COMMON RESPONSE , CONFOUNDING VARIABLES,
COINCIDENCE
To establish causality, you need to conduct an experiment. In an
experiment, the value of the explanatory variable is deliberately
manipulated, while all other possible explanatory variables are kept
constant or controlled. In these circumstances, the observed
difference in the response variable can reasonably be attributed to
the explanatory variable.
However, in Further Maths, all we ever see is observed data without
any experiment taking place. All we can ever see is an association
between two variables, without knowing other possible variables,
and without any information whatsoever about causes. Therefore, in
Further Maths, we can NEVER conclude that one variable causes
changes in the other, however obvious this might appear.
Possible non-causal explanations for an association
Common response
Sometimes two variables between which we see an association on a
scatterplot are actually related to a third variable. This is called
common response, because both variables are responding to a third,
unseen variable.
Ex: There is a positive association between Number of people who
apply sunscreen and Number of people who faint. Both variables are
responding to a third common variable: Temperature
Confounding variables
Almost always a situation is more complex that simply involving two variables.
Often there are many possible variables which might be causing a response,
and we are unable to disentangle them by merely observing a scatterplot.
Ex: There might be a positive association between the two variables: No. of
Edrolo videos watched and Results in a Further Maths test. But other factors
are involved : Mathematical ability, No. of exercises completed, No. of minutes
spent on revision, No. of hours sleep the night before, etc. It is impossible to
disentangle all the effects of the different variables – all of them might be
playing a role in causing changes in test results.
In this case, we say that the effects of the many other possible explanatory
variables are said to be confounded.
Coincidence
It turns out that there is a strong correlation (r=0.99) between the
consumption of margarine and the divorce rate in the American
state of Maine. Can we conclude that eating margarine causes
people in Maine to divorce?
A better explanation is that this association is purely coincidental.
Occasionally, it is almost impossible to identify any feasible
confounding variables to explain a particular association. In these
cases we often conclude that the association is ‘spurious’ and it has
happened just happened by chance. We call this coincidence.