Why IQ is not a covariate in cognitive studies of neurodevelopmental disorders

Abstract

IQ scores are volatile indices of global functional outcome, the final common path of an individual's genes, biology, cognition, education, and experiences. In studying neurocognitive outcomes in children with neurodevelopmental disorders, it is commonly assumed that IQ can and should be partialed out of statistical relations or used as a covariate for specific measures of cognitive outcome. We propose that it is misguided and generally unjustified to attempt to control for IQ differences by matching procedures or, more commonly, by using IQ scores as covariates. We offer logical, statistical, and methodological arguments, with examples from three neurodevelopmental disorders (spina bifida meningomyelocele, learning disabilities, and attention deficit hyperactivity disorder) that: (1) a historical reification of general intelligence, g, as a causal construct that measures aptitude and potential rather than achievement and performance has fostered the idea that IQ has special status and that in studying neurocognitive function in neurodevelopmental disorders; (2) IQ does not meet the requirements for a covariate; and (3) using IQ as a matching variable or covariate has produced overcorrected, anomalous, and counterintuitive findings about neurocognitive function.

Fig. 1

The ellipses in the figure represent the 99% quantiles in a bivariate normal distribution for two groups where the correlation between IQ (graphed on the horizontal axis) and Memory (graphed on the vertical axis) is .6 for each group. In the margins of the figure are graphed the univariate probability density functions (i.e., the univariate distributions) for the groups. The normal distribution below the horizontal axis shows the marginal distribution for IQ, while the two normal distributions on the left side of the figure show the marginal distribution of Memory for Groups 1 and 2, respectively. Note that in the margin of the horizontal axis, only a single normal distribution is graphed because the populations are equated on IQ. In contrast, on the vertical axis, two distributions are shown in the margin, reflecting the difference in the mean of Memory for the two populations. The dashed horizontal lines are plotted at the mean of Memory for each group to make it easy to compare the group means on Memory. The vertical line is plotted at the mean of IQ. The fact that there is only one vertical line indicates that the populations are equated on IQ. If we ignore information about IQ, comparing the two groups on Memory would amount to examining the difference in the heights of the two horizontal lines relative to the variability in the marginal distributions of Memory (i.e., the normal distributions on the left side of the figure). When information on IQ is included in the analysis, then groups are implicitly being compared on Memory at the grand mean for IQ, and this difference is evaluated relative to the variability in the conditional distribution of Memory, which is much less than the variability in the marginal distribution of Memory.

Fig. 2

This figure differs systematically from Figure 1 because the two groups differ on the mean of IQ. As in Figure 1, the correlation between the IQ and the Memory is .6 for each group. In addition, Figure 2 includes two heavy lines that depict the regression of Memory on IQ for each group and also includes a second set of horizontal lines. As in Figure 1, the horizontal dashed lines depict the unconditional mean of Memory for each group. The solid horizontal lines, in contrast, depict the conditional mean of Memory for each group; that is, the solid horizontal lines show the expected value for Memory, for individuals in each group with scores on IQ that are equal to the grand mean of IQ, which is depicted by the solid vertical line.

Fig. 3

This figure is similar to Figure 2, but in this case, the displacement of groups on IQ is opposite what would be expected given the overall positive correlation between IQ and Memory in both groups. The two solid horizontal lines show the difference in the conditional (i.e., adjusted) means. The separation between the two dashed horizontal lines shows the difference in the unadjusted means, which are also referenced by the centers of the marginal distributions for Memory.

Fig. 4

In this figure, the ellipses are of different sizes reflecting the overall weaker relation between IQ and Memory in the lower performing group. In this case, the correlation between the two measures is only .4, whereas in the higher performing group, the correlation is .8.