REGRESSION TOWARD THE MEAN

What exactly is regression toward the mean? It sounds rather terrifying, should it something I should be afraid off? Well, no. This web site will hopefully a step-by-step guide to help allay all the fears associated with understanding Regression toward the Mean. So, are you ready? Let's start with Step One...

Step One: What is it?

Regression to the mean is a statistical phenomenon that is a fact of life in statistics. It essentially occurs on the posttest where the measures (for example test scores) on the average regress toward the mean on average. The net effect of regression toward the mean is that the lower scores (or measurements) on the pretest tend to be higher on the posttest, and the higher scores (or measures) on the pretest tend to be lower on the posttest. It is important to note that regression is always to the population mean of a group. But essentially, there is no change that takes place from the pretest to the posttest due to the treatment or the dependent variable.

Shaughnessy and Zechmeister (1990) said that regression toward the mean is a phenomenon that is similar to several everyday expressions such as "law of averages", "things will even out" or "we are due for a good day after a string of bad ones". And one that I would like to add is "it can't possibly get worse (or better) than this!" Basically what all these phrases are saying is that "extreme experiences tend to be balanced by less extreme experiences" (Shaughnessy and Zechmeister, 1990).

Cook and Campbell (1979, pp52-53) explained regression toward the as a phenomenon that:

1) operates to increase obtained pretest-posttest gain scores among the low pretest scores since this group's pretest scores are more likely to have been depressed by error;

2) operates to decrease the obtained change in scores among persons with high pretest scores since their pretest scores are likely to have been inflated by error; and

3) does not affect obtained scores among scorers at the center of the pretest distribution since the group is likely to contain as many units whose pretest scores are inflated by error as units whose pretest scores are deflated by it.

Now that wasn't so bad was it? Let's proceed with the next step...

Step Two: Why is it important?

It is an important phenomenon to take note of in conducting experiments because it affects the internal validity of the experimental design. What happens here is that one can end up concluding that the significant difference or effect is due to the treatment when in fact it is due to chance and by this phenomenon known as regression toward the mean.

Phew, now that we've gotten through that, shall we continue with step three?

Step Three: When does it occur?

It occurs whenever the sample or subjects are chosen on the basis of extreme pretest scores. Examples of this are students with the worst math ability, workers with the lowest morale or patients with the most severe symptoms. Regression toward the mean is expected in these cases where there is non-random sampling or assignment in experiments.

There are cases of experimental designs where the researcher tries to improve on the random group designs by conducting more stringent tests of their hypotheses. This is usually done by comparing groups in the extremes of the distribution of the sample. Through this, they hope to show that groups who start out very different (i.e. from opposite ends of the spectrum), can be made to become more alike when one of the experimental groups is given the treatment. An example of such an experiment is the testing of a math program that is postulated to help students who are poor in their math ability. Researchers who want to make their tests more stringent would treat the group of students who is the poorest in their math ability and compare them to the group who is good in their math ability.

The results of such experiments would most probably show that the difference between the two groups is significantly lesser on the posttest than on the pretest. However, the source of this significant reduction in the difference is likely to be due to regression toward the mean rather than by the treatment in question. This would happen in the example above even if the math program does not work. Researchers have been known to mistake such an effect as something due to the treatment rather than something totally due to chance.

Wow, you're more than halfway through! Just a few more steps...

Step Four: How does it happen?

Shaughnessy and Zechmeister (1990) explains that when one takes a measurement in an experiment, the measurement is made up of two components; the true score/measure and the error.

The true score reflects what the test is validly measuring and tends to be stable from one measurement to another. The error component includes extraneous factors which are nonsystematic. These can include lack of concentration, inappropriate testing conditions or improper question wording. This component is the part that averages out from one measurement to another. According to Shaughnessy and Zechmeister (1990) , what this means is that an individual who scored extremely high on the first test is "likely to score lower on a second test simply because the error component is like to be less extreme and closer to the average." They mentioned that the less reliable the test, the more likely regression toward the mean will occur.

You're on the homestretch now!

Step Five: Where does it occur?

It occurs in all experimental designs and especially in quasi-experiments where nonequivalent groups and non-random assignment are used. Examples of such quasi-experiments are the Nonequivalent Group Designs and the Regression-Discontinuity Designs.

Yes, just one more step!

Step Six: What can I do about it?

The solution to this problem is a simple one. It basically involves the use of control groups. For Randomized Design Experiments, just simply adding a control group to the design will help determine if regression toward to mean is in effect in the experiment. This is because when the sampling is randomized, the control and treatment groups are considered to be equivalent.

With regards to quasi-experiments where there is no randomized sampling or assignment to groups, the solution is slightly different. For example in the case where the treatment is only to be given to the group that needs it most or is at one extreme of the distribution, one would need to form a control group and a treatment group from each of the extreme groups of the sample. This will help check for regression toward the mean. In the case of the Regression-Discontinuity Design experiments, regression toward the mean is not an issue because this design determines a treatment effect through a discontinuity in the regression line at the cutoff point.

OK, you can take a deep breath now and sit back and relax because you made it!

Step Seven: Where can I find out more about Regression Toward the Mean?

An excellent Web site to read is one set up by Dr. William Trochim. Other references that can be read and have been used in writing up this Web site are:

Hays, W. L. (1988). Statistics. Holt, Rinehart and Winston: New York.

Kerlinger, F. N. (1986). Foundations of Behavioral Research - Third Edition. Holt, Rinehart and Winston: New York.

Shaughnessy, J. J. (1985). Research Methods in Psychology. Alfred A. Knopf Inc.: New York.

Shaughnessy, J. J. and Zechmeister, E. B. (1990). Research Methods in Psychology. McGraw-Hill: New York.

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