In the field of Social science, Behavioral science, and Medical science, a discriminant analysis for qualitative data proposed by Hayashi(Quantification Theory Type II)has been widely used among Japanese researchers with spread of its computer program. However, as the program has provided no procedure for estimating the variability of the estimated parameters, we could not examine the variability of the results, which might have sometimes led to misuse and misinterpretation of the results. This paper proposes an application of the jackknife and the bootstrap method to estimate the variability of the estimated parameters. Using these resampling methods we also propose a procedure for amalgamation of categories and selection of items. Applications are illustrated with two kinds of cohort data on circulatory diseases in Japan(Komazawa, 1982).
It cannot be assumed a priori that the number of candidates to beselected in the first stage of two-stage votingsystems should be two. This optimality, however, is shown by Fishburn(1976)by comparing the results of the two-stage voting with those of the simple malority voting, i. e., the pair comparison rule. This paper shows the same conclusion through computer simulation, with another framework for evaluating election, and indicates that the performance of two-stage voting systems is better than that of one-stage voting systems.
Suppose we have only40places to be filled in a department, and there are N candidates writing a two stage selection entrance examination to an university. We wish to determine a reasonable number m such that40×m=n, where N-n is the number of candidates failing the first stage. In this paper, this number m is termed the multiplier. Then, we evaluate the group-size of candidates who could not pass the examination in practice, but would pass it provided that the preliminary selection would not be done. Under the normality assumption on the marks, we give a method which estimates the probability corresponding to the group-size from censored data, and propose a method to decide the reasonable multiplier in the preliminary examination. Simulation is carried out for the combination of some parameters using random numbers and discussion is made on the results. Robustness on the normality and the influence of estimating parameters are also discussed briefly.