國中基測量尺分數轉換議題探討

The Scale Score Transformation Issues of the BCTEST

本文目的在於探討基本學力測驗各科量尺分數對照表經過微調時，對於考生總分名次排序的影響以及對於目前考生全錯或僅答對數題時，皆對應到量尺分數1分的情形，是否能夠加以改善。在所模擬的5000考生資料中，當原始分數與量尺分數的對照表經過微調之後，至少有14.3%的考生之總分排名受到影響，排序名次降低的遠多於名次升高。在維持目前的將原始分數轉換成量尺分數以及量持分數維持在1-60分的架構之下，利用將IRT中的1PL模式所估計得到的考生能力值加以直線轉換以得到量尺分數的作法，似乎是可行的，雖然可能需要進一步的調整；而若以3PL模式所估計得到的考生能力值加以直線轉換以得到量尺分數的作法，有許多困難需要克服。

Two issues of BCTEST scale scores were investigated in this study. The first of them is that the scale score an examinee will receive when he/she correctly answers all but one items is five or six points less than the examinees who get all items correctly. Some suggest that the rank order of examinees would be different if scale score had been one or two points higher for those who nearly get all items correctly. The second issue is that the scale score for the examinees who answered only a few items correctly tend to be the same, always 1. The purposes of this study are to investigate the effect of adjusting the scale score conversion table on the rank order of examinees' total score and to explore if the ability parameter obtained from the IRT calibration could be used to construct a meaningful score scale. The results indicated that at least 14.3% of examinees would be ranked differently when the scale score conversion table for one of the five subjects was modified. And it seems that the ability estimate given by 1PL model can be linearly transformed into 1-60 scale scores, although further adjustment is needed. For using the ability estimate obtained by 3PL model to form the scale scores, there still are some difficulties needed to overcome.