Appraisal of a school's relative effectiveness is complicated by: (1) the need to control for input differences; (2) measurement error in input measures; and (3) small sample size within schools. This study compares the performance of two successive cohorts in 19 schools in a small midwestern city on the five Iowa Tests of Basic Skills using both a classical analysis of covariance and a Bayesian method. The Bayesian estimates were less different from cohort to cohort than the classical estimates and they were more consistent with expectations based on knowledge of school practices. (Author/CTM)