IRT下猜测现象和失误现象的原因阐释与数学推导

Possible Reasons and Rational Formula of Guessing Phenomenon and Sleeping Phenomenon under Item Response Theory

在测验中存在着被试在相对高难度试题上得分的猜测现象,也存在着被试在较容易试题上失分的失误现象。本文详细分析导致猜测现象和失误现象的各种可能原因。从数学公式推导的角度论证可得:在一定测验情境下,被试答对试题难度越大,获得前进的能力步长越大,被试能力被相对高估;被试答错试题难度越小,"被惩罚"后退的能力步长绝对值越大,被试能力被相对低估。

In the educational and psychological tests, there exist guessing phenomena that the low - ability examinee makes correct answers on difficult items, and sleeping phenomena that the high - ability examinee makes wrong answers on easy items, which would lead to errors. Many research have been done on the issues of these phenomena, and various methods have been proposed to rectify the overestimation and underestimation. In this paper the authors analyze the possible reasons for guessing phenomenon and sleeping phenomenon. From point of view of the mathematical formula for the ability estimation in CAT is further reckoned. Under two - parameter Logistic model, the more difficult the item that the subjects answered correctly is, the greater the ability step of the low - ability examinees is, that is, the ability of low - ability examinees is to be overestimated. The more easy the item that the high - ability examinees answered wrong is, the greater the absolute value of the ability step of the high - ability examinees is, that is, the ability of high - ability examinees is to be underestimated.