4 6

5 6 6 2

Statistical analysis for education and psychology researchers 330