Multiple sources of complications in the analysis of multilevel educational data are described with emphasis on the determination of a method of analysis that will provide accurate estimates of teacher/class effects even when there are systematic differences in within-class regressions of outcome on input associated with teacher/class characteristics. Multilevel approaches are considered as well as traditional pupil-level and class-level analytical models. The results from a simulated model of educational effects which allowed the effects of teacher quality on the variation in the within-class slopes to vary over a range of meritocratic, random and compensatory conditions illustrated that overall between-student analyses, between-class analyses, and proposed multilevel methods can all yield misleading estimates of the magnitude of teacher effects on mean class outcome. However, selected multilevel methods provide some indication of misspecification and can identify the direction of the bias in estimating teacher effects on mean class outcomes. (Author/MV)