Bulletin of the Computational Statistics of Japan

For a 2×2 table from a matched pair experiment, we examine McNemar tests with and without continuity correction, Minimum chi-square test by Bhapkar and likelihood ratio test, with respect to null and non-null exact distributional properties. McNemar test without continuity correction achieves the best approximation to the nominal significance level. Formulae for power calculation and required number of subjects are also discussed.

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Consider the ranked set sampling which is useful to estimate the population mean when the order of a sample of small size can be found without measurements or with rough methods. Consider m sets of elements each set having size m. All elements of each set are ranked but only one is selected and quantified. Continue the process n times and the average of the quantified elements is adopted as the point estimator. In this paper we shall try to construct interval estimators of the population mean. In order to construct interval estimators, we derive estimators of the variance of the average and standardize the average. Normal approximation and t-approximations with predetermined or adjusted degrees of freedom are considered. We find that the t-approximations with adjusted degrees of freedom are effective except for heavily skewed distributions.

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In this paper, a method for classifying items and judges from ranked observations by using the rank graph is proposed. The rank graph was proposed originally as a descriptive one in which an average rank and a degree of concordance of ranks assigned to each item are represented by the vector called item vector. As the distribution of an item vector is asymptotically approximated by a 2-dimensional normal distribution, we can obtain an elliptic confidence region of the item vector. According to whether confidence regions of the items overlap or not each other, the items can be classified. On the other hand, the judges may rank items such that there is little difference in quality between the items belonging to the same group. After classifying the items, ranking of the items reduces to ranking of the groups of the items. Thus, the judges are classified with the patterns that the judges order the groups. It will be shown that it is possible to classify the items and the judges hierarchically according to the confidence coefficient.

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In this paper, we propose a framework based on "Frame Theory" for data analysis supporting system to construct the set of the knowledge for data analyses. There is some research to which the technique of knowledge processing to data analysis is applied. In the field of knowledge processing, a knowledge base and an inference function are to be independent for flexibility of a system. Most reports about the application, however, may not tell us that both parts are separated clearly. In this paper, we compare some methods about knowledge representation shown in the previous works for data analysis supporting systems and show that "Frame Theory" is the most available when we focus on the supporting function to select appropriate statistical procedures. We also offer how to implement the knowledge of data analysis on the framework and show two examples about supporting functions based on our knowledge base and the independence of the knowledge base and the inference functions through these examples.

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