Statistical Analysis for Education and Psychology Researchers

(treatments) and each subject takes all tests (treatments—the repeated measures). The
usual ANOVA assumptions should be met. Often the type of subjects in a design are of
particular interest and the investigator wants to compare the effects of treatments for
different subcategories, such as sex, age groups, or different types of learning difficulty.
In this case different subjects are required hence the between subjects factor. However,
the same subjects in a subgroup will appear in the different treatment conditions or
different measures over time if the design is intended to examine differences between
pre-test, post-test and delayed post-test mean scores.

Example from the Literature

Teacher researchers have shown that a substantial proportion of teachers report high
levels of occupational stress, the main stressors being work conditions, pupils’ behaviour,
staff relationships and pressure of time. In a study to investigate the relationship between
teachers’ cognitive style and stress, Borg and Riding (1993) surveyed 212 secondary
school teachers in Malta. The investigators performed a split-plot ANOVA to determine
whether there was any interaction between teachers’ perception of four stressors (pupil
misbehaviour, poor staff relationships, poor working conditions, time pressure), the
within subjects factor, and cognitive style between subjects factor (wholists vs. analytics).
They reported a highly significant within-subjects factor, teacher perception of stress,
F=20.31, df 3,312, p<0.001, which indicated that teachers’ stress factor perceptions
differed. No post hoc tests were reported, but the authors commented that the most
stressful factor for the group of teachers was pupil misbehaviour. A significant
interaction between stress and cognitive style was also reported, F=3.13, df3, 312,
p=0.026. The authors examined plots of simple effects and concluded that ‘Analytic
thinkers reported greater stress than wholists for “pupil misbehaviour” and “working
conditions” but the converse was true for “poor staff relations” and “time pressure”.’ The
authors reported no significant between-subjects effect (for the wholist-analytics
comparison).
Data referred to in an earlier section taken from a student’s thesis study on
augmentation and children’s vocabulary acquisition is used to illustrate computer analysis
of a split-plot ANOVA. Children were read a story based on a folktale containing target
words on which they would be tested. The target words did not occur naturally in the
story; they replaced easier words, such as ‘pinnacle’ for ‘top’. The fourteen target words
consisted of eight nouns, three adjectives and three verbs. Each pupil was tested
individually on three occasions: one week before the story was read to them by the
teacher, (Time 1); shortly after the storytelling by the teacher (Time 2); and two weeks
after the storytelling (Time 3). In the test situation a choice of six alternative words was
provided, one of which was similar in meaning to the target word. A score of 1 was given
for each correct answer. Boys and girls were treated as a between-subjects factor in the
analysis. Data from ten subjects is shown in Table 8.15.

Table 8.15: Vocabulary acquisition data for split-

plot analysis

Factor
(Sex)

Subjects Before story

(Time1)

Factor (Time) Shortly after

story (Time2)

Delayed post-test

(Time3)

Statistical analysis for education and psychology researchers 338