Statistical Analysis for Education and Psychology Researchers

patterns. Fifty-six student teachers and forty-two practising teachers participated in the
study.
The authors do not specifically say anything about the distribution of scores for the
reception questionnaire but it can be assumed to be a continuous measure because a
Cronbach alpha (measure of internal consistency) was reported. The observation
schedule used by the investigators enabled teachers to be placed into one of seven
behaviour categories. Again nothing was reported about the specific measurement
assumptions underpinning the behaviour schedule but in the analysis it appears to have
been treated as an ordinal scale.
Considering the two different categories of teachers, the authors reported a significant
relationship between student-teachers’ classroom interaction patterns and their reception
of the science curriculum, rs=0.87, p<0.05 and, rather confusingly, reported that; ‘the
magnitude of correlation between practising teachers’ interaction patterns and their
reception of the science curriculum was low and not statistically significant (rs=0.21,
p<0.05)’ (p. 26). The authors presumably meant rs=0.21, p>0.05. It is preferable to quote
the actual p value as this avoids mistakes and misunderstandings.
In the above situation it is reasonable to assume that a two-tailed test was being used.
The null hypothesis was that there was no association between reception of the science
curriculum materials and teacher classroom interaction patterns. Here we have pairs of
sample observations, two measures per teacher (interaction patterns and reception) and
two distinct samples, student and practising teachers. Assuming the samples were random
and representative of defined populations of student and practising teachers, the
conclusions drawn from this analysis are that among student teachers there is a strong and
statistically significant relationship between their reception of the curriculum and
classroom interactions. However, this relationship is weak and statistically not significant
(at the 5 per cent level) among practising teachers.

Worked Example

Data abstracted from a study on school funding for non-statemented special education
needs is used to illustrate computation of Spearman’s rank order correlation. Marsh
(1995) gives for each of ten schools the percentage of pupils with free school meal
entitlements (%FSME) and the aggregated percentage cognitive abilities test (%CAT)
score for pupils who scored within the bottom 21 per cent on the CAT. This data is
shown in Table 7.1.

Table 7.1: FSME and CAT measures for ten

schools

School%FSME %CAT

A 24.0 24.1

B 24.3 21.8

C 15.3 23.3

D 40.8 36.4

E 10.7 8.4

F 6.3 13.1

Inferences involving rank data 209