成就測驗組合分數議題探討

Issues Related to the Composite Score of Achievement Tests

本研究根據一個成就測驗題庫建置計畫的試題參數產生模擬資料來探討組合分數計算的相關議題，文獻中曾提到的組合分數的加權數計算方法多達十餘種，本研究主要探討信度加權法和IRT加權法;另外以菜市一般智能資優學生甄選資料來探討多元迴歸和主成份分析法。結果發現在信度加權法的部分，用原始分數之間的相關矩陣或是用各科能力值之間的相關矩陣所計算得到的各科分數之加權數類似，且二者所得到的組合分數之信度你數雷同。利用四個科目的能力值所計算得到的主成份分數和組合分數與將四科資料視為一科目專利用3PL模式所估計得到的能力值之間的相關條數，對五年級來說，分別為.969和.982，而對六年級來說，則是.971和.990。最後，利用團體智力測驗的三個分測驗的資料計算主成份分數，或利用多元迴歸分析預測個別智力測驗的分數，結果發現主成份分數與個別智力測驗分數之間的相闕，和用多元迴歸所得到的預測分數與真正的個別智力測驗分數之間的相關，二者的值非常接近，都接近.95。

The purpose of this study is to survey four ways for computing the composite score of four tests from a test battery, which was simulated using the item parameters taken from a test item banking project. More than ten approaches of constructing composite scores can be found in the literature. Among them, reliability weighting, IRT weighting, principle component analysis and multiple regression were investigated in this study. With the data from Chinese, Math, Science, and Social Science achievement tests, the weights given by raw score and IRT trait score using reliability weighting method are very similar. Treating all items from four subject areas as items of a test and calibrating the trait level with 3PL model, the resulted trait scores has a Pearson correlation coefficient of .969 and .982, respectively, with the principal component score and composite score obtained from traits from that four achievement tests for the fifth grader, and .971 and .990, respectively, for the sixth graders.Finally, both the principal component scores, obtaining from the three subscales from a group intelligence test, and predicted individual intelligence test score correlated highly with the observed score of the individual intelligence test, near .95 for both cases.