我國學生成就測驗中的猜測現象：1PL-AG之適用性及特點

Student Guessing Behavior on Achievement Tests in Taiwan: Applicability and Properties of the 1PL-AG

「猜測」為非系統性誤差，對測驗之信、效度有負面影響。A. Birnbaum於1968年提出3PL模式（three-parameter logistic model），為現今與猜測有關研究之主要參考模式，其猜測參數屬隨機猜測（又稱pseudo-guessing）。San Martín等人於2006年提出1PL-AG模式（one-parameter logistic model with ability-based guessing），主張猜測非隨機並與能力有關，即能力較高者具有較多部分知識，據以猜測可有較高猜對率。由於San Martín等人提出1PL-AG是以智利學生成就測驗為基礎，本研究基於1PL-AG之應用價值，考量我國與智利學生在學習成就與文化的差異可能影響猜測行為，為驗證1PL-AG之適用性，本研究比較1PL-AG與競爭模式對我國兩筆實徵資料之適配度，並以所得參數產生模擬資料繼續探討「忽略1PL-AG之能力加權參數α」對參數估計結果的影響，以補充San Martín等人未探討的參數估計議題。實徵資料分析發現1PL-AG適配度較佳，與San Martín等人的研究結果一致，但我國資料所得之能力加權參數α較大，顯示我國學生有較強烈以能力猜測之傾向。模擬資料分析發現，若忽略能力加權參數α，能力參數及試題參數皆產生較大估計誤差，且誤差大小受到α影響：被忽略的α愈大，估計誤差愈大。此外，忽略偏大的參數α（如3.45）將產生較極端的能力值、低估難度參數、較趨中的猜測參數；忽略較小的參數α（如0.46）將產生較趨中的能力值、難度及猜測參數。本研究據此提出相關建議。

Guessing is a kind of random error and has impact on test reliability and validity. The guessing parameter of the 3PL (three-parameter logistic model) which proposed by A. Birnbaum in 1968, also termed pseudo-guessing, could be viewed as random guessing. The 3PL is currently the main reference model of related studies. The 1PL-AG (one parameter logistic model with ability-based guessing) which proposed by San Martín et al. in 2006, suggests that guessing is related to ability, i.e., a high-ability examinee tends to have more partial knowledge that may lead to a higher success rate if guess. Since the 1PL-AG is based on the analysis results of Chilean student achievement tests, considering students in Taiwan and Chile have different learning achievements and cultures and may have different guessing behaviors, this study compares model-data fit indexes of 1PLAG and another competing model for two empirical datasets to examine the applicability of 1PL-AG. In order to supplement the uninvestigated issues in San Martín et al.’s study, the obtained parameter estimates from empirical analyses are used to generate simulated datasets to explore the influences of ignoring the ability-weighted parameter α. The results of empirical data analyses are consistent with San Martín et al.’s study that 1PL-AG fits two datasets both significantly better than the competing model, but the values of parameter α are larger in Taiwan’s datasets, which means that students in Taiwan tend to guess with their ability, compared to students in Chile. The consequences of simulation analyses reveal that larger estimation biases for ability and item parameters may be obtained if the ability-weighted parameter α is ignored, and the magnitude of bias is influenced by the size of parameter α: The larger the parameter α being ignored, the larger the estimation bias is. Additionally, ignoring extreme parameter α (e.g. 3.45 in the current study) may lead to more extreme ability estimates, lower item difficulty estimates, and more centered guessing parameter estimates; ignoring non-extreme parameter α (e.g. 0.46 in the current study) may lead to more centered ability estimates, item difficulty and guessing parameter estimates. Suggestions are provided according to these results.