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Raju, Nambury S. – Educational and Psychological Measurement, 1982
A necessary and sufficient condition for a perfectly homogeneous test in the sense of Loevinger is stated and proved. Using this result, a formula for computing the maximum possible KR-20 when the test variance is assumed fixed is presented. A new index of test homogeneity is also presented and discussed. (Author/BW)
Descriptors: Mathematical Formulas, Mathematical Models, Multiple Choice Tests, Test Reliability
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Wilcox, Rand R. – Educational and Psychological Measurement, 1982
Results in the engineering literature on "k out of n system reliability" can be used to characterize tests based on estimates of the probability of correctly determining whether the examinee knows the correct response. In particular, the minimum number of distractors required for multiple-choice tests can be empirically determined.…
Descriptors: Achievement Tests, Mathematical Models, Multiple Choice Tests, Test Format
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Melzer, Charles W.; And Others – Educational and Psychological Measurement, 1981
The magnitude of statistical bias for the phi-coefficient was investigated, using computer simulated examinations in which all the students had equal knowledge. Several modifications of phi were tested, but when applied to real examinations, none succeeded in improving its reproducibility when items are re-used on equivalent student groups.…
Descriptors: Correlation, Item Analysis, Mathematical Models, Multiple Choice Tests
Peer reviewed Peer reviewed
Wilcox, Rand R. – Educational and Psychological Measurement, 1981
A formal framework is presented for determining which of the distractors of multiple-choice test items has a small probability of being chosen by a typical examinee. The framework is based on a procedure similar to an indifference zone formulation of a ranking and election problem. (Author/BW)
Descriptors: Mathematical Models, Multiple Choice Tests, Probability, Test Items