On the "association between two things": the case of student surveys and classroom observations of teaching quality

This study examines the association between two measures of teaching effectiveness—a student survey measure and a classroom observation measure—to determine whether their correlation depends on the study design. The sample includes 160 classroom observations of 56 teachers across 15 classes, in which students also rated the teachers with a survey. Dependencies are examined using generalizability theory. Results suggest that the correlation between the survey and observation measures depends on the number of classroom observations, the number of student ratings, and whether the designs are nested or partially nested. The effect is substantial: Predicted correlations range between 0.10–0.80 for the same variables with different study designs. In particular, the number of classroom observations has a notable influence, such that across all investigated scenarios, the correlation doubles when observers visit three lessons instead of one. Correlations also tend to be positively biased when research designs are nested.