受測者能力相等性之檢定

Testing Equality of Examinees' Ability

10.6773/JRMS.199612.0001

應立志(Li-Chih Ying)

能力相等性之檢定 ； 項目反應理論 ； 條件機率 ； 貝氏架構 ； Ishii-Yamasaki程序 ； testing equality of abilities ； item response theory ； conditional probability ； Bayes framework ； Ishii-Yamasaki's procedure

測驗統計年刊

4期（1996 / 12 / 01）

1 - 17

繁體中文

在教育心理測驗文獻中，大多探討受測者能力之估計，很少論及受測者能力相等性之檢定。本文採用項目反應理論（Item Response Theory簡稱IRT）中的二元二參數羅吉斯模式（dichotomous two-parameter logistic model），先探討兩位受測者能力相等性之檢定。當項目參數值均相等時，經由條件機率可算出兩位受測者得分之差的正確臨界值。當項目參數值不全相等時，可藉貝氏架構及條件機率算出檢定之臨界值。另外，亦考慮測驗項目個數很多之情況。本文繼而延伸此能力相等性之檢定到多位受測者之情形，此時採用Ishii-Yamasaki之程序作檢定而得保守的臨界值，並將此結果與上述兩位受測者之正確臨界值作比較。

There have been plenty of investigations about estimation of examinees' abilities, but lack of researches about hypothesis test of equality of examinees' abilities. This study first tests the equality of two examinees' abilities using dichotomous two-parameter logistic model on the basis of item response theory. When item parameters are all equal, we can compute the exact critical values of difference of two examinees' scores by the derived conditional probability. When item parameters are not equal, we consider Bayes framework and conditional probability to find the critical values. And then we considers the case of a large number of items. Finally, we extend this test procedure to more than two examinees' case and use Ishii-Yamasaki's procedure to obtain conservative critical values, and then compare them with the exact values of two examinees' case.