如何將原始分數轉換成量尺分數--以國中生基本學力測驗為例

Transforming Raw Scores into Scale Scores: BCTEST as an Example

本文示範如何將答對題數原始分數轉換成為量尺分數，並以中生基本學力測驗為例探討強真分數模鋨以及試題反應理論模式等二種方式所得結果之間的差異。結果發現強真分數模式若以廣義的beta-binomial模式來取代原先Lord的beta4模式時，原始分數分配的適配情形非常好，以而單一向度的試題反應模式來將原始分數轉換成量尺分數時，模式的適配情形也不錯。因為本研究歐用的資料是模擬產生的，且為單峰分配的，因此所觀察到的現象是否適用在實際基本學力測驗施測時所部到的雙峰陽配的資料，需要進一步的研究。

The purpose of this study is to illustrate how to transform number-correct raw scores into scale scores using BCTEST scores as an example. In this study， two methods of transforming raw scores into scale scores including using extended beta-binomial model or IRT to obtain the raw score distribution will be described and the results given by these methods will be also compared and discussed. The findings of this study indicate both extended beta-binomail model and item response model fitted the distributions of raw score well and gave similar results. The simulated data used in the study were unimodal， but in the real test it was found that the raw score distribution for English test was bimodal. More studies are needed before the findings given by this study are generalized to other situations.