RESEARCH METHOD COHEN ok

516 QUANTITATIVE DATA ANALYSIS
The two kinds of hypothesis are usually written
thus:
H 0 :
H 1 :
the nullhypothesis
the alternativehypothesis
Sometimes the alternative hypothesis is written as
H A .So,forexample,theresearchercouldhave
null hypotheses and alternative hypotheses thus:
H 0 :
or
or
H 1 :
or
or
There is no difference between the results of
the control group and experimental group in
the post-test of mathematics.
There is no statistically significant difference
between males and females in the results of the
English examination.
There is no statistically significant correlation
between the importance given to a subject
and the amount of support given to it by the
headteacher.
There is a statistically significant difference
between the control group and experimental
groups in the post-test of mathematics.
There is a statistically significant difference
between males and females in the results of the
English examination.
There is a statistically significant positive
correlation between examination scores in
mathematics and science.
The null hypothesis is the stronger hypothesis,
requiring rigorous evidence not to support
it. The alternative hypothesis is, perhaps,
a fall-back position, taken up when the
first – null – hypothesis is not confirmed. The
latter is the logical opposite of the former. One
should commence with the former and cast the
research in the form of a null hypothesis, turning
to the latter only in the case of finding the null
hypothesis not to be supported.
Let us take an example from correlational
research to unpack further the notion of statistical
significance. A correlation enables a researcher
to ascertain whether, and to what extent, there
is a degree of association between two variables
(this is discussed much more fully later in this
chapter). Let us imagine that we observe that
many people with large hands also have large feet
and that people with small hands also have small
feet (see Morrison 1993: 136–40). We decide to
conduct an investigation to see if there is any
correlation or degree of association between the
size of feet and the size of hands, or whether it
is just chance that some people have large hands
and large feet. We measure the hands and the feet
of 100 people and observe that 99 times out of
100 people with large feet also have large hands.
Convinced that we have discovered an important
relationship, we run the test on 1,000 people, and
find that the relationship holds true in 999 cases
out of 1,000. That seems to be more than mere
coincidence; it would seem that we could say with
some certainty that if a person has large hands
then he or she will also have large feet. How do
we know when we can make that assertion When
do we know that we can have confidence in this
prediction
For statistical purposes, if we observe this
relationship occurring 95 times out of 100, i.e.
that chance accounts for only 5 per cent of the
difference, then we could say with some confidence
that there seems to be a high degree of association
between the two variables hands and feet; it
would occur by chance in 5 people in every
100, reported as the 0.05 level of significance
(0.05 being five-hundredths). If we observe this
relationship occurring 99 times out of every 100 (as
in the example of hands and feet), i.e. that chance
accounts for only 1 per cent of the difference, then
we could say with even greater confidence that
there seems to be a very high degree of association
between the two variables; it would occur by
chance once in every 100, reported as the 0.01
level of significance (0.01 being one-hundredth).
If we observe this relationship occurring 999 times
out of every 1,000 (as in the example of hands
and feet), i.e. that chance accounts for only 0.1
per cent of the difference, then we could say with
even greater confidence that there seems to be a
very high degree of association between the two
variables; it would not occur only once in every
1,000, reported as the 0.001 level of significance
(0.001 being one-hundredth).
We begin with a null hypothesis, which states
that there is no relationship between the size of