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DEPENDENT AND INDEPENDENT VARIABLES 505
influenced how much homework they did – the
higher the marks, the more they were motivated to
doing mathematics homework; (e) the increase in
homework increased the students’ motivation for
mathematics and this, in turn may have caused the
increase in the mathematics test; (f) the students
were told that if they did not perform well on the
test then they would be punished, in proportion
to how poorly they scored.
What one can observe here is important. In
respect of (a), there are other extraneous variables
which have to be factored into the causal
relationship (i.e. in addition to the homework).
In respect of (b), the assumed relationship is not
really present; behind the coincidence of the rise
in homework and the rise in the test result is
a stronger causal relationship of the liking of
the subject and the teacher which caused the
students to work hard, a by-product of which
was the rise in test scores. In respect of (c), an
intervening variable was at work (a variable which
affected the process of the test but which was not
directly observed, measured or manipulated). In
respect of (d) and (e), in fact the test caused the
increase in homework, and not vice versa, i.e.
the direction of causality was reversed. In respect
of (f), the amount of increase was negatively
correlated with the amount of punishment: the
greater the mark, the lesser the punishment.
In fact, what may be happening here is that
causality may be less in a linear model and more
multidirectional and multirelated, more like a web
than a line.
This example indicates a range of issues in
the discussion of dependent and independent
variables:
The direction of causality is not always clear:
an independent variable may, in turn, become
a dependent variable and vice versa.
The direction of causality may be bidirectional.
Assumptions of association may not be
assumptions of causality.
There may be a range of other factors that have
abearingonanoutcome.
There may be causes (independent variables)
behind the identified causes (independent
variables) that have a bearing on the
dependent variable.
The independent variable may cause something
else, and it is the something else that
causes the outcome (dependent variable).
Causality may be non-linear rather than linear.
The direction of the relationship may be
negative rather than positive.
The strength/magnitude of the relationship
may be unclear.
Many statistics operate with dependent and
independent variables (e.g. experiments using
t-tests and analysis of variance, regression
and multiple regression); others do not (e.g.
correlational statistics, factor analysis). If one uses
tests which require independent and dependent
variables, great caution has to be exercised in
assuming which is or is not the dependent or
independent variable, and whether causality is as
simple as the test assumes. Further, many statistical
tests are based on linear relationships (e.g.
correlation, regression and multiple regression,
factor analysis) when, in fact, the relationships
may not be linear (some software programs, e.g.
SPSS, have the capability for handling nonlinear
relationships). The researcher has to make
a fundamental decision about whether, in fact,
the relationships are linear or non-linear, and
select the appropriate statistical tests with these
considerations in mind.
To draw these points together, the researcher
will need to consider:
What scales of data are there
Are the data parametric or non-parametric
Are descriptive or inferential statistics
required
Do dependent and independent variables need
to be identified
Are the relationships considered to be linear
or non-linear
The prepared researcher will need to consider the
mode of data analysis that will be employed. This
is very important as it has a specific bearing on
the form of the instrumentation. For example,
a researcher will need to plan the layout and
Chapter 24