RESEARCH METHOD COHEN ok

MEASURES OF DIFFERENCE BETWEEN GROUPS AND MEANS 555
Box 24.56
Ranks and sums of ranks in a Wilcoxon test
The lecturer was well
prepared – the course was
just right
Negative ranks
Positive ranks
Ties
Total
Ranks
N Mean rank Sum of ranks
20 a
89 b
81 c
190
50.30
56.06
1006.00
4989.00
Chapter 24
a. the lecturer was well prepared < the course was just right
b. the lecturer was well prepared > the course was just right
c. the course was just right = the lecturer was well prepared
Box 24.57
Significance level in a Wilcoxon test
Test statistics b
The lecturer was
well prepared – the
course was just right
Z
−6.383 a
Asymp. sig. (2-tailed) 0.000
a. Based on negative ranks
b. Wilcoxon Signed Ranks Test
or more independent samples and the Friedman
test for three or more related samples, both
for use with one categorical variable and
one ordinal variable. These enable us to see,
for example, whether there are differences
between three or more groups (e.g. classes,
schools, groups of teachers) on a rating
scale (see http://www.routledge.com/textbooks/
9780415368780 – Chapter 24, file 24.20.ppt).
These tests operate in a very similar way to
the Mann-Whitney test, being based on rankings.
Let us take an example. Teachers in different
groups, according to the number of years that
they have been teaching, have been asked to
evaluate one aspect of a particular course that
they have attended (‘The teaching and learning
tasks and activities consolidate learning through
application’). One of the results is cross-tabulation
shown in Box 24.58. Are the groups of teachers
statistically significantly different from each other
We commence with the null hypothesis (‘there
is no statistically significant difference between
the four groups) and then we set the level of
significance (α) to use for supporting or not
supporting the null hypotheses; for example we
could say ‘Let α = 0.05’.
Is the difference in the voting between the
four groups statistically significantly different
The Kruskal-Wallis test calculates and presents
the following in SPSS (Boxes 24.59 and
24.60).
The important figure to note here is the 0.009
(‘Asymp. sig.) – the significance level. Because
this is less than 0.05 we can conclude that the null
hypothesis (‘there is no statistically significant
difference between the voting by the different
groups of years in teaching’) is not supported, and
that the results vary according to the number of
years in teaching of the voters. As with the Mann-
Whitney test, the Kruskal-Wallis test tells us only
that there is or is not a statistically significant
difference, not where the difference lies. To find
out where the difference lies, one has to return
to the cross-tabulation and examine it. In the
example here it appears that those teachers in the
group which had been teaching from 16 to 18
years are the most positive about the aspect of the
course in question.
In reporting the Kruskal-Wallis test one could
use a form of words such as the following: