# Some Application of Bayesian Statistics to Educational Data GMAT LSAT SAT

Author(s):
Rubin, Donald B.
Publication Year:
1982
Report Number:
RR-82-42, PSRTR-82-37
Source:
ETS Research Report
Document Type:
Report
Page Count:
35
Subject/Key Words:
Bayesian Statistics, Data Analysis, Graduate Management Admission Test (GMAT), Law School Admission Test (LSAT), Scholastic Aptitude Test (SAT), Validity Studies

## Abstract

Bayesian methods of inference are extremely powerful tools for the applied statistician. They have the ability to obtain sensible answers in a straightforward manner in problems where sampling theory approaches appear awkward. Several examples of Bayesian analyses of Educational Testing Service data are presented. In these examples, simple Bayesian approaches provide better answers than simple sampling theory approaches. Of course, the answers (i.e., estimators, intervals), although derived under Bayesian models, have distributions under repeated sampling, and these sampling distributions might be of substantial interest to the applied statistician in order to calibrate the Bayesian procedures. The first example involves law school admission data from 82 schools and concerns the best multiplier of UGPA (undergraduate grade point average) in an equation predicting FYA (first year average in law school) from LSAT (Law School Aptitude Test) and UGPA. The Bayesianly motivated multipliers are not only more sensible but also predict future FYA's better. The second example investigates the possibility of different prediction equations of FYA in business schools for White and minority students. Because the business schools have few minority students and there are several predictor variables being used, separate least squares equations cannot be calculated for minority students in each business school. Bayesian methods, however, can be used to calculate separate equations and so assess the evidence in the data that different relationships between FYA and predictors exist for White and minority students. The third example concerns eight experiments on special coaching programs for the SAT (Scholastic Aptitude Test), where interest focuses on the most successful coaching program. Here, Bayesian methods summarize the evidence about the largest effect in a natural manner. (35pp.)