RESEARCH METHOD COHEN ok

552 QUANTITATIVE DATA ANALYSIS
Box 24.49
Between-subject effects in two-way analysis of variance
Tests of between-subjects effects
Dependent variable: SCIENCE
Type III sum Mean Partial Eta Noncent. Observed
Source of squares df square F Sig. squared parameter power a
Corrected model 13199.146 b 7 1885.592 2.545 0.013 0.018 17.812 0.888
Intercept 2687996.888 1 2687996.9 3627.42 0.000 0.785 3627.421 1.000
SEX 2.218 1 2.218 0.003 0.956 0.000 0.003 0.050
AGE GROUP 10124.306 3 3374.769 4.554 0.004 0.014 13.663 0.887
SEX ∗ AGE GROUP 3089.630 3 1029.877 1.390 0.244 0.004 4.169 0.371
Error 735093.254 992 741.021
Total 5272200.000 1000
Corrected total 748292.400 999
a. Computed using alpha = 0.05
b. R squared = 0.018 (Adjusted R squared = 0.011)
Box 24.50
Graphic plots of two sets of scores on a dependent
variable
Estimated marginal means
74
72
70
68
66
64
62
60
15-20
Estimated marginal means of SCIENCE
Sex
male
female
21-25 26-45 46 and above
Age group
Subjects were divided into four groups by age: Group
1: 15–20 years; Group 2: 21–25 years; Group 3:
26–45 years; and Group 4: 46 years and above. There
was a statistically significant main effect for age group
(F = 4.554, ρ = 0.004), however the effect size was
small (partial eta squared = 0.014). The main effect
for sex (F = 0.003, ρ = 0.956) and the interaction
effect (F = 1.390, ρ = 0.244) were not statistically
significant.
The Mann-Whitney and Wilcoxon tests
The non-parametric equivalents of the t-test are
the Mann-Whitney U test for two independent
samples and the Wilcoxon test for two related
samples, both for use with one categorical variable
and a minimum of one ordinal variable. These
enable us to see, for example, whether there are
differences between males and females on a rating
scale.
The Mann-Whitney test is based on ranks,
‘comparing the number of times a score from
one of the samples is ranked higher than a
score from the other sample’ (Bryman and
Cramer 1990: 129) and hence overcomes the
problem of low cell frequencies in the chi-square
statistic (see http://www.routledge.com/textbooks/
9780415368780 – Chapter 24, file 24.19.ppt). Let
us take an example. Imagine that we have
conducted a course evaluation, using five-point
rating scales (‘not at all’, ‘very little’, ‘a little’,
‘quite a lot’, ‘a very great deal’), and we wish to
find if there is a statistically significant difference
between the voting of males and females on the
variable ‘The course gave you opportunities to
learn at your own pace’. We commence with the
null hypothesis (‘there is no statistically significant
difference between the two means’) and then
we set the level of significance (α) to use for