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Volume 40 (2011)
- Issue 3 Pages 125-
- Issue 2 Pages 81-
- Issue 1 Pages 1-
Volume 40, Issue 3
Displaying 1-5 of 5 articles from this issue
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Special Issue:Statistical Analysis of Achievement Tests
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Takamitsu Hashimoto2011 Volume 40 Issue 3 Pages 125-140
Published: 2011
Released on J-STAGE: March 26, 2012
JOURNAL OPEN ACCESSItem Relational Structure (IRS) analysis (Takeya, 1980) is frequently used to analyze test data. IRS analysis counts the frequency of examinees who answered correctly to one item and incorrectly to another item. It assesses the mutual dependence between the two items by comparing this frequency to the expected frequency under hypothetical independence. However, IRS analysis entails two problems: (1) the threshold of dependence is arbitrary and the results depend on the threshold; (2) when two items are conditionally independent given the examinees' ability variable, IRS analysis sometimes detects dependence between these items if the ability variable affects them strongly. This paper introduces a revised IRS analysis that uses the expected frequency described by Chen and Thissen (1997), which determines the threshold of dependence statistically and which controls the effect of the ability variable. Through numerical experiments, the revised IRS analysis detected fewer incorrect dependences and incorrect independences than traditional IRS analysis with various thresholds. However, the error ratio of detecting incorrect dependence is not controlled sufficiently. Applications to actual data must be analyzed carefully when the test includes many dependent items.View full abstractDownload PDF (695K) -
Kojiro Shojima2011 Volume 40 Issue 3 Pages 141-156
Published: 2011
Released on J-STAGE: March 26, 2012
JOURNAL OPEN ACCESSIn test data analysis, it is often important to examine the inter-item dependency structure underlying the test data. However, this structure often varies according to the academic ability level of the examinees. In this paper, a latent rank theory (LRT) model incorporating a Bayesian network model is proposed. Although the conventional LRT model is formulated under the assumption of local independence among test items, the proposed LRT model supposes local dependence among test items. The proposed model can be used to efficiently analyze the data of math and science tests in which inter-item dependency relationships among items are not negligible.View full abstractDownload PDF (718K) -
Shuichi Shinmura2011 Volume 40 Issue 3 Pages 157-172
Published: 2011
Released on J-STAGE: March 26, 2012
JOURNAL OPEN ACCESSIn this paper, we discuss problems of discriminant analysis by mark sense test data. The test consists of 100 questions with 10 choices. The correct or incorrect answers are converted to 1/0 values. Therefore, this data is the discrimination of two groups (pass and fail) with 100 independent variables xi. And 100 questions are summarized in six or nine sub-total scores.
Two groups are trivial linear separable data. Linear discriminant function such as y=ƒ(x) = Score (∑ixi) - pass/fail score. If y ≥ 0, students pass the examination. Otherwise, students don't pass. Therefore, the number of misclassification by this linear discriminant function is 0.
Fisher's linear discriminant function (LDF), quadratic discriminant function and logistic regression are compared are with optimal linear discriminant function (Revised IP-OLDF) based on MNM (Minimum number of misclassifications) criterion by these data.
In the cases of 100 independent variables discrimination, the following problems are found. The stepwise variable selection methods chose over 28 independent variables, nevertheless Revised IP-OLDF find that these data is linear separable less than 12 independent variables. In some cases, quadratic discriminant function misclassified all pass/fail students to other group. The standard error of coefficients of logistic regression becomes very big.
In the cases of summarized sub-total scores discrimination, the number of misclassifications of LDF, quadratic discriminant function are mostly greater than 0, nevertheless MNM of Revised IP-OLDF and 0.View full abstractDownload PDF (703K) -
Tatsuo Otsu2011 Volume 40 Issue 3 Pages 173-191
Published: 2011
Released on J-STAGE: March 26, 2012
JOURNAL OPEN ACCESSThe National Center Test (NCT) is a nation-wide university entrance examination organized annually by the National Center for University Entrance Examinations (NCUEE) and Japanese universities. Increased archived data relating to the examinations require well organized management. The growing ubiquitous use of XML is enforced by the technical necessity for managing electrical data and documents. We introduced processing by Prolog, a logic-based language, for this purpose. At first, simple examples were given of the basic mechanisms of Prolog language. Some comparisons of list processing performances were presented. Then an XML parser on Prolog systems was introduced. An example was given of the parsing of a small XML document, and XML document generaion with the parser was explained. Finally, a method for analysing stratified contingency tables that considers G-Markov structure was presented.View full abstractDownload PDF (796K) -
Tsunenori Ishioka2011 Volume 40 Issue 3 Pages 193-209
Published: 2011
Released on J-STAGE: March 26, 2012
JOURNAL OPEN ACCESSRandom Forest, one of the ensemble learning methods for classification and non-linear regression model, provides a stable and an accurate data imputation for the missing data. This paper shows that the algorithm works well for a large dataset containing missing data. The examples are science and society examination scores appearing in the Japanese National Center Test in 200x.View full abstractDownload PDF (804K)
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