Statistical Analysis for Education and Psychology Researchers

(^) Understanding of Educational Issues
(^) An increase reported No increase reported
Gender: Total
Male 21 27 48
Female 10 69 *49
Total 31 96 127

Figure 6.1: Number of former students

reporting increased understanding of

educational issues as an effect of the

MEd programme

*see Comment on the Analysis below

The investigators reported that there were some interesting gender differences in the
teachers’ responses. Males reported an increased understanding of educational issues

more frequently than did females, ( means a Chisquare
with 1df).
In this study the investigators used a χ^2 test of independence with a fixed total sample
size of 127 but random observed row and column marginal totals. Each subject was
categorized on two variables, reported understanding of educational issues (increased/not
increased) and gender (male/female). The distribution of frequencies in each of the four
cells was recorded in a 2×2 contingency table, see Figure 6.1. The research question
addressed was whether, after the MEd programme, there was any association between
increased understanding of educational issues and gender? Put another way this
alternative hypothesis could be stated as: There is a statistical relationship between
increased understanding of educational issues and gender following completion of an in-
service MEd programme.
It would follow that if understanding and gender are related, then the row and column
proportions would not be independent. That is the probability that a member of the
population reported increased understanding and the probability that the person is a male
would not be independent.
The null hypothesis tested by the investigators was that of no interaction between the
row and column variables, namely increased understanding and gender. If the null
hypothesis were true, the row and column variables would be independent (no
interaction) and there would be no significant differences between observed cell
frequencies and expected cell frequencies.

Comment on the Analysis

The three measurement assumptions are clearly met, namely, data is in the form of
observed frequency counts; observations are assumed to be independent (the probability
of reporting does not depend on gender); and each observation falls into only one cell of
the contingency table. The sampling assumption, namely respondents are representative
of part-time MEd students, in the absence of any data to suggest otherwise can also be

Statistical analysis for education and psychology researchers 166