What is a causal relationship and why is an understanding of it important in the
interpretation of the value of a correlation coefficient
Causation indicates that one event is the result of the occurrence of the other event; i.e. there is a
causal relationship between the two events. This is also referred to as cause and effect.
A causal relation between two events exists if the occurrence of the first causes the other. The
first event is called the cause and the second event is called the effect. A correlation between two
variables does not imply causation. On the other hand, if there is a causal relationship between
two variables, they must be correlated.
Example:
A study shows that there is a negative correlation between a student's anxiety before a test and
the student's score on the test. But we cannot say that the anxiety causes a lower score on the
test; there could be other reasons—the student may not have studied well, for example. So the
correlation here does not imply causation.
However, consider the positive correlation between the number of hours you spend studying for
a test and the grade you get on the test. Here, there is causation as well; if you spend more time
studying, it results in a higher grade.
Correlation is a statistical measure that describes how two variables are related and indicates that
as one variable changes in value, the other variable tends to change in a specific direction. We can
therefore pinpoint some real life correlations as income & expenditure, supply & demand,
absence & grades decrease…etc.
Every correlation has a sign and a form, the sign could be positive, negative or neutral:
Positive correlation: the two variables move in the same direction (i.e., one variable
increases as the other increases. Or, one decreases as the other decreases).
Negative correlation : the two variables move in opposite directions (i.e., one variable
increases as the other decreases, and vice versa).
Neutral correlation : the two variables show no relationship to one another.
Concerning the form of a correlation , it could be linear, non-linear, or monotonic :
Linear correlation : A correlation is linear when two variables change at constant rate
and satisfy the equation Y = aX + b (i.e., the relationship must graph as a straight line).
Non-Linear correlation : A correlation is non-linear when two variables don’t change at
a constant rate. In this case the relationship between the variables does not graph as a straight
line, but as a curved pattern (parabola, hyperbola … etc).
Monotonic correlation : In a monotonic relationship, the variables tend to move in the
same relative direction, but not necessarily at a constant rate. So all linear correlations are
monotonic but the opposite is not always true, because we can have also monotonic non-
linear relationships.
