Consider an n-item multiple-choice test where it
is decided that an examinee knows the answer if
and only if he/she gives the correct response. The k
out of n reliability of the test, Qk, is defined to be
the probability that, for a randomly sampled examinee,
at least k correct decisions are made about
whether the examinee knows the answer to an item.
The paper describes and illustrates how an extension
of a recently proposed latent structure model
can be used in conjunction with results in Sathe,
Pradhan, and Shah (1980) to estimate upper and
lower bounds on Qk. A method of empirically checking
the model is discussed.
Wilcox, Rand R. (1982). Bounds on the k out of n reliability of a test, and an exact test for hierarchically related items. Applied Psychological Measurement, 6, 327-336. doi:10.1177/014662168200600309
Wilcox, Rand R..
Bounds on the k out of n reliability of a test, and an exact test for hierarchically related items.
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