Background: The COSMIN checklist (COnsensus-based Standards for the selection of health status Measurement INstruments) was developed in an international Delphi study to evaluate the methodological quality of studies on measurement properties of health-related patient reported outcomes (HR-PROs). In this paper, we explain our choices for the design requirements and preferred statistical methods for which no evidence is available in the literature or on which the Delphi panel members had substantial discussion. Methods: The issues described in this paper are a reflection of the Delphi process in which 43 panel members participated. Results: The topics discussed are internal consistency (relevance for reflective and formative models, and distinction with unidimensionality), content validity (judging relevance and comprehensiveness), hypotheses testing as an aspect of construct validity (specificity of hypotheses), criterion validity (relevance for PROs), and responsiveness (concept and relation to validity, and (in) appropriate measures)./nConclusions: We expect that this paper will contribute to a better understanding of the rationale behind the items, thereby enhancing the acceptance and use of the COSMIN checklist.