本研究之目的在結合認知成分分析與心理計量分析的觀點來了解影響數字系列完 成作業試題難度的試題成分，以及分析在數字系列完成測驗中所測量之心理構念是否因為數 列規則破壞與否而有所不同，研究題材乃採用青年智力測驗中的數學測驗446名高二學生預 試資料:在分析方法方面，同時採用多元逐步迴歸方法以及線性對數潛在特質模式來了解試題 成分對於試題難度的影響。本研究之王要發現如下:(一)編製數字系列完成測驗時，加入不規 則數列不會造成試題反應維度的改變。(二)影響數字系列完成測驗試題難度的試題成分為「是 否為移動數列」、「週期長度」與「字串間是否有假造相同的數字」等三類;此三類試題成分對 於試題難度皆具有正向的預測力。(三)試題成分之間的交互作用也是試題難度變異的來源之 一。(四)利用多元逐步迴歸方法以及線性對數潛在特質模式進行試題成分分析所得結果頗為 一致。

　　　　　The purposes of this study were to decompose the difficulty level of number　 series completion task, and to examine if the constructs for detecting regular number　 series and irregular number series are different. The study was conducted with the　 pretest data of the math test in the Youth Intelligence Test, and focused on the test　 component analysis and the component parameter estimation that were calculated by　 using stepwise regression model and the Liner Logistic Latent Trait Model. The major findings of this study are as follows: 1.The constructs to solve both regular number series items and irregular number　 series items are of the same dimension. 2.The major difficulty accountability of number series completion task comes from　 three components: If the series is moving or not, period of the series, and if the series is spurious identity or not. These three components significantly and positively related to the difficulty level of number series completion task. 3.In several cases, the interaction term among the components is able to account for the difficulty level of number series completion task. 4.The result shows that both stepwise regression and LLTM methods for estimation of component parameter are similar.