RESEARCH METHOD COHEN ok

542 QUANTITATIVE DATA ANALYSIS
that ‘intelligence’ exerted a negative but statistically
insignificant influence on level of achievement.
In using regression techniques, one has to
be faithful to the assumptions underpinning
them. Gorard (2001: 213) sets these out as follows:
The measurements are from a random sample
(or at least a probability-based one).
All variables used should be real numbers (or
at least the dependent variable must be).
There are no extreme outliers.
All variables are measured without error.
There is an approximate linear relationship
between the dependent variable and the
independent variables (both individually and
grouped).
The dependent variable is approximately
normally distributed (or at least the next
assumption is true).
The residuals for the dependent variable (the
differences between calculated and observed
scores) are approximately normally distributed.
The variance of each variable is consistent
across the range of values for all other variables
(or at least the next assumption is true).
The residuals for the dependent variable at
each value of the independent variables have
equal and constant variance.
The residuals are not correlated with the
independent variables.
The residuals for the dependent variable at
each value of the independent variables have
a mean of zero (or they are approximately
linearly related to the dependent variable).
No independent variable is a perfect
linear combination of another (not perfect
‘multicollinearity’).
For any two cases the correlation between
the residuals should be zero (each case is
independent of the others).
Although regression and multiple regression
are most commonly used with interval and ratio
data, more recently some procedures have been
devised for undertaking regression analysis for
ordinal data (SPSS Inc 2002). This is of immense
value for calculating regression from rating scale
data (see http://www.routledge.com/textbooks/
9780415368780 – Chapter 24, file SPSS Manual
24.8).
Pallant (2001: 136) suggests that attention
has to be given to the sample size in using
multiple regression. She suggests that 15 cases
for each independent variable are required, and
that a formula can be applied to determine the
minimum sample size required thus: sample size ≥
50 + (8 × number of independent variables), i.e.
for ten independent variables one would require a
minimum sample size of 130 (i.e. 50 + 80).
Measures of difference between groups
and means
Researchers will sometimes be interested to find
whether there are differences between two or more
groups of subsamples, answering questions such
as: ‘Is there a significant difference between the
amount of homework done by boys and girls’;
‘Is there a significant difference between test
scores from four similarly mixed-ability classes
studying the same syllabus’; ‘Does school A
differ significantly from school B in the stress
level of its sixth form students’ Such questions
require measures of difference. This section
introduces measures of difference and how to
calculate difference. The process commences with
the null hypothesis, stating that ‘there is no
statistically significant difference between the two
groups’, or ‘there is no statistically significant
difference between the four groups’, and, if this
is not supported, then the alternative hypothesis
is supported, namely, there is a statistically
significant difference between the two (or more)
groups’.
Before going very far one has to ascertain the
following:
The kind of data with which one is working, as
this affects the choice of statistic used.
The number of groups being compared, to
discover whether there is a difference between
them. Statistics are usually divided into those
that measure differences between two groups
and those that measure differences between
more than two groups.