Abstract This study introduces a new chi-square test statistic for testing the equality of response frequencies among distracters in multiple-choice tests. The formula uses the information from the number of correct answers and wrong answers, which becomes the basis of calculating the expected values of response frequencies per distracter. The method was applied to a statistics test response data and found to effectively detect unequally plausible distracters. Furthermore, the statistic had a quadratic relationship with item difficulty, indicating that at a certain range of plausibility values, there is an optimal item difficulty.
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Sherwin Balbuena (2024) studied this question.
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