RESEARCH METHOD COHEN ok

MEASURES OF DIFFERENCE BETWEEN GROUPS AND MEANS 551
Box 24.47
Means and standard deviations in a two-way
analysis of variance
Descriptive statistics
Dependent variable: Science
Sex Age group Mean SD N
Male 15–20 71.92 24.353 125
21–25 63.33 31.459 111
26–45 70.95 28.793 21
46 and above 64.69 28.752 128
Total 66.99 28.390 385
Female 15–20 70.33 25.768 182
21–25 68.82 25.396 221
26–45 69.59 28.059 49
46 and above 61.66 28.464 163
Total 67.43 26.731 615
Total 15–20 70.98 25.173 307
21–25 66.99 27.646 332
26–45 70.00 28.079 70
46 and above 62.99 28.581 291
Total 67.26 27.369 1000
Box 24.48
The Levene test of equality of variances in a twoway
analysis of variance
Levene’s test of equality of error variances a
Dependent variable: Science
F df1 df2 Sig.
3.463 7 992 0.001
Tests the null hypothesis that the error variance of the
dependent variable is equal across groups.
a. Design: Intercept+SEX+AGE GROUP +SEX ∗ AGE
GROUP
This simply presents the data, with means and
standard deviations. Next SPSS calculates the
Levene test for equality of error variances, degrees
of freedom and significance levels (Box 24.48).
This test enables the researcher to know
whether there is equality across the means. He
or she needs to see if the significance level is
greater than 0.05. The researcher is looking for
a significance level greater than 0.05, i.e. not
statistically significant, which supports the null
hypothesis that holds that there is no statistically
significant difference between the means and
variances across the groups (i.e. to support the
assumptions of ANOVA). In our example this
is not the case as the significance level is .001.
This means that the researcher has to proceed
with caution as equality of variances cannot be
assumed, i.e. one of the assumptions of ANOVA
is not present. SPSS provides her with important
information, thus (Box 24.49).
Here one can see the three sets of independent
variables listed (SEX, AGE GROUP, SEX*AGE
GROUP). The column headed ‘Sig.’ shows
that the significance levels for the three
sets are, respectively: 0.956, 0.004 and 0.244.
Hence one can see that sex does not have
a statistically significant effect on Science
examination performance. Age group does have
astatisticallysignificanteffectontheperformance
in the Science examination (ρ = 0.004). The
interaction effect of sex and age group does
not have a statistically significant effect on
performance, i.e. there is no difference in the effect
on Science performance for males and females
(ρ = 0.244). SPSS also computes the effect size
(Partial Eta squared). For the important variable
AGE GROUP this is given as 0.014, which shows
that the effect size is very small indeed, suggesting
that, even though statistical significance has been
found, the actual difference in the mean values is
very small.
As with one-way ANOVA, the Tukey test
can be applied here to present the homogeneous
groupings of the subsample means. SPSS can also
present a graphic plot of the two sets of scores,
which gives the researcher a ready understanding
of the effects of the males and females across
the four age groups in their Science examination
(Box 24.50).
In reporting the results of the two-way analysis
of variance one can use the following form of
words:
Atwo-waybetween-groupsanalysisofvariancewas
conducted to discover the impact of sex and age
group on performance in a Science examination.
Chapter 24