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Rankings and scores are two common data types used by judges to express preferences and/or perceptions of quality in a collection of objects. Numerous models exist to study data of each type separately, but no unified statistical model captures both data types simultaneously without first performing data conversion. We propose the Mallows-Binomial model to close this gap, which combines a Mallows $$\phi$$ ranking model with Binomial score models through shared parameters that quantify object quality, a consensus ranking, and the level of consensus among judges. We propose an efficient tree-search algorithm to calculate the exact MLE of model parameters, study statistical properties of the model both analytically and through simulation, and apply our model to real data from an instance of grant panel review that collected both scores and partial rankings. Furthermore, we demonstrate how model outputs can be used to rank objects with confidence. The proposed model is shown to sensibly combine information from both scores and rankings to quantify object quality and measure consensus with appropriate levels of statistical uncertainty. 

Considerable attention has focused on studying reviewer agreement via inter-rater reliability (IRR) as a way to assess the quality of the peer review process. Inspired by a recent study that reported an IRR of zero in the mock peer review of top-quality grant proposals, we use real data from a complete range of submissions to the National Institutes of Health and to the American Institute of Biological Sciences to bring awareness to two important issues with using IRR for assessing peer review quality. First, we demonstrate that estimating local IRR from subsets of restricted-quality proposals will likely result in zero estimates under many scenarios. In both data sets, we find that zero local IRR estimates are more likely when subsets of top-quality proposals rather than bottom-quality proposals are considered. However, zero estimates from range-restricted data should not be interpreted as indicating arbitrariness in peer review. On the contrary, despite different scoring scales used by the two agencies, when complete ranges of proposals are considered, IRR estimates are above 0.6 which indicates good reviewer agreement. Furthermore, we demonstrate that, with a small number of reviewers per proposal, zero estimates of IRR are possible even when the true value is not zero. 

In the absence of gold standard for evaluating quality of peer review, considerable attention has been focused on studying reviewer agreement via inter-rater reliability (IRR) which can be thought of as the correlation between scores of different reviewers given to the same grant proposal. Noting that it is not uncommon for IRR in grant peer review studies to be estimated from some range-restricted subset of submissions, we use statistical methods and data analysis of real peer review data to illustrate behavior of such local IRR estimates when only fractions of top-quality proposal submissions are considered. We demonstrate that local IRR estimates are smaller than those obtained from all submissions and that zero local IRR estimates are quite plausible. We note that, from a measurement perspective, when reviewers are asked to differentiate among grant proposals across the whole range of submissions, only IRR measures that correspond to the complete range of submissions are warranted. We recommend against using local IRR estimates in those situations. Moreover, if review scores are intended to be used for differentiating among top proposals, we recommend peer review administrators and researchers to align review procedures with their intended measurement. 

Previous research has found that funding disparities are driven by applications’ final impact scores and that only a portion of the black/white funding gap can be explained by bibliometrics and topic choice. Using National Institutes of Health R01 applications for council years 2014–2016, we examine assigned reviewers’ preliminary overall impact and criterion scores to evaluate whether racial disparities in impact scores can be explained by application and applicant characteristics. We hypothesize that differences in commensuration—the process of combining criterion scores into overall impact scores—disadvantage black applicants. Using multilevel models and matching on key variables including career stage, gender, and area of science, we find little evidence for racial disparities emerging in the process of combining preliminary criterion scores into preliminary overall impact scores. Instead, preliminary criterion scores fully account for racial disparities—yet do not explain all of the variability—in preliminary overall impact scores.