Abstract: Using the evaluation questionnaire of Teachers' Teaching Level Evaluation Scale for College Students(TTLES-CS), 566 students were asked to evaluate 19 teachers, and the data were generalized to four kinds of designs such as t×i,(s:t)×i,(s:t)×(i:v) and(s:t)×(i:v)×o. Based on generalizability theory, we combined the budget constraints and derived a unification algorithm adapting with the optimal sample size estimation for different designs of generalizability theory, i.e. LaGrange multiplication. On this basis, we applied LaGrange multiplication to estimate the optimal observation number in different generalizability designs. The results show that: (1) LaGrange multiplication that we derived has a stronger robustness, which can apply to different study designs effectively under budget constraints. (2) Occasion is an important factor that has a great effect on teachers' teaching level evaluation. So, we need attach importance to it. (3) According to the actual circumstances under the budget constraints, the design of(s:t)×(i:v)×o is the optimal generalized design. (4) Under budget constraints of teachers' teaching level evaluation for college teachers in generalizability theory, the best sample size of students is 20 for each teacher and the best sample size of items is 3 for each dimension.

Key words: generalizability theory, budget constraints, estimating the best sample size, college teachers, teaching level evaluation