THE WEIBULL DISTRIBUTION AND A PRACTICAL ANALYSIS OF MENTAL TEST SCORES

SHIGEO KASHIWAGI

doi:10.4992/psycholres1954.11.54

SHIGEO KASHIWAGI

著者情報

ジャーナルフリー

1969 年 11 巻 2 号 p. 54-65

DOI https://doi.org/10.4992/psycholres1954.11.54

詳細

Published: 1969 Received: 1969/06/09 Available on J-STAGE: 2009/02/24 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2009/02/24 訂正理由: - 訂正箇所: 論文抄録訂正内容: Wrong : We propose to apply the Weibull distribution to the analysis of mental test scores. As the first place, we review the distribution theory of test scores by Lord (1952) and suggest the relationship between the theory and the shape parameter of this distribution.
First of all, we describe the simple Weibull distribution and the discussion concerning the estimation of the shape parameter is made. Especially, the emphasis is placed on the method by means of the Weibull Probability Paper (wpp), and it is pointed out that the method is very useful and recommendable in view of being accurate practically.
Secondly, we discuss the concept of measurability of test, and make comment on the difference between the discriminability of test and the measurability. And further, the mixed or composite Weibull distribution is suggested to be useful under a certain condition.
Finally, several numerical examples are presented and we discuss some of the important aspects of our method based on the Weibull distribution.
Right : We propose to apply the Weibull distribution to the analysis of mental test scores. As the first place, we review the distribution theory of test scores by Lord (1952) and suggest the relationship between the theory and the shape parameter of this distribution.
First of all, we describe the simple Weibull distribution and the discussion concerning the estimation of the shape parameter is made. Especially, the emphasis is placed on the method by means of the Weibull Probability Paper (wpp), and it is pointed out that the method is very useful and recommendable in view of being accurate practically.
Secondly, we discuss the concept of measurability of test, and make comment on the difference between the discriminability of test and the measurability. And further, the mixed or composite Weibull distribution is suggested to be useful under a certain condition.
Finally, several numerical examples are presented and we discuss some of the important aspects of our method based on the Weibull distribution.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : ARAKI, M. 1968 A data processing computer system on the parts reliabilities of rolling stocks. Railway Tech. Res. Report No. 664 (in Japanese).
BERRETTONI, J. N. 1964 Practical applications of the Weibull distribution. Industrial quality control, August, 71-79.
COHEN, A. C. 1965 Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples. Techno-metrics, 7, 579-588.
KASHIWAGI, S. 1968 Recommendation for use of the Weibull distribution for the analysis of the frequency distribution of test scores. Jap. J. of Educ. Psychol., 16, 203-215 (in Japanese).
KEATS, J. A., & LORD, F. M. 1962 A theoretical distribution for mental test scores. Psychometrika, 27, 59-72.
KEATS, J. A. 1964 Some generalizations of a theoretical distribution of mental test scores. Psychometrika, 29, 215-231.
LORD, F. M. 1952 A theory of test scores. Psychometric Monogr., No. 7.
LORD, F. M. & NOVICK, M. R. 1968 Statistical theories of mental test scores. Addison Wesley.
OHTSU, W. 1967 The analysis of data in the field of reliability. Nikkagiren, Tokyo: Pp. 98-100 (in Japanese).
SHIBA, S. 1969 The distributions of mental test scores by Birnbaum's model (unpublished material).
WEIBULL, W. 1951 A statistical distribution function of wide applicability. J. of applied mechanics, Sept., 293-297.

Right : ARAKI, M. 1968 A data processing computer system on the parts reliabilities of rolling stocks. Railway Tech. Res. Report No.664 (in Japanese).
BERRETTONI, J. N. 1964 Practical applications of the Weibull distribution. Industrial quality control, August, 71-79.
COHEN, A. C. 1965 Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples. Technometrics, 7, 579-588.
KASHIWACI, S. 1968 Recommendation for use of the Weibull distribution for the analysis of the frequency distribution of test scores. Jap. J. of Educ. Psychol., 16, 203-215 (in Japanese).
KEATS, J. A., & LORD, F. M. 1962 A theoretical distribution for mental test scores. Psychometrika, 27, 59-72.
KEATS, J. A. 1964 Some generalizations of a theoretical distribution of mental test scores. Psychometrika, 29, 215-231.
LORD, F. M. 1952 A theory of test scores. Psychometric Monogr., No.7.
LORD, F. M. & Novicx, M. R. 1968 Statistical theories of mental test scores. Addison Wesley.
OHTSU, W. 1967 The analysis of data in the field of reliability. Nikkagiren, Tokyo: Pp.98-100 (in Japanese).
SHIBA, S. 1969 The distributions of mental test scores by Birnbaum's model.
WEIBULL, W. 1951 A statistical distribution function of wide applicability. J. of applied mechanics, Sept., 293-297.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : ARAKI, M. 1968 A data processing computer system on the parts reliabilities of rolling stocks. Railway Tech. Res. Report No.664 (in Japanese).
BERRETTONI, J. N. 1964 Practical applications of the Weibull distribution. Industrial quality control, August, 71-79.
COHEN, A. C. 1965 Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples. Technometrics, 7, 579-588.
KASHIWACI, S. 1968 Recommendation for use of the Weibull distribution for the analysis of the frequency distribution of test scores. Jap. J. of Educ. Psychol., 16, 203-215 (in Japanese).
KEATS, J. A., & LORD, F. M. 1962 A theoretical distribution for mental test scores. Psychometrika, 27, 59-72.
KEATS, J. A. 1964 Some generalizations of a theoretical distribution of mental test scores. Psychometrika, 29, 215-231.
LORD, F. M. 1952 A theory of test scores. Psychometric Monogr., No.7.
LORD, F. M. & Novicx, M. R. 1968 Statistical theories of mental test scores. Addison Wesley.
OHTSU, W. 1967 The analysis of data in the field of reliability. Nikkagiren, Tokyo: Pp.98-100 (in Japanese).
SHIBA, S. 1969 The distributions of mental test scores by Birnbaum's model.
WEIBULL, W. 1951 A statistical distribution function of wide applicability. J. of applied mechanics, Sept., 293-297.

Right : ARAKI, M. 1968 A data processing computer system on the parts reliabilities of rolling stocks. Railway Tech. Res. Report No.664 (in Japanese).
BERRETTONI, J. N. 1964 Practical applications of the Weibull distribution. Industrial quality control, August, 71-79.
COHEN, A. C. 1965 Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples. Technometrics, 7, 579-588.
KASHIWAGI, S. 1968 Recommendation for use of the Weibull distribution for the analysis of the frequency distribution of test scores. Jap. J. of Educ. Psychol., 16, 203-215 (in Japanese).
KEATS, J. A., & LORD, F. M. 1962 A theoretical distribution for mental test scores. Psychometrika, 27, 59-72.
KEATS, J. A. 1964 Some generalizations of a theoretical distribution of mental test scores. Psychometrika, 29, 215-231.
LORD, F. M. 1952 A theory of test scores. Psychometric Monogr., No.7.
LORD, F. M. & NOVICK, M. R. 1968 Statistical theories of mental test scores. Addison Wesley.
OHTSU, W. 1967 The analysis of data in the field of reliability. Nikkagiren, Tokyo: Pp.98-100 (in Japanese).
SHIBA, S. 1969 The distributions of mental test scores by Birnbaum's model.
WEIBULL, W. 1951 A statistical distribution function of wide applicability. J. of applied mechanics, Sept., 293-297.

抄録

We propose to apply the Weibull distribution to the analysis of mental test scores. As the first place, we review the distribution theory of test scores by Lord (1952) and suggest the relationship between the theory and the shape parameter of this distribution.
First of all, we describe the simple Weibull distribution and the discussion concerning the estimation of the shape parameter is made. Especially, the emphasis is placed on the method by means of the Weibull Probability Paper (wpp), and it is pointed out that the method is very useful and recommendable in view of being accurate practically.
Secondly, we discuss the concept of measurability of test, and make comment on the difference between the discriminability of test and the measurability. And further, the mixed or composite Weibull distribution is suggested to be useful under a certain condition.
Finally, several numerical examples are presented and we discuss some of the important aspects of our method based on the Weibull distribution.

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