An Investigation of the Rasch Simple Logistic Model: Sample Free Item and Test Calibration1

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Abstract
This research investigated the use of the Rasch simple logistic model in item and test calibration. Tests employing word, picture, symbol, and number analogies were administered to high school students, college students, civil service clerical employees, and clients of the Minnesota Division of Vocational Rehabilitation. The results indicated that Rasch item easiness ratios and z item difficulty ratios were invariant with respect to the ability of the calibrating sample when an adequate sample was employed and the test design did not incorporate biasing factors. The invariance of the Rasch item easiness ratios was shown to be related to the goodness-of-fit of the items to the Rasch model in that the deletion of items with low Rasch probabilities increased the invariance of the Rasch item easiness ratios. The estimation of the amount of ability indicated by the raw scores on a test was also shown to be invariant with respect to the ability of the calibrating sample for tests of 25 or more items, even when samples of fewer than 100 subjects were studied.

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