Statistical Analysis for Education and Psychology Researchers

multiple comparison tests for all possible pairwise comparisons and adjusts for
experimentwise error (see Figure 13, Appendix A3). The initial alpha level should be set
to a liberal level; output from this programme using the data from Table 7.7 is shown in
Figure 7.11.
Friedmans ANOVA by ranks test—worked example post hoc multiple
comparison tests between the groups
Significance is is based on an initial alpha of 0.1 (two-tailed test) but adjusted for
the number of pairwise comparisons tests
First
group

Second

group

Abs. diff in

mean ranks

SE Of

diff.

critical Z

value

Adjusted

alpha

sig. at

adjusted alpha

1 2 11.5 4.47214 2.39398 .0083333 yes

3 9.5 4.47214 2.39398 .0083333 no

1 4 9.0 4.47214 2.39398 .0083333 no

2 3 2.0 4.47214 2.39398 .0083333 no

2 4 2.5 4.47214 2.39398 .0083333 no

3 4 0.5 4.47214 2.39398 .0083333 no

Figure 7.11: Post hoc multiple

comparisons for Friedman’s ANOVA

by ranks using data from Table 7.7

(four repeated measures)

Interpretation

Looking at these pairwise comparisons, groups 1 and 2 are the only conditions that are
significantly different, the initial alpha level was set to 10 per cent in this analysis and the
pairwise comparisons should also be evaluated at this alpha level.

Summary

In this chapter six nonparametric tests based on rank data have been illustrated. These
nonparametric procedures are probably not used in educational research as often as they
should be. They are generally thought to be less powerful than their parametric analogues
although it is not widely known that under certain circumstances nonparametric statistical
tests can be as powerful or more powerful than their parametric counterparts. For this
reason alone researchers should be familiar with these procedures.
A well known problem with many parametric tests is that the assumption of
independence of sample observations should be met. Violation of this assumption
strongly influences statistical tests. It is generally less well known that certain
nonparametric tests are also subject to this assumption and are influenced by dependence
among initial scores. Any dependence amongst scores also results in dependence amongst
ranks (Zimmerman, 1993).
The general principle to follow when choosing a nonparametric rank test is the same
as that outlined in Chapter 1, use your judgment and common sense, consider what is

Statistical analysis for education and psychology researchers 246