RESEARCH METHOD COHEN ok

MEASURES OF DIFFERENCE BETWEEN GROUPS AND MEANS 547
Box 24.42
The paired samples t-test
Paired samples test
Paired differences
95 % confidence
interval of the
difference
Chapter 24
Pair 1
The attention given to
teaching and learning
at the school – the
quality of the lesson
preparation
Mean SD SE mean Lower Upper t df Sig. (2-tailed)
−1.69 2.430 0.077 −1.84 −1.54 −21.936 999 0.000
governors) and one is a continuous variable (e.g.
marks on a test).
One-way analysis of variance
Let us imagine that we have four types of school:
rural primary, rural secondary, urban primary and
urban secondary. Let us imagine further that all
of the schools in these categories have taken
the same standardized test of mathematics, and
the results have been given as a percentage thus
(Box 24.43).
The table gives us the means, standard
deviations, standard error, confidence intervals,
and the minimum and maximum marks for each
group. At this stage we are interested only in the
means:
Rural primary:
Rural secondary:
Urban primary:
Urban secondary:
mean = 59.85 per cent
mean = 60.44 per cent
mean = 50.64 per cent
mean = 51.70 per cent
Are these means statistically significantly different
Analysis of variance will tell us whether
they are. We commence with the null hypothesis
(‘there is no statistically significant difference
between the four means’) and then we set the
level of significance (α) to use for supporting or
not supporting the null hypothesis; for example
we could say ‘Let α = 0.05’. SPSS calculates the
following (Box 24.44).
This tells us that, for three degrees of freedom
(df), the F-ratio is 8.976. The F-ratio is the between
group mean square (variance) divided by the within
group mean square (variance), i.e.:
F =
Between group variance
Within group variance = 3981.040
443.514 = 8.976
By looking at the final column (‘Sig.’) ANOVA
tell us that there is a statistically significant
difference between the means (ρ = 0.000). This
does not mean that all the means are statistically
significantly different from each other, but that
some are. For example, it may be that the means
for the rural primary and rural secondary schools
(59.85 per cent and 60.44 per cent respectively)
are not statistically significantly different, and that
the means for the urban primary schools and urban
secondary schools (50.64 per cent and 51.70 per
cent respectively) are not statistically significantly
different. However, it could be that there is
astatisticallysignificantdifferencebetweenthe
scores of the rural (primary and secondary) and
the urban (primary and secondary) schools. How
can we find out which groups are different from
each other
There are several tests that can be employed
here, though we will only concern ourselves with
averycommonlyusedtest:theTukeyhonestly