# 合否判定データによる判別分析の問題点Problems of Discriminant Analysis by Mark Sense Test Data

## 抄録

In 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 <I>x<SUB>i</SUB></I>. And 100 questions are summarized in six or nine sub-total scores. <BR>Two groups are trivial linear separable data. Linear discriminant function such as <I>y=ƒ(x)</I> = Score (∑<I><SUB>i</SUB>x<SUB>i</SUB></I>) - pass/fail score. If <I>y</I> ≥ 0, students pass the examination. Otherwise, students don't pass. Therefore, the number of misclassification by this linear discriminant function is 0. <BR>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. <BR>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. <BR>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.

## 収録刊行物

• 応用統計学

応用統計学 40(3), 157-172, 2011-12-30

Japanese Society of Applied Statistics

## 各種コード

• NII論文ID(NAID)
10030153100
• NII書誌ID(NCID)
AN00330942
• 本文言語コード
JPN
• 資料種別
ART
• ISSN
02850370
• NDL 記事登録ID
023458090
• NDL 請求記号
Z15-401
• データ提供元
CJP書誌  NDL  J-STAGE

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