Comparative public health research makes wide use of self-report instruments. For example, research identifying and explaining health disparities across demographic strata may seek to understand the health effects of patient attitudes or private behaviors. Such personal attributes are difficult or impossible to observe directly and are often best measured by self-reports. Defensible use of self-reports in quantitative comparative research requires not only that the measured constructs have the same meaning across groups, but also that group comparisons of sample estimates (eg, means and variances) reflect true group differences and are not contaminated by group-specific attributes that are unrelated to the construct of interest. Evidence for these desirable properties of measurement instruments can be established within the confirmatory factor analysis (CFA) framework; a nested hierarchy of hypotheses is tested that addresses the cross-group invariance of the instrument's psychometric properties. By name, these hypotheses include configural, metric (or pattern), strong (or scalar), and strict factorial invariance. The CFA model and each of these hypotheses are described in nontechnical language. A worked example and technical appendices are included.