RESEARCH METHOD COHEN ok

STATISTICAL SIGNIFICANCE 515
alongtailatthepositiveendandthemajorityof
the data at the negative end, and a negative skew
has a long tail at the negative end and the majority
of the data at the positive end.
Statistical significance
Much statistical analysis hinges on the notion of
statistical significance. Kirk (1999: 337) indicates
that ‘a statistically significant result is one
for which chance is an unlikely explanation’.
Research in a hypothetico-deductive mode often
commences with one or more hypotheses. This is
the essence of hypothesis testing in quantitative
research. Typically hypotheses fall into two types.
The null hypothesis, amajortypeofhypothesis
states that, for example, there is no relationship
between two variables, or that there has been
no change in participants between a pretest
and a post-test, or that there is no difference
between three school districts in respect of
their examination results, or that there is no
difference between the voting of males and females
on such-and-such a factor. The null hypothesis
sits comfortably with the Popperian notion of
the hallmark of a science being its essential
falsifiability.
The point here is that by casting the hypothesis
in a null form the burden of proof is placed
on the researcher not to confirm that null hypothesis.
The task is akin to a jury starting with a
presumption of innocence and having to prove
guilt beyond reasonable doubt. Not only is it often
easier simply to support a straightforward positive
hypothesis, but also, more seriously, even if that
positive hypothesis is supported, there may be insufficient
grounds for accepting that hypothesis,
as the finding may be consistent with other hypotheses.
For example, let us imagine that our
hypothesis is that a coin is weighted and, therefore,
unfair. We flip the coin 100 times, and find
that 60 times out of 100 it comes out as heads.
It would be easy to jump to the conclusion that
the coin is weighted, but, equally easily, other reasons
may account for the result. Of course, if the
coin were to come out as heads 99 times out of
100 then perhaps there would be greater truth in
the hypothesis. The null hypothesis is a stronger
version of evidence, not only requiring that the
negative hypothesis be ‘not supported’, but also indicating
a cut-off point only above which the null
hypothesis is ‘not supported’, and below which the
null hypothesis is supported. In our coin example
it may be required to find that heads comes up
95 times out of 100 or 99 times out of 100, or
even 999 times out of 1,000, to say, with increasing
confidence in respect of these three sets
of figures, that the null hypothesis is not supported
(see http://www.routledge.com/textbooks/
9780415368780 – Chapter 24, file 24.8.ppt).
We use terminology carefully here. Some
researchers state that the null hypothesis is
‘rejected’; others say that it is ‘confirmed’ or ‘not
confirmed’; other say that it is ‘accepted’ or ‘not
accepted’. We prefer the terminology of ‘supported’
or ‘not supported’. This is not mere semantics or
pedantry; rather it signals caution. Rejecting a
null hypothesis is not the same as ‘not confirming’
or ‘not supporting’ that null hypothesis, rejection
implying an absolute and universal state which the
research will probably not be able to demonstrate,
being bounded within strict parameters and not
being applicable to all cases. Further, ‘confirming’
and ‘not confirming’, like ‘rejecting’, is too strong,
absolute and universal a set of terms for what is,
after all, research that is bounded and within
delineated boundaries. Similarly, one cannot
‘accept’ a null hypothesis as a null hypothesis
can never be proved unequivocally.
A second type of hypothesis is termed the
alternative hypothesis. Whereasthenullhypothesis
states that there is no such-and-such (e.g.
change, relationship, difference), the alternative
hypothesis state that there is such-and-such, for
example: there is achangeinbehaviourofthe
school students; there is a difference between
students’ scores on mathematics and science;
there is a difference between the examination
results of five school districts; there is adifference
between the pretest and post-test results of suchand-such
a class. This weaker form of hypothesis
is often supported when the null hypothesis is
‘not supported’, i.e. if the null hypothesis is not
supported then the alternative hypothesis is.
Chapter 24