國中基本學力測驗自民國九十年實施，今年邁入第五年，學力測驗量尺分數之理論基礎，主要以Lord所提出之強真分數模式(Strong True Score Model)為主，以適當的模式對考生答對題數資料進行轉換，進一步計算出現在的量尺分數；然而國內針對學力測驗之量尺分數所做之相關研究甚少，因此本研究在第一部份先描述量尺分數轉換之理論，並詳細描述資料轉換之過程與方法。 目前學力測驗小組所採用之模式有上限模式與下限模式兩種，以考生答對題數資料估計出此兩種模式，以較低的均方差決定採用之模式，再接下來進行數據轉換之工作，然而此兩種模式都只適用於描述單峰分佈的考生答對題數之分配，英語科在歷年的學測資料，皆呈現之雙峰分佈之情形，故本研究提出混合雙峰模式，該模式較現有學力測驗之上限模式、下限模式更能清楚描述考生答對題數之分配，且具有較低之均方差。 本研究亦對量尺分數之轉換過程提出新的見解，本研究資料顯示在指定量尺平均數時，採用平均數之加權數，會比現行各科量尺指定平均分數皆固定為30分來得好，且具有較低之量尺標準差。 最後本研究總結上述方法與結論，對量尺分數的計算方式提出新的流程，以供學力測驗小組以及學者專家作為研究之參考。

實施十二年國民基本教育，目的是為促進學生五育均衡發展，兼顧國中學習品質及日常生活表現。由於各校對成績的評分標準與評分方式皆不相同，因此如何使在校成績採計達到公平性將成為一項重要的問題。 戴岑熹(2011) 考慮了國中在校綜合學科分數與基測總分間的相關性，以決定在校各學科的權重。而本研究延伸其概念與方法，將基測各科量尺分數考慮進來，於在校綜合學科分數與基測綜合量尺分數的關聯性最密切的情況下，分析各學科權重的取決方式，希望能找出較理想的模式來代表學生在校三年的整體學習表現與成果，以做為免試升學採計在校成績的參考與依據。 本文的研究方法是運用典型相關分析的理論，但因權重的限制條件與傳統典型相關分析的要求不同，因此，便將其命名為「類典型相關分析」。在類典型相關分析中，我們證明了在校各學科分數及基測各科量尺分數的最佳權重，可先透過典型相關分析求得典型相關向量，若有必要的話，使用Rao-Ghangurad 方法加以修正，最後，再將所獲得的非負典型相關向量正規化，即可獲得所要的結果，這是一個求最佳權重向量極便捷的途徑。在實例分析方面，我們發現了一個有趣的現象，即在校學科分數與基測考科量尺分數的最佳權重向量相當接近，即名稱相同的學科與考科幾乎有相同的權重。在比較了幾個權重分配方式不同的在校綜合學科分數後，我們也發現一般學校常用的等加權模式，其表現結果也頗優異。 / The purpose of implementing the twelve-year compulsory education is to promote the balanced development of learning in students, taking into account their learning quality and normal daily performances in school. As the evaluation standard and method vary among schools, achieving fairness in calculating in-school grades has become an important issue. Dai (2011) considered the correlations between the scores of in-school academic performance and the total score of the BCTEST for junior high schools, which decided to the weightings of all learning subjects. This study extended his concept and method, and took into account the scale scores of all learning subjects. In the closest case of the weightings of all learning subjects and find out the correlations between the scores of in-school academic performance and the BCTEST, and analyse the weightings of all learning subjects. We hope the study can find a better approach that can not only reflect students’ learning situations and achievements for the three years in school but also provide a reference for the evaluation of entering senior high schools without entrance examinations. The research method in this paper employs the theory of canonical correlation analysis.However, due to that fact that weight restrictions are different from the requirements of canonical correlation analysis, it is named as the canonical correlation analysis type approach. In the canonical correlation analysis type approach, we proved that the optimal weights for school subject score and test subject score scales can be obtained by finding the canonical correlation vectors using canonical correlation analysis. Then the Rao-Ghangurad method can further be used for amending, if needed. Finally, the nonnegative canonical correlation vectors generated would be normalized to get the desired result. It is an extremely convenient way to obtain the optimal weight vector. In the case study, we found an interesting phenomenon as follows: When the optimal weight vectors for school subject score and test subject score scales were very close, subjects and tests of the same name had almost the same weight. After comparing several comprehensive school subject scores of different weight distribution, we also found that the results of the equal weighting model commonly used in schools also showed quite good results.