RESEARCH METHOD COHEN ok

554 QUANTITATIVE DATA ANALYSIS
in question has afforded them the opportunity to
learn at their own pace.
In reporting the Mann-Whitney test one could
use a form of words such as the following:
When the Mann-Whitney Wallis statistic was
calculated to determine whether there was any
statistically significant difference in the voting
of the two groups (U = 2732.500, ρ = 0.019), a
statistically significant difference was found between
the males and females. A cross-tabulation found that
males felt more strongly than the females that the
course in question had afforded them the opportunity
to learn at their own pace.
(See http://www.routledge.com/textbooks/
9780415368780 – Chapter 24, file SPSS Manual
24.11.)
For two related samples (e.g. the same group
voting for more than one item, or the same
grouping voting at two points in time) the
Wilcoxon test is applied, and the data are
presented and analysed in the same way as the
Mann-Whitney test. For example, in Boxes 24.54
and 24.55 are two variables (‘The course was just
right’ and ‘The lecturer was well prepared’), voted
on by the same group. The frequencies are given.
Is there a statistically significant difference in the
voting
As it is the same group voting on two
variables, the sample is not independent, hence
the Wilcoxon test is used. Using SPSS output, the
data analysis shows that the voting of the group
on the two variables is statistically significantly
different (Boxes 24.56 and 24.57).
The reporting of the results of the Wilcoxon
test can follow that of the Mann-Whitney test.
For both the Mann-Whitney and Wilcoxon
tests, not finding a statistically significant
difference between groups can be just as important
as finding a statistically significant difference
between them, as the former suggests that nominal
characteristics of the sample make no statistically
significant difference to the voting, i.e. the voting
is consistent, regardless of particular features of the
sample.
The Kruskal-Wallis and the Friedman tests
The non-parametric equivalents of analysis of
variance are the Kruskal-Wallis test for three
Box 24.54
Frequencies and percentages of variable one in a Wilcoxon test
The course was just right
Valid
Strongly disagree Disagree Neither agree nor disagree Agree Strongly agree Total
Frequency 2 14 65 76 34 191
Valid percent 1.0 7.3 34.0 39.8 17.8 100.0
Box 24.55
Frequencies and percentages of variable two in a Wilcoxon test
The lecturer was well prepared
Valid
Strongly disagree Disagree Neither agree nor disagree Agree Strongly agree Total Total
Frequency 3 5 25 85 72 190 191
Valid percent 1.6 2.6 13.2 44.7 37.9 100.0