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。研究之進行分成研究一與研究二兩部分，其中研究一之題材乃採用
青年智力測驗中的數學測驗446名高二學生預試資料；研究二則是採用研究者自行設計之
數字系列完成測驗所蒐集2426名國二學生反應資料。在分析方法方面，研究一與研究二皆
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。研究之主要發現如下：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、研究一中，影響青年智力測驗之數學測驗預試資料試題難度的試題
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、研究二中，影響數字系列完成測
驗試題難度的試題成分為「相同數字是否鄰近」、「是否為規則數列」、「單一字串中相
同數字個數與該字串週期長度是否相等」、「字串間是否有假造相同的數字」等四類，其
中「相同數字是否鄰近」、「是否為規則數列」、「單一字串中相同數字個數與該字串週
期長度是否相等」三類試題成分對於試題難度具有附項的預測力，而試題成分「字串間是
否有假造相同的數字」則對於試題難度具有正向的預測力。四、試題成分之間的交互作用
也是試題難度變異的來源之一。五、當試題增多時，相對需要更多的成分以解釋試題難度
的變異。六、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 se
ries completion task, and to examine if the constructs for detecting regular n
umber series and irregular number series are different. Two studies were condu
cted, studyⅠwith the pretest data of the math test in the Youth Intelligence
Test, and studyⅡwith the number series completion test developed by the autho
r. Both studies focused on the test component analysis and the component param
eter estimation that were calculated by using stepwise regression model and th
e Linear Logistic Latent Trait Model.The major findings of this study are as f
ollows:1. The constructs to solve both regular number series items and irregul
ar number series items are of the same dimension.1. In studyⅠ, the major diff
iculty accountability of number series completion task comes from three compon
ents: 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 positive
ly related to the difficulty level of number series completion task.3. In stud
yⅡ, the difficulty accountability of number series completion task comes from
four components: if the same figures of the series are adjacent or not, if th
e series is regular or not, if the number of the same figures equals to the pe
riod of the string or not, and if the series is spurious identity or not. The
first three components negatively related to difficulty level of number series
completion task, while the last component positively related to the difficult
y level of number series completion task.4. In several cases, the interaction
term among the components is able to account for the difficulty level of numbe
r series completion task.5. More components are needed to increase the account
ability of items' difficulty of number series completion task according to the
result, especially when the test size is getting large.6. The result shows th
at both stepwise regression and LLTM methods for estimation of component param
eter are similar.