Chance success due to guessing is treated as a component of the error variance of a multiple-choice test score. It is shown that for a test of given item structure the minimum standard error of measurement can be estimated by the formula . where N is the total number of items, X is the score, and a is the number of alternative choices per item. The significance of non-independence of true score and this component of error score on multiple-choice tests is discussed.
Get full access to this article
View all access options for this article.
References
1.
BoxG. E. P.Non-normality and tests on variances. Biometrika, 1953, 40, 318–335.
2.
HorstA. P.The difficulty of a multiple choice test item. J. educ. Psychol., 1933, 24, 229–232.
NortonD. W.An empirical investigation of some effects of non-normality and heterogeneity on the F-distribution. Unpublished Ph.D. thesis in Education, State Univer. of Iowa. Reported in E. F. Lindquist, Design and analysis of experiments in psychology and education. Boston: Houghton-Mifflin, 1953.
