A psychologist was interested in developing an English Language Usage test for HSSC students. She wrote 120 questions trying to cover several areas of language usage. Each question had five alternatives, out of which only one was right. The draft version of the test was given to a sample of 200 students. The test items were analysed in two ways — carrying out item-remainder correlation and discrimination index for each item. For the purpose of computing item discrimination index, she labelled those who had a total score below P27 as low scorers, and those who had a total score above P73 as high scorers (assume that P27 and P73 had non-fractional, i.e. full integer, values). The statistical significance of the discrimination index of each item was evaluated by an appropriate test. Ninety items were retained in item analysis. The ninety-item version was administered to a fresh sample of 400 subjects. Cronbach alpha was computed. The psychologist also wondered if she could compute Kuder-Richardson (K-R) reliability for her test. Since the Cronbach alpha was pretty high, i.e. .947, and the test was quite long, she decided to develop two parallel forms, each of 45 items. She randomly assigned the items to two halves, labelling them as Form A and Form B. For each form, she assessed average inter-item correlation, mean, standard deviation and Cronbach alpha. The two forms satisfied the criteria for parallel forms.
Which one of the following tests can be used for evaluating the statistical significance of the discrimination index?
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Correct answer: A. Chi-square test
Explanation
The discrimination index compares pass proportions in two groups; its significance is tested with chi-square on the 2 × 2 table.
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