Dangers of residual confounding: A cautionary tale featuring cognitive ability, socioeconomic background, and education

Cognitive ability and socioeconomic background (SEB) have been previously identified as determinants of achieved level of education. According to a “discrimination hypothesis”, higher cognitive ability is required from those with lower SEB in order to achieve the same level of education as those with higher SEB. Support for this hypothesis has been claimed from the observation of a positive association between SEB and achieved level of education when adjusting for cognitive ability. Here we propose a competing hypothesis that the observed association is due to residual confounding. To adjudicate between these hypotheses, we tested both on data from the 1997 National Longitudinal Survey of Youth (NLSY97, N = 8984), including a check of the logic where we switched places between predictor and outcome. We found the expected positive association between SEB and achieved level of education when adjusting for cognitive ability (predicted by both hypotheses), but we also observed a positive association between cognitive ability and SEB when adjusting for level of education (predicted only by the residual confounding hypothesis). Under the logic of the discrimination hypothesis, a contradictory interpretation emerges: higher cognitive ability is required from those with higher SEB in order to achieve the same level of education as those with lower SEB. These results highlight the potential use of reversing predictors and outcomes to test the logic of hypothesis testing, and support a residual confounding hypothesis over a discrimination hypothesis in explaining associations between SEB, cognitive ability, and educational outcome.