# Hierarchial model superior to multiple single-test analysis

In an ongoing analysis of psychometric test results from 176 children aged 6 to 11 years, half of whom may have been prenatally exposed to a certain category of environmental toxicants, the other half being control subjects, a hierarchical modelof intellectual abilities is superior to a multiple single-test analysis in detecting theadverse effect of toxicant exposure.

In the multiple single-test analysis only two of a greater number of tests (one verbal and the other manual motor) reached statistical significance for an adverse effect ofprenatal exposure (for girls only) after correction for covariates. Several of the other tests showed a tendency towards a negative effect, but none reached statistical significance.

A conclusion from this analysis would only allow for negative effects on specific or differential abilities in two different domains. The tendencies seen in other tests would not count. Furthermore one would have to express caution in accepting the validity of the results because of multiple statistical testing, and the consequent possibility of capitalizing on chance.

In a hierarchical model (established by confirmatory facor analysis – CFA) of the same tests, a statistically significant negative effect on the *g*-factor from prenatal exposure (in a structural equation model – SEM) could be demonstrated (for girls only) after correction for covariates.

Presumably the greater purity of the latent variable, the *g*-factor, is the reason for this. In a hierarchical model true variance is extracted from all the manifest psychometric tests, while error variance is cancelled out. In addition the problem ofmultiple testing and capitalizing on chance is avoided, since only one statistical test is performed.

This analysis allows for the conclusion, that there is a negative effect on the general factor of the universe of human abilities. This is a much stronger conclusion, since the toxicant adversely affects a more general construct, and because the g-factor is known to be a strong predictor of success in a long time frame in real-life areas like education and occupation, and many others.

This example may serve as a recommendation for adopting hierarchical models in epidemiological research, whenever effects on human mental abilities are examined.