Evidence of social inequalities in cognitive abilities in early childhood has been documented in many societies; however, three characteristics of the data used to measure cognitive constructs make it difficult to quantify inequalities across groups. First, a causal understanding of validity is not compatible with the standard validation framework, which forces researchers to think critically what it means to measure unobserved constructs. Second, test scores only provide ordinal information about individuals, they are not interval scales and require the use of suitable corresponding methods for their study. Third, measurement invariance, which causes measurement error, may make comparison of test scores across groups invalid. The paper explores these three data problems applied to standardized tests---one mathematics and two language assessments---taken by a cohort of German children. The paper proposes a comparative validation framework for researchers based on nonparametric psychometric models and the representational theory of measurement. This framework can help researchers to determine if data fit the assumptions of a measurement model, to check for various forms of measurement error, and to overcome potential issues. A comparison of competing statistical modeling alternatives reveals substantial differences: By conceptualizing ability as ordinal instead of interval and excluding items that do not fit the assumptions of measurement models, I find a reduction in effect sizes for typical covariates studied in social stratification research.
Social inequalities in early childhood competences, and the relative role of social and emotional versus cognitive skills in predicting adult outcomes
