I have data for three different
groups- Treatment group and Comparison group is the treatment school and the
comparison school itself. First I was confused whether
I need to test the normality for individual groups or all the samples together.(??)
Later on I
have run the analysis for all the samples together later on. (Kolmogorov-Smirnov test showed not significant results
for individual groups, yet sample size is less than 30)
EXAM SCORE DATA:
In the Kolmogorov-Smirnov
test the results are not significant for science and religion course before
intervention and the maths score after intervention i.e. these data are normal.
The scores for all other elements are significant which proves non-normality of
the data. However, the skewness and kurtosis value for all the elements of the
exam scores are within the acceptable range of normality that is -2 to 2
(George and Mallery 2010). The lowest value is -1.320 and highest is 0.873. The
average skewness value is 0.316 and the kurtosis value is -0.438. So the exam scores
data are within the acceptable range of normal distribution. The histograms look good, though not good for few of them.
QUESTIONNAIRE
SURVEY DATA:
Kolmororov-Smirnov test yielded significant results for all
of the elements in the questionnaire which means the data are not normal. Yet
this test can be conservative for some of the cases. However the average value
for the skewness and kurtosis is -0.599 and -0.577 which is within the
acceptable range of the normal distribution which is -2 to 2 (George and
Mallery 2010).
So what shall I consider?- the test of normality? Or the skewness
and kurtosis value?
I was looking for
solutions as I learnt from Field, Andy (2000) about the strength of parametric
statistics over non-parametric ones. My concern is we might miss a significant
effect in non-parametric analysis which might actually exist there (proved in
Parametric tests). "If there is a genuine effect in the data then a parametric test is more likely to detect it."(Field, Andy 2000, p 49)
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