each condition for the spatial and verbal tasks. Data from the authors’ paper is presented
in Table 8.10:
Table 8.10: Spatial imagery data
(^) Mean number correct per trial
(^) Eyes shut Blank screen Square Pattern
Spatial task 6.8 6.7 5.5 5.5
(1.0) (0.9) (1.2) (0.9)
Verbal task 4.6 4.6 4.4 4.8
(0.8) (1.2) (1.0) (0.9)
In this example there is one response variable (mean number of correctly recalled
sentences) and one repeated measures factor, interference, with four levels corresponding
to the four conditions. A One-way repeated measures ANOVA is therefore an appropriate
analytic procedure if the researchers want to determine whether there is a significant
interference effect-difference among condition means. To do this the researchers need to
compare subjects’ performance over the four experimental conditions (between treatment
groups). Differences between subjects within the conditions is not usually of interest in
this design. The treatments are counterbalanced to reduce serial effects (learning) from
one treatment to the next. Each subject takes all tasks and conditions and the general idea
is to see whether differences between condition means account for more variance than
differences between individuals within each of the four conditions. Differences in scores
among subjects as a whole are treated as a separate source of variance in this design.
The null hypothesis would be that variance between conditions is equal to the variance
between individuals within conditions. Should this be true it implies that differences
among condition means are no greater than chance variations, or stated another way the
condition means are equal. In this design, the total degrees of freedom (df) are the
number of measurements −1. Three subjects were assigned to each row of 4 trials (12
measures) and there were 4 experimental blocks giving 48 measures, total df is therefore
- The degrees of freedom for subjects is given by number of subjects −1=(12−1) 11,
and degrees of freedom for conditions is number of conditions −1=(4−1)3. The degrees
of freedom for error term is given by dftotal−dfbetween (^) conditions−dfsubjects,=(47− 3 −11)=33.
The authors reported a significant interference effect for the spatial task, F = 23.1, df
3,33, p<0.0001. They followed this F-test with a post hoc Newman-Keuls test on all
pairwise comparisons. This procedure is designed for equal sample sizes. Inspection of
these comparisons showed that performance on the square and changing-pattern
conditions was significantly poorer than in either of the other two conditions (p<0.01).
Worked Example
A subset of data is taken from an evaluation of a reading recovery programme and used
here to illustrate the principles and computational details of a repeated measures analysis.
In the recovery programme five children were tested for reading accuracy on three
occassions, when they entered the programme (Time 1); two weeks after entry (Time
two); and one month after entry (Time 3). All pupils remained in the programme for a
period of at least one month. The data is shown in Table 8.11.
Inferences involving continuous data 327