The data meets the necessary requirements for this test: two independent random samples
(need not be of the same size), ordinal measurement, (ranked as percentages), and similar
shaped distributions, although the dispersion of scores is less among upper-school
teachers (see Figure 7.3).
Figure 7.3: Plot of upper- and lower-
school teachers estimated percentage
of active learning maths lessons
The alternative hypothesis is non-directional (two-tailed, alpha set to 5 per cent) and
simply states that the distribution of scores in the two groups is different. This is
equivalent to saying the median scores are different, we can see from the box and whisker
plots that the median scores for the two groups are not the same but it is not possible to
judge from the plots whether this difference is statistically significant. The Wilcoxon M-
W test is therefore performed.
The computational steps are:
1 Combine the two samples and rank the entire data set, assign the rank 1 to the lowest
score. In the case of two or more raw score values being equal assign the average rank
to each.
2 Sum the rank scores for each group separately.
Statistical analysis for education and psychology researchers 222