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Quantitative Techniques-II

Notes The Nature of a Relationship

Figure 3.1

While all relationships tell about the correspondence between two variables, there is a special
type of relationship that holds that the two variables are not only in correspondence, but that
one causes the other. This is the key distinction between a simple correlational relationship and
a causal relationship. A correlational relationship simply says that two things perform in a
synchronized manner.
For instance, we often talk of a correlation between inflation and unemployment. When inflation
is high, unemployment also tends to be high. When inflation is low, unemployment also tends to
be low. The two variables are correlated. But knowing that two variables are correlated does not
tell us whether one causes the other. We know, for instance, that there is a correlation between the
number of roads built in Europe and the number of children born in India. Does that mean that is
we want fewer children in India, we should stop building so many roads in Europe? Or, does it
mean that if we don’t have enough roads in Europe, we should encourage Indian citizens to have
more babies? Of course not. While there is a relationship between the number of roads built and
the number of babies, we don’t believe that the relationship is a causal one. This leads to
consideration of what is often termed the third variable problem. In this example, it may be that
there is a third variable that is causing both the building of roads and the birthrate that is causing
the correlation we observe. For instance, perhaps the general world economy is responsible for
both. When the economy is good more roads are built in Europe and more children are born in
India. The key lesson here is that you have to be careful when you interpret correlations. If you
observe a correlation between the number of hours students use the computer to study and their
grade point averages (with high computer users getting higher grades), you cannot assume that
the relationship is causal: that computer use improves grades. In this case, the third variable might
be socioeconomic status – richer students who have greater resources at their disposal tend to both
use computers and do better in their grades. It’s the resources that drive both use and grades, not
computer use that causes the change in the grade point average.

Patterns of Relationships

We have several terms to describe the major different types of patterns one might find in a
relationship. First, there is the case of no relationship at all. If you know the values on one
variable, you don’t know anything about the values on the other.

Then, we have the positive relationship. In a positive relationship, high values on one variable
are associated with high values on the other and low values on one are associated with low
values on the other. In this example, we assume an idealized positive relationship between
years of education and the salary one might expect to be making.

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