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The Jonathan Dolhenty Archive |
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PAGE SEVEN by Jonathan Dolhenty, Ph.D.
There are a number of statistical techniques used in the various sciences. Most of these are of no concern to most of us unless we work within some scientific field. The technique of statistical correlation, however, is one of the most widely used and reported techniques and a general understanding of what correlation consists of is important to everyone, especially since so many people confuse the concept of correlation with the concept of cause. In statistics, correlation is a technique that measures the degree of relationship between variables. It can be used either to describe the degree of relationship that exists between variables or to test hypotheses regarding the relationship between variables. The critical point to emphasize here is that correlations can demonstrate only that a relationship exists or does not exist between variables, but correlations cannot indicate whether or not the relationship is causal. Correlation and cause are often confused in the minds of many people and this confusion can be taken advantage of by those offering spurious proposals for social change by inferring that correlations between two variables are necessarily evidence of a causal relationship. It has been argued, for instance, that there is a high correlation between the increase in juvenile delinquency and the increase in the divorce rate in recent years. This may be so. This does not, however, indicate that the increase in the divorce rate has caused the increase in juvenile delinquency. In a similar manner, it has been argued that there is a high correlation between the incidence of lung cancer and the smoking of cigarettes. That may be true. But it does not establish a causal relationship between cigarette smoking and lung cancer, no matter what some anti-smoking activists might want you to believe. The dangers of cigarette smoking must be based on considerations other than correlational data. Types of Relationships The degree of relationship that exists between variables is measured by an index called a correlation coefficient. This is a numerical value that exists at some point on a line between zero and plus one and zero and minus one.
We can see, by looking at the line, that a possibility exists for three kinds of relationships to occur with regard to the relationship between variables. There can be a positive relationship, a negative relationship, or a zero relationship. A Positive relationship between two variables means that as one variable increases, the second variable increases somewhat in proportion. It is rare in actual practice to find a perfect positive relationship between two variables and when a positive relationship does occur, it will be something less than plus one. This is often referred to as a positive correlation. A Negative relationship between two variables means that as one variable decreases, the second variable increases. Again, in actual practice, a perfect negative relationship would be rare. A realistic assessment would be something between zero and minus one. This is often referred to as a negative correlation. 
A Zero relationship would be a rare event, although it is theoretically possible. When no relationship exists between variables, the coefficient will be near zero, although it will not be absolute zero. This is often referred to as a zero correlation or no correlation at all. It is possible to have a relationship between two variables that is a Curvilinear relationship. This occurs when the second variable follows the pattern of the first variable to a point and then reverses direction.  The size of the correlation coefficient will range from -1 to +1. The closer the coefficient is to =1 or -1, the more the second variable is in proportion to the first variable. How close must a coefficient come to +1 or -1 to be considered "good"? Generally speaking, the size of a correlation coefficient is neither good nor bad. It must be interpreted in terms of the variables involved. A correlation coefficient of .48 might be considered satisfactory in one situation, whereas a coefficient of .82 might be considered unsatisfactory in another situation. The coefficient probably should not be labeled at all, but simply accepted as the degree that two variables are related. When we find the degree of relationship between two variables, we can use this information in these ways: 1. We can describe the degree of relationship that exists. If we find that age is related to attitudes toward the legalization of marijuana, and the degree of relationship is -.71, we can simply stop at that point and describe the relationship in terms of the coefficient obtained. 2. We can test a hypothesis. If we want to determine if the observed relationship exceeds what chance would allow, we could take the coefficient to a probability table and ascertain its significance. 3. We can predict one variable from our knowledge of the other. Once the relationship between two variables has been confirmed, we can go on to predict data for individuals within a specified degree of error. If we know the relationship between age and attitude toward legalization of marijuana, we can use an individual's age to make a prediction regarding attitude toward legalization of marijuana. The accuracy of this prediction, of course, is based largely upon the degree of relationship, the correlation coefficient, between age and attitude toward legalization of marijuana. FOR YOUR INFORMATION Variables that are normally positively correlated:
Variables that are normally negatively correlated:
Variables that are not normally correlated at all:
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