• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.289-303
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• 1998

For square contingency tables with ordered categories, Tomizawa (1995) considered two kinds of measures to represent the degree of departure from global symmetry, which means that the probability that an observation will fall in one of cells in the upper-right triangle of square table is equal to the probability that the observation falls in one of cells in the lower-left triangle of it. This paper proposes a generalization of those measures. The proposed measure is expressed by using Cressie and Read's (1984) power divergence or Patil and Taillie's (1982) diversity index. Special cases of the proposed measure include TomiBawa's measures. The proposed measure would be useful for comparing the degree of departure from global symmetry in several tables.

• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.245-254
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• 2016

Many surveys provide categorical data and there may be one or more missing categories. We describe a nonignorable nonresponse model for the analysis of two-way contingency tables from small areas. There are both item and unit nonresponse. One approach to analyze these data is to construct several tables corresponding to missing categories. We describe a hierarchical Bayesian model to analyze two-way categorical data from different areas. This allows a "borrowing of strength" of the data from larger areas to improve the reliability in the estimates of the model parameters corresponding to the small areas. Also we use a nonignorable nonresponse model with Bayesian uncertainty analysis by placing priors in nonidentifiable parameters instead of a sensitivity analysis for nonidentifiable parameters. We use the griddy Gibbs sampler to fit our models and compute DIC and BPP for model diagnostics. We illustrate our method using data from NHANES III data on thirteen states to obtain the finite population proportions.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.69-76
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• 1996

In a two-way contingency table, the analyst is most interested in the hypotheses of either homogeneity or independence. For testing this as a null hypothesis, Pearson's ${\chi}^2$ statistic is most commonly used in practice. Once the null Hypothesis is rejected, he will further search forcells which caused the rejection of the null hypothesis. For this purpose, so called cell${\chi}^2$ components are used. In this paper, we derive the influence function of an obsevation to the ${\chi}^2$ statistic, with which cells with high influence can be identified.

• The Korean Journal of Applied Statistics
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• v.32 no.1
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• pp.29-40
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• 2019

Categorical data with non-responses are frequently observed in election poll surveys, and can be represented by incomplete contingency tables. To estimate supporting rates of candidates, the identification of the missing mechanism should be pre-determined because the estimates of non-responses can be changed depending on the assumed missing mechanism. However, it has been shown that it is not possible to identify the missing mechanism when using observed data. To overcome this problem, sensitivity analysis has been suggested. The previously proposed sensitivity analysis can be applicable only to two-way incomplete contingency tables with binary variables. The previous sensitivity analysis is inappropriate to use since more than two of the factors such as region, gender, and age are usually considered in election poll surveys. In this paper, sensitivity analysis suitable to an multi-dimensional incomplete contingency table is devised, and also applied to the 19th Korean presidential election poll survey data. As a result, the intervals of estimates from the sensitivity analysis include actual results as well as estimates from various missing mechanisms. In addition, the properties of the missing mechanism that produce estimates nearest to actual election results are investigated.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.411-416
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• 1998

A simple nonparametric test of complete or total independence is suggested for continuous multivariate distributions. This procedure first discretizes the original variables based on their order statistics, and then tests the hypothesis of complete independence for the resulting contingency table. Under the hypothesis of independence, the chi-squared test statistic has an asymptotic chi-squared distribution. We present a simulation study to illustrate the accuracy in finite samples of the limiting distribution of the test statistic. We compare our method to another nonparametric test of complete independence via a simulation study. Finally, we apply our method to the residuals from a real data set.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.291-303
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• 2003

This work is proposed an alternative identification method of outlying cell which is one of important issues in categorical data analysis. One finds that there is a strong relationship between the location of an outlying cell and the corresponding parameter estimates of the well-fitted log-linear model. Among parameters of log-linear model, an outlying cell is affected by interaction terms rather than main effect terms. Hence one could identify an outlying cell by investigating of parameter estimates in an appropriate log-linear model.

• 대한예방의학회:학술대회논문집
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• 2002.10a
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• pp.449-450
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• 2002

• Journal of the Korean Statistical Society
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• v.16 no.2
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• pp.117-127
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• 1987

The Simpson's paradox is a paradoxical phenomenon which might occur when analyzing $2 \times 2$ contingency table. This paper considers the role of probability assignment of the experimental units in reducing the chances of Simpson's paradox. Numerical results are given to illustrate how the chance of Simpson's paradox behaves.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.489-497
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• 1996

Lower bounds for the full level probabilities are derived under order restrictions in weights. Discussions are made on typical isotonic cones such as linear order, simple tree order, and unimodal order cones. We also discuss applications of these results for constructing conditional likelihood ratio tests for ordered hypotheses in a contingency table. A real data set on torus mandibularis will be analyzed for illustrating the testing procedure.

• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.419-433
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• 2004

We suggest the modified computing algorithm for raking ratio estimation under the assumption that the population total is partially known, and the sample total is completely known about survey variable in contingency table. We show that the proposed estimation procedure is useful to estimate the population cell count in this situation through an empirical study.