RECOMMENDATION FOR USE OF THE “WEIBULL” DISTRIBUTION FOR THE ANALYSIS OF THE FREQUENCY DISTRIBUTION OF TEST SCORES

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  • ワイブル分布関数によるテスト得点分布の解析
  • ワイブル分布関数によるテスト得点分布の解析--信頼性工学における故障関数の理論と方法の導入
  • ワイブル ブンプ カンスウ ニ ヨル テスト トクテン ブンプ ノ カイセキ シンライセイ コウガク ニ オケル コショウ カンスウ ノ リロン ト ホウホウ ノ ドウニュウ
  • RECOMMENDATION FOR USE OF THE ^|^ldquo;WEIBULL^|^rdquo; DISTRIBUTION FOR THE ANALYSIS OF THE FREQUENCY DISTRIBUTION OF TEST SCORES
  • An Application of the Theory of the Failure Distribution of System Reliability
  • 信頼性工学における故障関数の理論と方法の導入

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One of the purposes of this paper is to apply the theory of the failure distribution of system reliability (e. g., cf. Barlow et al; 1967) to the analysis of the frequency distribution of test scores.<BR>Assuming that test scores, x s, correlate positively with a underlying ability, we define as follows: (1) where _??_ And further we define (2) which is called the ratio of success. From (2) we get (3)(Davis; 1952, McGill et al; 1965).<BR>Another one of the purposes is to recommend for the use of “Weibull” (1952) distribution in order to analyze the frequency distribution of test scores. The distribution has often been used in the studies of system reliability because of its wide applicability. We define the ratio of success of this distribution as follows: (12) then,(10) are obtained. Here, m, α, and γ are shape, scale, and location parameters. Tha shape parameter m of Weibull distribution plays an important role in discriminating the degree of the difficulties and validities of psychological tests. We investigate several data by Lord (1952) and it is shown that the shape parameter m is a suprisingly useful and powerful measure in psychological testing (cf. Fig. 1).<BR>Finally, it should be noted the following. That is, our proposal which is based upon a differential. equation model is comparable to Lord's (1952) integral equation model in that the former aims to analyze directly the frequency distribution of test scores and the latter to estimate true-score or latent trait distribution.

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