Two tests at the same time point
Consider first the use of two tests at the same time point to identify a person as LD. This practice is epitomized by the IQ- achievement discrepancy definition in the Federal regulatory definition of LD. Although IQ-achievement discrepancy has been operationalized with a variety of IQ and achievement tests, and with a variety of approaches to defining discrepancy, the problems addressed in this paper pertain to any comparison of two correlated assessments that involve the determination of a child's performance relative to a cut point on a continuous distribution.
Discrepancy involves the calculation of a difference score (D) for the sake of estimating the true difference (∆) between two latent constructs. Thus, in talking about discrepancy, we must distinguish between problems with the manifest (i.e., observed) difference (D) as an index of the true difference (∆) , but we must also consider whether the true difference (∆) reflects the construct of interest. If the true difference (∆) does reflect the construct of interest, then the problem is a simple one of improving the measurement of the true difference (∆) by strengthening the relationship between the observed difference (D) and the true difference (∆) . Problems with D as a measure of (∆) are well known and have been widely studied, albeit not in the LD context (Bereiter, 1967). However, there is nothing that fundamentally limits the applicability of this research to LD if we are willing to accept a notion of (∆) as the notion of LD that we seek. Additional problems with the observed difference (D) include the need to adjust for the correlation of aptitude and achievement measures to address the problem of regression to the mean in developing identification procedures (Reynolds, 1984). However, improving D as a measure of (∆) involves not only correlation, but also the measurement error associated with any test. In the case of D, error in D as a measure of (∆) results from error in each of the observed measures (IQ and Achievement) that go into its calculation.
IQ and achievement are always measured with error. After all, IQ and achievement are latent constructs that are only imperfectly measured by any particular observed measure of each. The error in the observed measures may be relatively small; such tests are certainly more reliable than other tests used to assess normally distributed traits in the population, such as blood pressure. However, even a small amount of measurement error leads to regression effects if two moderately correlated tests are compared or the same test is repeated. Regression to the mean indicates that on average, scores that are above the mean will be lower when the test is repeated, or on a second correlated test. Thus, individuals who have IQ scores above the mean will obtain achievement test scores that, on average, will be lower than the IQ test score because of regression effects. The opposite is true for individuals whose IQ score falls below the mean: on average, achievement test scores will move towards the population mean.
These effects of measurement error hold for comparisons of correlated tests, or for re-administration of the same test. Many papers have been written about regression to the mean as well as difficulties involved in the computation of reliable difference scores (see Christensen, 1992; Francis et al., in press). Although the use of a regression model that takes into account the correlation of tests helps with the regression problem, there is still unreliability that stems from computation of differences as well as issues involving the attempt to assess a person's standing relative to a cut point on a continuous distribution. As we see in the next section, the problems with a single test with even small amounts of measurement error make it difficult to use low achievement models for identification of LD. But none of this discussion addresses the fundamental question concerning (∆) . Specifically, does (∆) embody LD as we would want to conceptualize it (e.g., as unexpected underachievement), or is (∆) merely a convenient conceptualization of LD because it is a conceptualization which leads directly to easily implemented, operational definitions, however flawed they might be? The use of (∆) as the basis of LD definitions privileges intelligence in determining a student's "expected" achievement to the exclusion of all other factors. In a sense, the discrepancy model is paramount to asserting that the contributions of all other factors to expectations about students' achievement are mediated through intelligence. Approaches which involve RTI recognize that intelligence is one of a host of factors that contribute to students' achievement expectations, and ascribe central importance to the roles of instruction and the opportunity to learn.
Previous Page | Next page
(Introduction) | (One Test)
