Parental socioeconomic status (SES) is a well-established predictor of children's neurocognitive development. Several theories propose that specific cognitive skills are particularly vulnerable. However, this can be challenging to test, because cognitive assessments are not pure measures of distinct neurocognitive processes, and scores across different tests are often highly correlated. Aside from one previous study by Tucker-Drob, little research has tested if associations between SES and cognition are explained by differences in general cognitive ability rather than specific cognitive skills. Using structural equation modelling (SEM), we tested if parental SES is associated with individual cognitive test scores after controlling for latent general cognitive ability. Data from three large-scale cohorts totalling over 16,360 participants from the UK and USA (ages 6-19) were used. Associations between SES and cognitive test scores are mainly (but not entirely) explained through general cognitive ability. Socioeconomic advantage was associated with particularly strong vocabulary performance, unexplained by general ability. When controlling for general cognitive ability, socioeconomic disadvantage was associated with better executive functions. Better characterizing relationships between cognition and adversity is a crucial first step toward designing interventions to narrow socioeconomic gaps.