RESEARCH METHOD COHEN ok

EFFECT SIZE 523
Box 24.17
The Levene test for equality of variances
Levene’s test
for equality
of variances
Independent samples test
t-test for equality of means
Chapter 24
How well
learners are
cared for,
guided and
supported
Equal variances
assumed
Equal variances
not assumed
95 % confidence
interval of the
difference
Sig. Mean SE
F Sig. t df (2-tailed) difference difference Lower Upper
8.344 0.004 1.923 998 0.055 0.30 0.155 −0.006 0.603
2.022 811.922 0.044 0.30 0.148 0.009 0.589
The effect size can be worked out thus (using
SPSS):
t 2
t 2 + (N 1 − 1) = 16.588 2
16.588 2 + (1000 − 1)
=
275.162
275.162 + 999 = 0.216
In this example the effect size is 0.216, a very large
effect, i.e. there was a very substantial difference
between the scores of the two groups.
For analysis of variance (discussed later) the
effect size is calculated thus:
Eta squared =
Sum of squares between groups
Total sum of squares
In SPSS this is given as ‘partial eta squared’. For
example, let us imagine that we wish to compute
the effect size of the difference between four
groups of schools on mathematics performance
in a public examination. The four groups of
schools are: rural primary; rural secondary; urban
primary; urban secondary. Analysis of variance
yields the result shown in Box 24.20.
Working through the formula yields the
following:
Sum of squares between groups
= 7078.619
Total sum of squares
344344.8 =0.021 alternative equations to take account of
Box 24.18
Mean and standard deviation in a paired sample
test
Paired samples statistics
Mean N SD SE mean
Pair Maths 81.71 1,000 23.412 0.740
1 Science 67.26 1,000 27.369 0.865
The figure of 0.021 indicates a small effect size, i.e.
that there is a small difference between the four
groups in their mathematics performance (note
that this is a much smaller difference than that
indicated by the significance level of 0.006, which
suggests a statistically highly significant difference
between the four groups of schools.
In regression analysis (discussed later) the effect
size of the predictor variables is given by the beta
weightings. In interpreting effect size here Muijs
(2004: 194) gives the following guidance:
0–0.1 weak effect
0.1–0.3 modest effect
0.3–0.5 moderate effect
>0.5 strong effect
Hedges (1981) and Hunter et al. (1982) suggest