Open AccessA Bayesian predictive analysis of test scores
Author(s) -
Ishii Hidetoki,
Watanabe Hiroshi
Publication year - 2001
Publication title -
japanese psychological research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.392
H-Index - 30
eISSN - 1468-5884
pISSN - 0021-5368
DOI - 10.1111/1468-5884.00156
Subject(s) - test (biology) , statistics , reliability (semiconductor) , bayesian probability , mathematics , variance (accounting) , statistical hypothesis testing , econometrics , paleontology , power (physics) , physics , accounting , quantum mechanics , business , biology
In the classical test theory, a high‐reliability test always leads to a precise measurement. However, when it comes to the prediction of test scores, it is not necessarily so. Based on a Bayesian statistical approach, we predicted the distributions of test scores for a new subject, a new test, and a new subject taking a new test. Under some reasonable conditions, the predicted means, variances, and covariances of predicted scores were obtained and investigated. We found that high test reliability did not necessarily lead to small variances or covariances. For a new subject, higher test reliability led to larger predicted variances and covariances, because high test reliability enabled a more accurate prediction of test score variances. Regarding a new subject taking a new test, in this study, higher test reliability led to a large variance when the sample size was smaller than half the number of tests. The classical test theory is reanalyzed from the viewpoint of predictions and some suggestions are made.