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Determining Predicted Achievement

When determining predicted achievement, the Table provided take into account both the reliability of each measure used and the correlation between the ability and achievement.

The correlation between two tests is important when defining a severe discrepancy. Tests of ability and achievement do not correlate perfectly (measure the same thing). Just because someone has a low ability score, we should not assume that they would also, automatically, have an equally low score on some other, different measure. No one would assume that just because a person had a very high IQ that the person would obviously be able to excel at gymnastics, or be able to hold his or her breath longer than "normal." Just because someone is good or bad at one thing, it does not guarantee that the person will also be good or bad at other things. An ability (IQ) test does not measure the same thing as an achievement test. Common statistical methodology, utilizing concurrent validity coefficients, demonstrates that a child obtaining an extreme IQ score (e.g., 130) would be expected to obtain a mean achievement level of only about 120. Thus the expected achievement of the child with an IQ of 130 is not 130 at all, but more likely to be about 120. For child with a low IQ score, the reverse is true: the expected achievement of a child with an IQ of 70 would be approximately an achievement score of 80. If practitioners do not adjust (regress) the scores they obtain in determining the "expected" achievement score, they will produce over-identification of high IQ children and under-identification of low IQ children. Without accounting for the correlation between two tests, one would never be able to know what the "expected" score should be.

The best way to determine the correlation between two measures is to look the correlation up in the manual of the test used. Unfortunately, not all manuals offer that information; the information is often based on absurdly small samples; and not all tests have been compared to each other. One way around this shortcoming is to estimate the correlation between the two tests. If we know the reliability of the ability test and the reliability of the achievement test, the correlation between the two tests can be estimated.

The equation for estimating the correlation between two tests is:

**The values rxx and ryy are the internal consistency reliability coefficients for the aptitude and achievement tests used.

Using the Tables to Determine the Expected Achievement

The determination of expected achievement involves 2 basic steps:

1. Determine the estimated correlation between tests

2. Determine the expected achievement score

Go to Tables for Expected Achievement

Go to Determination of Severe Discrepancy