RESEARCH METHOD COHEN ok

MEASURES OF DIFFERENCE BETWEEN GROUPS AND MEANS 553
Box 24.51
Across-tabulationforaMann-WhitneyUtest
Sex ∗ The course gave you opportunities to learn at your own pace cross-tabulation
The course gave you opportunities to learn at your own pace
Strongly Neither agree Strongly
Disagree Disagree nor disagree Agree agree Total
Male Count 1 2 16 21 9 49
%withinsex 2.0% 4.1% 32.7% 42.9% 18.4% 100.0%
Female Count 4 11 61 57 8 141
%withinsex 2.8% 7.8% 43.3% 40.4% 5.7% 100.0%
Total Count 5 13 77 78 17 190
%withinsex 2.6% 6.8% 40.5% 41.1% 8.9% 100.0%
Chapter 24
Box 24.52
SPSS output on rankings for the Mann-Whitney
Utest
Box 24.53
The Mann-Whitney U value and significance level
in SPSS
Ranks
Mean Sum of
Sex N rank ranks
The course Male 49 110.23 5401.50
gave you Female 141 90.38 12743.50
opportunities Total 190
to learn at
your own
pace
Test statistics a
Mann-Whitney U 2732.500
Wilcoxon W 12743.500
Z −2.343
Asymp. sig. (2-tailed) 0.019
The course gave you
opportunities to learn
at your own pace
a. Grouping variable: Sex
supporting or not supporting the null hypothesis;
for example we could say ‘Let α = 0.05’. A crosstabulation
might reveal the following (Box 24.51).
Are the differences between the two
groups statistically significant Using SPSS, the
Mann-Whitney statistic indicates the following
(Boxes 24.52 and 24.53).
Mann-Whitney using ranks (as in Box 24.52)
yields a U-value of 2732.500 from the formula
it uses for the calculation (SPSS does this
automatically). The important information in
Box 24.53 is the ‘Asymp. sig. (2-tailed)’, i.e. the
statistical significance level of any difference found
between the two groups (males and females).
Here the significance level (ρ = 0.019, i.e. ρ<
0.05) indicates that the voting by males and
females is statistically significantly different and
that the null hypothesis is not supported. In
the t-test and the Tukey test researchers could
immediately find exactly where differences might
lie between the groups (by looking at the means
and the homogeneous subgroups respectively).
Unfortunately the Mann-Whitney test does not
enable the researcher to identify clearly where
the differences lie between the two groups, so the
researcher would need to go back to the crosstabulation
to identify where differences lie. In
the example above, it appears that the males feel
more strongly than the females that the course