RESEARCH METHOD COHEN ok

524 QUANTITATIVE DATA ANALYSIS
Box 24.19
Difference test for a paired sample
Paired samples test
Paired differences
95 % confidence
interval of the difference
Mean SD SE mean Lower Upper t df Sig. (2-tailed)
Pair 1 Maths-Science 14.45 27.547 0.871 12.74 16.16 16.588 999 0.000
Box 24.20
Effect size in analysis of variance
Maths
ANOVA
Sum of squares df Mean square F Sig.
Between groups 7078.619 3 2359.540 4.205 0.006
Within groups 337266.2 601 561.175
Total 344344.8 604
differential weightings due to sample size
variations. The two most frequently used indices of
effect sizes are standardized mean differences and
correlations (Hunter et al. 1982:373),although
non-parametric statistics, e.g. the median, can be
used. Lipsey (1992: 93–100) sets out a series of
statistical tests for working on effect sizes, effect
size means and homogeneity.
Muijs (2004: 126) indicates that a measure of
effect size for cross-tabulations, instead of chisquare,
should be phi, whichisthesquarerootof
the calculated value of chi-square divided by the
overall valid sample size. He gives an example:
‘if chi-square = 14.810 and the sample size is 885
then phi = 14.810/885 = 0.0167 and then take
the square root of this = 0.129’.
Effect sizes are susceptible to a range of
influences. These include (Coe 2000):
Restricted range: the smaller the range of scores,
the greater is the possibility of a higher effect
size, therefore it is important to use the standard
deviation of the whole population (and not just
one group), i.e. a pooled standard deviation,
in calculating the effect size. It is important to
report the possible restricted range or sampling
here (e.g. a group of highly able students rather
than, for example, the whole ability range).
Non-normal distributions: effect size usually
assumes a normal distribution, so any
non-normal distributions would have to be
reported.
Measurement reliability: the reliability (accuracy,
stability and robustness) of the instrument
being used (e.g. the longer the test, or the more
items that are used to measure a factor, the
more reliable it could be).
There are downloadable software programs
available that will calculate effect size simply by
the researcher keying in minimal amounts of data,
for example:
The Effect Size Generator by Grant Devilly:
http://www.swin.edu.au/victims