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How do scores between the Stanford-Binet®, OLSAT®, and WPPSI®-III correlate? If we know a child’s Stanford-Binet® score, does that indicate how they will score on one of the other tests?
Correlations involve some complicated issues. For a start, correlation coefficients, which can range from -1.0 to +1.0, are arrived at through group data. In other words, a group of children might be given two different IQ tests and the correlation would reflect how consistent the scores tended to be from one test to the other for the total group. It does not predict an individual child’s score.
The only time this would not be the case is a situation where you have a coefficient of 1.0. That represents a perfect correlation (i.e., a child’s ranking on one test would be identical to his or her ranking on the other test). But correlations of 1.00 are almost never found—particularly in the world of IQ testing. Further, as the number moves away from 1.0, there are rapid drops in the relationship. For example, anything from around .7 and upward is generally considered to be a high correlation. But a correlation of .7 allows you to predict only about 50% of the variance in the group. The end result is that you would not be able to predict, with any degree of confidence, what a particular child’s scores would be on one test once you know his or her scores on another test.
To get a better sense of what this means, it’s useful to take an example from outside the area of intelligence testing and consider the dimensions of height and weight. Those two variables are known to correlate so that, on average, the weight of people 5’5” is less than the average weight of people 5’6”, and their average weight is less than that of people 5’7”, and so on . But the actual weight of people who are 5’5” varies considerably and many of those people will be heavier than people who are 5’6” and many will be lighter than those who are 5’4”. Hence, if you were told that you would be meeting a 5’5” person and had to predict his or her weight, you would rightly feel somewhat uncomfortable. Based on population statistics, you could offer a reasonable estimate and possibly be right—but you are also very likely to be wrong. If you are allowed to expand your estimate to cover a 20 pound range, then the chances of your being “right” are much greater.
A similar situation holds for IQ scores. Most IQ tests have reasonably high correlations. They have to –or else they would not be published. But that does not permit you to predict, with any degree of confidence, what the child will do on one test once you know what he or she did on the other. However, the situation opens up somewhat if you are permitted to work in ranges. So if a child scores in the super bright range on one test, he or she might score only in the bright range on another test. Indeed a 10, 15 or even 20 point difference is not uncommon. However, it is unlikely that he or she would fall into the average or below average range in that other test.
Does this mean that we should be very careful about the interpretation of IQ scores? Certainly. Children’s IQ’s can vary considerably from test to test and from year to year. It is a valuable measure—but it is by no means a solid, unchanging measure.