Patters 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.

Then we have to consider defining some basic terms like variable, hypothesis, data, and unit of analysis. If you're like me, you hate learning vocabulary, so we'll quickly move along to consideration of two of the major fallacies of research, just to give you an idea of how wrong even researchers can be if they're not careful (of course, there's always a certainly probability that they'll be wrong even if they're extremely careful).