The effect of the scale of grant scoring on ranking accuracy

In this study we quantify the accuracy of scoring the quality of research grants using a finite set of distinct categories (1, 2, …., k), when the unobserved grant score is a continuous random variable comprising a true quality score and measurement error, both normally distributed. We vary the number of categories, the number of assessors that score the same grant and a signal-to-noise ratio parameter. We show that the loss of information of scoring a small number of categories (k > 5) compared to scoring on a continuous scale is very small, so that increasing the number of scoring categories is unlikely to lead to an improvement in the outcomes of scoring systems. In addition, we model the effect of grant assessors scoring too close to the mean and show that this results in only a very small reduction in the accuracy of scoring.