How Many Students and Items Are Optimal for Teaching Level Evaluation of College Teachers? Evidence from Generalizability Theory and Lagrange Multiplier

Budget and cost are two of the problems that cannot be ignored when conducting a measure study. Based on the application of generalizability theory, combined with Lagrange multiplier, this paper explores how many students and items are optimal for teaching level evaluation of college teachers under budget constraints to maintain the sustainable development of higher education. A total of 397 students are required to evaluate 10 teachers’ teaching level using the Teaching Level Evaluation Questionnaire for College Teachers, and we make different generalizability designs (i.e., (s:t) × i, (s:t) × (i:v) and (s:t) × (i:v) × o) for the collected data. The study unifies the Lagrange multiplier formula, derives the optimal sample size formula of different designs under budget constraints in generalizability theory, and calculates the optimal sample size for teaching level evaluation of college teachers in different designs with the estimated variance components. Results indicate that: (1) the unified formula of Lagrange multiplier has a stronger robustness and can be applied to different study designs under budget constraints in generalizability theory; (2) the occasion has a great effect on teaching level evaluation for college teachers; (3) the (s:t) × (i:v) × o design has a high efficiency in estimating the optimal sample size of teaching level evaluation for college teachers; (4) the design of (s:t) × (i:v) × o is the optimal generalizability design of teaching level evaluation for college teachers under budget constraints in generalizability theory; and (5) under budget constraints of teaching level evaluation for college teachers in generalizability theory, the optimal sample size of students is 31 for each teacher and the optimal sample size of items is 7 for each dimension.