Quantitative research depends on using measures to collect data that are valid (ie, reflect well the phenomena of interest) and perform equivalently across contexts. Demonstrating validity and cross-context equivalence requires specifically designed studies, but many such studies have problems that have limited their usefulness. This article explains validity and cross-context equivalence of measures (and important related concepts) and clarifies how to establish them. Validation is the process of determining whether a measure or indicator is suitable for providing useful analytical measurement for a given purpose and context. Cross-context equivalence means that a measure performs comparably across contexts. Four types of equivalence are construct, item, measurement, and scalar. Establishing validity and cross-context equivalence requires representing mathematically the errors (ie, imprecision, undependability, and inaccuracy) of a measure and using appropriate statistical methods to quantify these errors. Studies aiming to provide evidence about the validity of a measure need to clarify the purpose and context for use of that measure. Choose one of the two conceptual systems for validation; obtain data to establish the extent to which the measure is well constructed, reliable, and accurate; and use analytic methods beyond simple correlations to provide a basis for making reasoned judgment about whether the measure provides useful analytic measurement for the particular purpose(s) and context. Establishing accuracy of a measure requires having available other measures known to be accurate as comparators; in the case that no other measure understood to be more accurate is available, then the study will be able to establish agreement rather than validity.