MSPRT在精熟測驗上的應用－以2005年國中基本學力測驗數學科爲例

Application of MSPRT to Mastery Test on the Basic Competence Test in Math for Junior High School Students

盧宏益(Hung-Yi Lu)

《測驗學刊》 57卷1期 (2010/03) Pp. 85-105

https://doi.org/10.7108/PT.201003.0085

摘要

Wald(1947)提出的逐次機率比檢定(SPRT)被廣泛地使用在精熟測驗上。當受試之能力很接近精熟標準的分界點時，將很容易發生所需的測驗題數過多，導致在測驗終止時，仍無法做出精熟與否的判斷。在有限的測驗題數下，截斷SPRT是其中一種改進的方法，然而，決策將無法達到預設的精確水準。本研究採用Fu(1968)所提出的修正逐次機率比檢定(MSPRT)於精熟測驗上，利用變動決策邊界函數的逐次檢定決策過程，解決了SPRT無法做決策的問題。結果顯示，相較於SPRT而言，MSPRT可以提高正確分類率，並有效的降低決策所需的測驗題數。

關鍵字

修正逐次機率比檢定 ； 國中基本學力測驗 ； 逐次機率比檢定 ； 精熟測驗

並列摘要

Wald's (1947) Sequential Probability Ratio Test (SPRT) is one of the most popular tools used and discussed in the literature for being applied to sequential mastery testing. In case of the ability of an examinee is not protruding, the actual test length could be very large, the truncated SPRT is one possible modification of SPRT to prevent situation that the item bank will eventually be exhausted. But on the other hand, if the truncated boundary is reached before the decision boundary, the decision will not be precise. In this paper, we apply modified SPRT (MSPRT) (Fu, 1968) to mastery test which has the time-varying stopping boundaries and will not have the disadvantage of truncated SPRT, we found that the performance in correct decision rates of MSPRT are more stable than traditional SPRT for all given latent trait level. It is more efficient than the traditional SPRT in terms of test-length.

並列關鍵字

Basic Competence Test for Junior High School Students ； mastery test ； modified sequential probability ratio test ； sequential probability ratio test

參考文獻

Birnbaum, A.,F. M. Lord,M. R. Novick(1968).Statistical theories of mental tests scores.Reading, MA:Addison-Wesley.

Chang, Y.-C. I.(2004).Application of sequential probability ratio test to computerized criterion-referenced testing.Sequential Analysis.23(1),45-61.

Chang, Y.-C. I.,Ying, Z.(2004).Sequential estimation in variable length computerized adaptive testing.Journal of Statistical Planning and Inference.121(2),249-264.

Fe, K. C.(1968).Sequential methods in pattern recognition and machine learning.New York:Academic Press.

Glaser, R.(1963).Instructional technology and the measurement of learning outcomes: Some questions.American Psychologist.18,519-521.