学生评教研究的最佳样本量估算——基于拉格朗日乘数法的应用

Estimating the Best Sample Size for Students’Evolution of Teaching--Based on the Application of La Grange Multiplier Method

样本量是影响测量有效性的因素之一,受多个条件限制。文章阐述了拉格朗日乘数法用于推导预算限制下概化研究侧面最佳水平数的流程化操作思路;通过学生评教的实证研究,比较预算限制下概化研究不同设计各测量侧面的最优水平数,说明拉格朗日乘数法的广泛适用性。结果表明:(1)拉格朗日乘数法在预算限制下求解概化研究侧面最佳水平数时表现出稳健性;(2)结合测量研究设计需要及实际情况,可得概化研究中的最优设计。

The effectiveness of Students’Evolutions of Teaching(SET)is one of the problems that many colleges pay attention to.A great study of SET has the following influences:(1)Promoting the improvement of teaching quality;(2)Focusing on students’experience in class;(3)Providing decision-making ground for managers.The measurement study of SET is affected by the measurement design,the effectiveness of study tools,sample size,and so on.At present,Classical Test Theory(CTT)is most used in the analysis of measurement study of SET.The common problem is without consideration of the effectiveness of SET from the perspective of measurement.Generalizability Theory(GT)is a statistical theory to evaluate the reliability of behavior,holding the views that the total variance can be decomposed into variance component representing the error of object of measurement and other variance components.Generalization coefficient is the standard of reliability in Generalizability Theory.Generally speaking,the larger the sample size,the higher the generalization coefficient value and the test reliability.However,the measurement cost will increase due to the increasement of sample size,which are a dilemma.Therefore,researchers should consider the budget and cost when they explore a measurement procedure.How to get an optimal sample size under budget constraints is one of the problems that cannot be ignored.LaGrange multiplier method is a method to solve the extremum in the mathematical field,which is most widely used for obtaining the optimal levels of different facets of generalized design under budget constraints.According to a series of studies of Marcoulides and Goldstein,we summarized the steps of using LaGrange multiplier method to obtain the optimal facets of measurement in generalizability theory under budget constraints.The steps is following:(1)Discussing the the sources of errors and carry out generalizability design;(2)Estimating the variance components;(3)Quantizing the constraints on the basis of practical situation;(4)Imposing the LaGrange multiplier to structure the LaGrange function that used to solve the optimal levels of different facets in generalized design under budget constraints.This article used Teaching Quality Evaluation Scale for College Teachers(For Students)as a tool to collect data from three different colleges.A total of 530 students took the test and evaluate their teachers.We considered t×i design,(s:t)×i design,(s:t)×(i:v)design,and(s:t)×(i:v)×o design respectively,which t represents teachers,i represents items,s represents students,v represents the dimensionality of the scale,and o represents the times of evaluation.We estimated the variance components through urGENOVA.What’s more,the budget of one evolution was set at 2500 yuan.The generalization coefficient was used as the comparison index.The results showed:(1)Using LaGrange multiplier method and variance components to derive the function of optimal levels of different facets is feasible;(2)LaGrange multiplier method can be effectively applied to different designs in generalizability theory under budget constraints and has stronger robustness.(3)Combined with analysis of actual situation,we know the(s:t)×(i:v)design is the optimal generalized design in this SET study.