RESEARCH METHOD COHEN ok

548 QUANTITATIVE DATA ANALYSIS
Box 24.43
Descriptive statistics for analysis of variance
Descriptives
Standardized mathematics scores (percentages)
95 % confidence
interval for mean
N Mean SD SE Lower bound Upper bound Minimum Maximum
Rural primary 134 59.85 21.061 1.819 56.25 63.45 30 100
Rural secondary 136 60.44 19.470 1.669 57.14 63.74 30 100
Urban primary 141 50.64 22.463 1.892 46.90 54.38 30 100
Urban secondary 194 51.70 21.077 1.513 48.72 54.69 30 100
Total 605 55.22 21.473 0.873 53.51 56.94 30 100
Box 24.44
SPSS output for one-way analysis of variance
Standardized mathematics scores (percentages)
ANOVA
Sum of squares df Mean square F Sig.
Between groups 11943.119 3 3981.040 8.976 0.000
Within groups 266551.8 601 443.514
Total 278494.9 604
significant difference test, sometimes called the
‘Tukey hsd’ test, or simply (as in SPSS) the
Tukey test. (Others include the Bonferroni and
Scheffé test; they are more rigorous than the
Tukey test and tend to be used less frequently.)
The Tukey test groups together subsamples whose
means are not statistically significantly different
from each other and places them in a different
group from a group whose means are statistically
significantly different from the first group. Let
us see what this means in our example of
the mathematics results of four types of school
(Box 24.45).
This table takes each type of school and
compares it with the other three types, in
order to see where there may be statistically
significant differences between them. Here the
rural primary school is first compared with the rural
secondary school (row one of the left-hand column
cell named ‘Rural primary’), and no statistically
significant difference is found between them
(Sig. = 0.996, i.e. ρ>0.05). The rural primary
school is then compared with the urban primary
school and a statistically significant difference is
found between them (Sig. = 0.002, i.e. ρ