RESEARCH METHOD COHEN ok

26
Choosing a statistical test
There are very many statistical tests available to
the researcher. Which test one employs depends
on several factors, for example:
the purpose of the analysis (e.g. to describe
or explore data, to test a hypothesis, to seek
correlations, to identify the effects of one or
more independent variables on a dependent
variable, to identify differences between two or
more groups; to look for underlying groupings
of data, to report effect sizes)
the kinds of data with which one is working
(parametric and non-parametric)
the scales of data being used (nominal, ordinal,
interval, ratio)
the number of groups in the sample
the assumptions in the tests
whether the samples are independent of each
other or related to each other.
Researchers wishing to use statistics will need to
ask questions such as:
What statistics do I need to answer my research
questions
Are the data parametric or non-parametric
How many groups are there (e.g. two, three or
more)
Are the groups related or independent
What kind of test do I need (e.g. a difference
test, a correlation, factor analysis, regression)
We have addressed several of these points in
the preceding chapters; those not addressed in
previous chapters are addressed here. In this
chapter we draw together the threads of the
discussion of statistical analysis and address what,
for many researchers, can be a nightmare: deciding
which statistical tests to use. In the interests
of clarity we have decided to use tables and
graphic means of presenting the issues in this
chapter (see http://www.routledge.com/textbooks/
9780415368780 – Chapter 26, file 26.1.doc).
How many samples
In addition to the scale of data being used
(nominal, ordinal, interval, ratio), the kind of
statistic that one calculates depends in part
on, first, whether the samples are related to,
or independent of, each other, and second, the
number of samples in the test. With regard to
the first point, as we have seen in previous
chapters, different statistics are sometimes used
when groups are related to each other and when
they are independent of each other. Groups will
be independent when they have no relationship
to each other, e.g. in conducting a test to see if
there is any difference between the voting of males
and females on a particular item, say mathematics
performance. The tests that one could use here are,
for example: the chi-square test (for nominal data),
the Mann-Whitney U test and Kruskal-Wallis
(for ordinal data), and the t-test and analysis of
variance (ANOVA) for interval and ratio data.
However, there are times when the groups
might be related. For example, we may wish to
measure the performance of the same group at
two points in time – before and after a particular
intervention – or we may wish to measure the
voting of the same group on two different factors,
say preference for mathematics and preference for
music. Here it is not different groups that are being
involved, but the same group on two occasions and
the same two on two variables respectively. In this
case different statistics would have to be used, for
example the Wilcoxon test, the Friedman test, the
t-test for paired samples, and the sign test. Let us