Purpose: In education research, the standardized mean difference (symbolized by d) is the predominant effect size index. It is calculated as the difference between the treatment-group and control-group means, divided by the pooled standard deviation. Using d allows the impacts of education interventions to be compared even when they have been evaluated using different measures or study designs. Calculating d is relatively straightforward for simple-randomized trials. However, calculating d becomes difficult when using cluster-randomized trials (CRTs). Previous work to develop formulas to compute effect size d and its standard error for CRTs ended up identifying the complexity of the procedure and the additional difficulties raised by the use of real data. This project will develop a computer program that can be used by mainstream education researchers to compute d and its standard error for both researchers conducting CRTs and researchers working with published data from CRTs conducted by others. Project Activities: The project will develop a software program to calculate d and its standard error for CRTs. Five modules (each for a different type of CRT including two 2-level and three 3-level designs) will be developed and these will be united by a common interface for entering, saving, retrieving, and exporting data. Development will include different formulas for each design and for each d within each design. Simulated data, for which the actual d's and their standard errors are known, will be used to evaluate the validity of results produced by each module. The computer program will address four complications for the calculation of d and its standard error for CRTs that occur when: (1) defining the effect size; (2) computing d; (3) computing the standard error of d; and (4) working with published data for which inappropriate analysis was used. In defining the effect size, CRTs offer more than one population that can be used as the reference (e.g., for a student-in-school design the reference can be all students, all students within a single school, or all schools). The standard deviation used in calculating d will vary depending on the reference population. Complicated adjustments must be made when computing d and its standard error. When using data reported from incorrect analysis, complicated adjustments must be to done to impute the results that would have been reported if appropriate analysis had been performed.
