• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.33-44
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• 2016

There are many situations that the outcome for clinical decision and credit assessment should be predicted more than two categories. Five kinds of statistics which are used the concordance are proposed and used for these polytomous problems. However, these statistics are defined without exact distinction of categories, so that we have difficulty to use both the pair and set approaches and it is hard to understand the meanings of these statistics. Hence, it is not possible to compare and analyze them. In this paper, the polytomous confusion matrix is standardized and the concordance statistic can be represented based on the confusion matrix. The five kinds of statistics by using the concordance are defined. With the methods proposed in this paper, we could not only explain their meanings but also compare and analyze these statistics. Based on various data sets, properties of these five statistics are explored and explained.

• Journal of the Korean Data and Information Science Society
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• v.27 no.2
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• pp.337-351
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• 2016

There exist many real situations that statistical decision problems are classified into more than two categories. In these cases, the concordance statistics by the pair approach are mostly used. However, the expression of the classification of categories are ambiguous. Recently, the standardized evaluation data and re-expressed concordance statistics are defined and could be explained their meanings. They have still some non-specific problems for standard criteria of the statistics. Since these can be considered between result and truth categories additionally, two alternative concordance statistics might be proposed in this paper. Some advantages are founded that the proposed statistics could be discriminated all possible cases for two randomly selected categories. Moreover since the proposed statistics are represented with indicator functions, these could be transformed non-parametrically, so that these concordances are used for hypothesis testing.