Which type of analysis studies the functional relationship between two or more existing variables?

A relationship refers to the correspondence between two variables. When we talk about types of relationships, we can mean that in at least two ways: the nature of the relationship or the pattern of it.

The Nature of a Relationship

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, there has often been talk of a relationship between ability in math and proficiency in music. In general people who are good in one may have a greater tendency to be good in the other; those who are poor in one may also tend to be poor in the other. If this relationship is true, then we can say that 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 the United States. Does that mean that if we want fewer children in the U.S., 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 U.S. citizens to have more babies? Of course not. (At least, I hope 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 the U.S. 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 drives 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. For instance, I suspect that there is no relationship between the length of the lifeline on your hand and your grade point average. If I know your GPA, I don’t have any idea how long your lifeline is.

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.

On the other hand a negative relationship implies that high values on one variable are associated with low values on the other. This is also sometimes termed an inverse relationship. Here, we show an idealized negative relationship between a measure of self esteem and a measure of paranoia in psychiatric patients.

These are the simplest types of relationships we might typically estimate in research. But the pattern of a relationship can be more complex than this. For instance, the figure on the left shows a relationship that changes over the range of both variables, a curvilinear relationship. In this example, the horizontal axis represents dosage of a drug for an illness and the vertical axis represents a severity of illness measure. As dosage rises, severity of illness goes down. But at some point, the patient begins to experience negative side effects associated with too high a dosage, and the severity of illness begins to increase again.