RESEARCH METHOD COHEN ok

HYPOTHESIS TESTING 519
selection from the table of significance for the third
example above concerning hand and foot size, the
first column indicates the number of people in
the sample and the other two columns indicate
significance at the two levels. Hence, if we have
30 people in the sample then, for the correlation
to be statistically significant at the 0.05 level,
we would need a correlation coefficient of 0.36,
whereas, if there were only 10 people in the sample,
we would need a correlation coefficient of 0.65
for the correlation to be statistically significant
at the same 0.05 level. Most statistical packages
(e.g. SPSS) automatically calculate the level of
statistical significance, indeed SPSS automatically
asterisks each case of statistical significance at
the 0.05 and 0.01 levels or smaller. We discuss
correlational analysis in more detail later in this
chapter, and we refer the reader to that discussion.
Hypothesis testing
The example that we have given above from
correlational analysis illustrates a wider issue of
hypothesis testing. This follows four stages.
There is no significant prediction capability
between one independent variable X and
dependent variable Y.
There is no significant prediction capability
between two or more independent variables X,
Y, Z ... and dependent variable A.
The task of the researcher is to support or not to
support the null hypothesis.
Stage 2
Having set the null hypothesis, the researcher then
sets the level of significance (α) that will be used
to support or not to support the null hypothesis;
this is the alpha (α) level.Thelevelofalphais
determined by the researcher. Typically it is 0.05,
i.e. for 95 per cent of the time the null hypothesis
is not supported. In writing this we could say ‘Let
α = 0.05’. If one wished to be more robust then
one would set a higher alpha level (α = 0.01 or
α = 0.001). This is the level of risk that one wishes
to take in supporting or not supporting the null
hypothesis.
Chapter 24
Stage 1
In quantitative research, as mentioned above, we
commence with a null hypothesis, for example:
There is no statistical significance in the
distribution of the data in a contingency table
(cross-tabulation).
There is no statistically significant correlation
between two factors.
There is no statistically significant difference
between the means of two groups.
There is no statistically significant difference
between the means of a group in a pretest and
apost-test.
There is no statistically significant difference
between the means of three or more groups.
There is no statistically significant difference
between two subsamples.
There is no statistically significant difference
between three or more subsamples.
Stage 3
Having set the null hypothesis and the level at
which it will be supported or not supported,
one then computes the data in whatever form
is appropriate for the research in question (e.g.
measures of association, measures of difference,
regression and prediction measures).
Stage 4
Having analysed the data, one is then in a position
to support or not to support the null hypothesis,
and this is what would be reported.
It is important to distinguish two types of
hypothesis (Wright 2003: 132): a causal hypothesis
and an associative hypothesis. As its name suggests,
acausalhypothesissuggeststhatinputXwillaffect
outcome Y, as in, for example, an experimental
design. An associative hypothesis describes how
variables may relate to each other, not necessarily
in a causal manner (e.g. in correlational analysis).