Admissible statistics of educational achievement scores

Labor economists regularly regress educational achievement scores on covariates to examine what aects achievement. I discuss the mea surement and interpretation of achievement scores, and argue that, as the scores are typically measured on an ordinal scale, their analysis in terms of higher level statistics such as means is inappropriate, and that we should use quantile-based analysis instead. I investigate how large possible bias from mean-based methods is by comparing test score distributions to the distribution of monetary value of the same scores. In most cases, the bias will be quantitatively small, and conclusions qualitatively robust.