The present study was designed to examine both concurrent and predictive associations between scores on a measure of executive function (EF) skills, the Contingency Naming Test (CNT), during the early school-age years. A secondary aim of the study was to examine the association between EF skills and mathematics performance. We administered tests of mathematics ability, and the CNT, to 178 children at ages 6 to 7, 8 to 9, and 10 to 11 years. From the CNT we obtained measures of response fluency/efficiency, working memory, and inhibition. The results demonstrate main effects of age on all CNT measures of EF, as anticipated, and inconsistent main effects of gender or mathematics learning disability status. Rates of improvement in EF varied as a function of the working memory demands present during a given task. There were differences in concurrent and predictive correlations for different CNT performance measures. EF scores obtained during the first assessment were as strongly associated with each other as they were with EF scores obtained four years later, suggesting a moderately stable source of individual differences on cognitive performance. EF scores at age 6 to 7 years were associated with concurrent and later mathematics scores, and most of these correlations were stronger than the significant associations found between response fluency on a baseline task (with no working memory demand) and mathematics performance. These findings have implications for the stability of EF skills during the school-age years, and the role of EF in early and later elementary school mathematics performance.

This methodological review draws attention to the challenges faced by intellectual and developmental disabilities researchers in the appropriate design and analysis of group comparison studies. We provide a brief overview of matching methodologies in the field, emphasizing group-matching designs used in behavioral research on cognition and language in neurodevelopmental disorders, including autism spectrum disorder, Fragile X syndrome, Down syndrome, and Williams syndrome. The limitations of relying on p values to establish group equivalence are discussed in the context of other existing methods: equivalence tests, propensity scores, and regression-based analyses. Our primary recommendation for advancing research on intellectual and developmental disabilities is the use of descriptive indices of adequate group matching: effect sizes (i.e., standardized mean differences) and variance ratios.

The Autism Diagnostic Interview-Revised (ADI-R) was used to examine diagnostic profiles and age-related changes in autism symptoms for a group of verbal children and adolescents who had fragile X syndrome, with and without autism. After controlling for nonverbal IQ, we found statistically significant between-group differences for lifetime and current autism symptoms for the Communication and Restricted Interests/Repetitive Behaviors domains, but not the Reciprocal Social Interaction domain. Effect sizes for differences in Reciprocal Social Interaction also were smaller than effect sizes for the other domains, with one exception. Overall, severity of autism symptoms improved with age for all participants, with the least improvement noted for Restricted Interests and Repetitive Behaviors. FMRP did not account for unique variance in autism symptoms over and above nonverbal IQ.