任意實數計分之改進廣義多元計分順序理論

順序理論又稱為次序理論（Ordering Theory），可分為問題順序理論與試題順序理論，其原理相同，只是順序係數之方向相反。為節省篇幅，本研究只論述改進之廣義多元計分順序理論，如何能滿足本文所提完備化順序理論之六準則：(1)關聯性準則；(2)公平性準則；(3)規格性準則；(4)單調性準則；(5)完全性準則；(6)決定性準則。Airasian與Bart（1973）首先提出第一類順序理論，簡稱OT理論；Takeya（1980）提出較靈敏之第二類順序理論，也就是試題關聯結構理論（IRS）；上述兩類理論均不夠完備，尚需改進發展。本研究專論第一類完備化順序理論，第二類完備化順序理論將另文發表。當各試題之多元計分只為等選項依序排列之整數時，Takeya（1987）提出最簡單之規格化順序理論，也就是問題語意結構分析理論（semantic structure analysis, SS）。但當各試題之多元計分為任何實數計分時，劉湘川（2003）兼顧鑑別度，提出混合型問題語意結構分析理論（mixing semantic structure analysis, MS），該理論已是鑑別度最大之廣義多元計分順序理論；之後，劉湘川、楊志良（2003）再以全距代替標準差，提出另一種劉氏簡明之混合型問題語意結構分析理論（Liu's simple mixing semantic structure analysis, LS），並將之應用於醫學調查問卷，此模式亦可適用於任何混合計分及實數計分，但兩者比較基準不同，中心度不如標準值具鑑別力，故LS遠不如MS靈敏。林原宏（2007）也提出非等選項依序排列等級計分之廣義多元計分順序理論（generalized polytomous ordering theory, GPOT），但GPOT只是LS 在整數計分時之特例。上述諸順序理論都屬第一類順序理論，都未臻完備。本研究將MS與LS使其滿足關聯性準則，分別提供可隨選項數改變之動態決斷值，提出改進之廣義多元計分順序理論。本研究證明此二新理論能滿足完備化順序理論之六大準則外，亦討論各種順序理論之關係，非但比既往對應順序理論更為嚴謹靈敏，且同時適用於常用之等選項等級計分以及非等選項任何混合計分與任意實數計分之試卷或問卷。

關鍵字

問題語意結構分析；試題順序理論；試題關聯結構理論

並列摘要

The basal principal of Ordering Theory for testing and questionnaire are the same, only their ordering coefficients have the opposite direction. For saving space, this study only discusses how to completely modify the method of the former, according to following six criteria: (a) association, (b) fairness, (c) normalization, (d) monotonicity, (e) totality, (f) determination. Airasian and Bart (1973) proposed the first kind of ordering theory (OT). Takeya (1980) proposed the second kind of ordering theory: Item Relational Structure theory (IRS). Both of them are not completed to be modified. Liu (2003) proposed a standardized ordering theory: the mixing Semantic Structure Analysis (MS). It can be applicable to ordering theory with rating scale by any real numbers, and it is one of the most generalized polytomous ordering theory. Liu and Yang (2003) replaced the standard deviation of the ordering coefficient of MS with the range to propose a more simplified method called Liu's simple mixing semantic structure analysis (LS) and had applied to a medical questionnaire. But it is not so sensitive like Lin (2007) also proposed his generalized polytomous ordering theory (GPOT), it can also be applicable to any two items with unequal options, but GPOT is a special cases of LS. All of above mentioned ordering theories are not completed ordering theories, they did not satisfy the association criterion, all of them did not prove the fairness property, and do not provide any dynamic cutoff score of their ordering coefficient based on its deferent integers of options. This study has completely modified MS and LS to satisfy the association criterion, to prove the fairness as supplement, and to provide the dynamic cutoff score of their ordering coefficient based on its deferent integers of options for any real number scoring. These two new methods are more sensitive than previous ordering theories and can be applicable to any test and questionnaire whose any two items with equal options or unequal option, and its arithmetic series options are arranged in sequence for any real number scoring.