Journal of Educational and Behavioral Statistics

This paper reports the development of indices reflecting the probability that the observed correspondence between the multiple-choice test responses of two examinees was due to chance. Applications of the indices are presented both with respect to apprehending persons who cheat by copying answers and with respect to monitoring the prevalence of this form of cheating in order to evaluate methods of preventing it.

The relationship between quantitative predictors and the probability of occurrence of one or more levels of a qualitative criterion can be analyzed by quantal response techniques. This paper presents two quantal response models. The first model treats the predictors as mathematical variables used as a stratification dimension; the second model uses random variables as predictors. Model II estimation techniques are presented for dichotomous and polychotomous criteria and for single and multiple predictors. The estimation techniques are illustrated with examples of the use of MMPI scale scores to predict the diagnostic classification of psychiatric patients and to model the actual diagnostic classifications of judges. These uses of quantal response methodology are contrasted with those of multiple linear regression and discriminant analysis. Many of the dependent variables collected in school settings are qualitative, e.g., the passing or failing of an item, the mastery or non-mastery of a task, the presence or absence of a behavioral trait or skill. When the interest of the researcher is to relate these variables to quantitative variables, quantal response procedures are potentially applicable for such educational data analyses.

False-positive and false-negative decisions are the two possible errors committed with a mastery test; yet the estimation of the likelihood of committing these errors has not been investigated. Accordingly, two methods of estimating the likelihood of committing these errors are described and then investigated using Monte Carlo techniques. Conditions for obtaining accurate estimates are noted.