questions about how helpful they thought the course would be with different aspects of
the writing process. Each response was scored on a scale from 1, ‘not at all helpful’ to 5
‘very helpful’. Data presented in the authors’ original paper is shown in Table 8.8.
Table 8.8: Students’ assessment of how helpful the
course would be in producing a piece of writing
(^) Product-centred COURSE Cognitive strategies Generative writing
Getting started 4.0(0.87) 4.5(0.78) 4.2(0.81)
In the middle 3.6(1.0) 3.9(0.92) 3.7(1.0)
Finishing off 3.5(0.97) 3.8(1.1) 3.3(1.2)
Developing thinking 3.7(0.92) 4.5(0.78) 4.2(0.98)
Expressing ideas 3.1(1.1) 3.8(0.87) 3.8(1.1)
- Differences between courses significant at p<0.01
This is an example of an independent One-way analysis of variance based on survey type
data. Mean responses across the three independent subgroups (represented by participants
who attended the three different writing courses) are compared. As five questions were
asked, there are five one-way ANOVAS (one for each question). The authors reported,
however, that there were significant differences for only two of the ANOV As (two
questions) among the three courses, Developing thinking: F=7.34 [df](2, 102), p<0.001;
and Expressing ideas: F=5.40 [df] (2, 98), p<0.01. The two hypotheses tested here were:
i) no differ-ences in mean scores across the three courses on students; response to the
question about Developing thinking; and ii) the same null hypothesis with respect to
Expressing ideas. The degrees of freedom between subgroups is given by the number of
groups−1=(3−1)=2, the total degrees of freedom would be n−1, and therefore the error
degrees of freedom are given by subtraction, dftot−dfbetween. In the authors’ original table
the sample sizes are not reported for each question mean, but it is evident from the
reported degrees of freedom in the two F-tests (102 and 98) that the number of responses
for at least two of the questions must have been different.
Once a significant F-test had been found, establishing that the three means
corresponding to the three writing courses were different, the investigators performed a
post hoc test, (called a Scheffe test) on pairwise comparisons of which there would be
three. The authors reported that these post hoc tests indicated that in both cases
(developing thinking and expressing ideas), the product-centred course was perceived as
being significantly less help than both the cognitive strategies course and the generative
writing course (p<0.05).
Worked Example
In a simplified example taken from a PhD student’s project on pupils’ understanding of
probability and cultural background, pupils’ attributions about chance events were
determined by asking them to respond to a series of statements, such as ‘Getting a 6 on a
normal dice depends on knowing how to throw the dice’. Attribution scores for eight
pupils from each of three separate religious communities, Christian, Muslim and Jewish
(24 pupils in total) are shown in Table 8.9.
Statistical analysis for education and psychology researchers 316