高校教师教学水平评价概化理论预算限制下最佳样本量估计

使用“高校教师教学水平评价问卷”，要求566名学生对19名教师进行评价，对收集到的数据作不同的概化设计，包括t×i、（s：t）×i、（s：t）×（i：v）和（s：t）×（i：v）×o四种设计。基于概化理论，结合预算限制，统一LaGrange乘法公式，自行推导不同设计的最佳样本量公式，联合估计的方差分量，计算出不同设计的最佳样本量。结果表明：（1）LaGrange乘法统一公式表现出较强的通用性，能够适用于预算限制下各种概化设计；（2）评价场合是影响高校教师教学水平评价一个相当重要的因素；（3）（s：t）×（i：v）×o是高校教师教学水平评价概化理论预算限制下最优概化设计；（4）高校教师教学水平评价概化理论预算限制下，每位教师最佳评价学生人数为20人，每个维度最佳评价题目数为3题。

Estimating the Best Sample Size of Teaching Level Evaluation for College Teachers under Budget Constraints in Generalizability Theory

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.