Correlation

This is a straightforward concept. If we say two things are similar in certain ways, or the test score of one variable is associated with the test score of another, we are talking about a correlation (Hayes, 2000). The terms relationship or co-relation are synonyms for correlation. It attempts to answer questions such as: "What is the correlation (relationship) between longevity of drinking and treatment outcome?" or "What is the correlation between early physical abuse and onset of drug use?"

There are a couple of things to know about correlation. First, it does not equal causation. That means that just because you see a strong correlation between certain variables (e.g., longevity of drinking and poor treatment outcome) this does not mean one is causing the other. Producing a causal factor is not the job of correlations. Another unknown force could be influencing the variables under examination. You just don't know with correlation. (Determining cause is the job of a true experiment and the associated statistics, which are coming up in the near future.)

However, correlation is evidence. A better way to state this point is that correlation does not necessarily equal causation (Vogt, 1999).

Second, correlations can be both a descriptive (note amount or direction of a relationship), and an inferential statistic (test a hypothesis). Ask a descriptive question such as, is there a relationship between longevity of drinking and treatment outcome, and you get a descriptive answer. That answer will come with a mean and standard deviation. Ask an inferential question like, using treatment "X" results in better outcomes than using treatment "Y" and you will get an inferential answer. (An inferential equation will confirm your belief or not.)

Third, typical correlational scores range from +1 to - 1. These scores are called correlation coefficients (Salkind, 2000). You see these figures in journal results sections. The closer a number is to 1, the stronger the relationship. This applies for a positive direction and the negative. The closer the number is to 0, the weaker the relationship. Results that have either a strong positive or negative result are extremely rare. If we have something close to perfect positive correlation we can be sure that one variable is highly related to another. Whereas, if we have something close to a perfect negative correlation, we can be sure one variable is inversely related to another. Only if the correlation is close to zero, can we say there is little or no relation.

A correlation statistic often used in addiction research is called the Pearson Product Moment Correlation (Kranzler & Moursund, 1999; Salkind, 2000). It is a complicated formula, but what you really need to know is the final tabulation. That will be expressed as the small letter r. For example, if you seen r = .52 in the results section of a research article, you can assume that the variables that were measured have a moderate relationship.

Let's examine one last item in the correlation section. This is called the correlation of determination (Kranzler & Moursund, 1999; Salkind, 2000). You will see it represented as r2. For example, in your program say you determine somehow that r = .52 exists between longevity of drinking and treatment outcome. Square that figure and you get .27 or the correlation of determination. This means that 27 percent of the longevity of drinking variable is accounted for in the treatment outcome variable, but you have no idea of what accounts for the other 73 percent. Again, this doesn't mean one thing is causing another, but you can now account for some percentage of what is going on between longevity of drinking and outcome. Even with its limitations, correlation is much better than guessing, or relying on unsubstantiated theories.

Regression

A close cousin of correlation is regression. Its goal, however, is not to determine a relationship but to predict. The concept of regression can be one of those confusing statistical terms. Think of deterioration or falling off and the concept becomes a little more understandable. For example, in terms of counseling, the average counselor never performs at their best. Some days are better than others. This weaving between best and worst can be said to represent a deterioration toward what we could call our normal counseling behavior. Following our best days, we will deteriorate to that normal level, and following our worse days we also deteriorate toward our normal. In another words, we regress or best fit our most normal counseling behavior the majority of the time. It comes in two forms, simple and multiple.

The simple regression equation is not as intimidating as those in correlation. What you need to recognize is the regression formula will be expressed as Y. As with correlation, the stronger this number (Y) the stronger the prediction between variables (Kranzler & Moursund, 1999; Salkind, 2000). (Regression findings do not go into negative numbers, however). Using our ongoing example, if we determine a strong relationship exists between longevity of drinking and poor treatment outcome; we can also strongly predict that clients who come into treatment with a long history of drinking will not do well after treatment. (Even though this is an example, such an illustration does not mean such clients are doomed to failure. Clinically, if you used a regression equation and received this prediction, you would be duly warned that the outcome might not be good. Therefore, at the outset of treatment you would have to adjust your strategies accordingly.)

With simple regression we are making predictions between two variables. As I have pointed out - nothing is that simple in addiction counseling. So, if you want to use a regression formula to make predictions, you have to rely on multiple regression (Jaeger, 1993). The coefficient will be expressed as R. Here you would have multiple independent variables (e.g., length of drinking, associated problems, stable family, employed, etc.) impinging on a dependent variable (e.g., treatment outcome). Again, the stronger the finding the stronger the prediction. Like the correlation, square the R and you get R2 or the coefficient of multiple determination. In this case, you will get a figure that accounts for a percentage of the prediction you are seeking (see correlation).

Postscript

I have simplified this information to accommodate the reader who is not comfortable with research and statistics. A great deal of information was left out of correlation and regression, but this is a good grounding in the fundamentals. Should you be moved to find out more, the references that follow all the columns will guide you. You will now be able to read and comprehend the results sections in research journals using correlation and regression.

Michael J. Taleff, PhD, CADC, MAC, is the Alcohol & Drug Education Program Coordinator for the University of Hawai'i at Manoa.

References
    Jaeger, R.M. (1993). Statistics: A spectator sport (2nd ed.). Newbury Park, CA: Sage.
    Kranzler, G. & Moursund, J. (1999). Statistics for the terrified (2nd ed.). Upper Saddle River, NJ: Prentice Hall.
    Salkind, N.J. (2000). Statistics for people who (think they) hate statistics. Thousand Oaks, CA: Sage.
    Vogt, W.P. (1999). Dictionary of statistics and methodology: A nontechnical guide for the social sciences. Thousand Oaks, CA: Sage.