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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