• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.381-391
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• 1996

In the analysis of contingency table with ordered categories, the relationship between odds for adjacent categories has received con-siderable interest. We consider likelihood ratio tests of independence against an order restriction on odds in 2 $\times$ k contingency tables.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.717-729
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• 2004

The contour method which was originally designed for $2{\times}2{\times}2$ contingency table is studied for $2{\times}2{\times}K$ and $2{\times}3{\times}K$ tables. Whereas a contour plot for a $2{\times}2{\times}K$ table is represented on unit squared two dimensional plane, a contour plot of a $2{\times}3{\times}K$ table can be expressed with a regular hexahedron on three dimensional space. Based on contour plots for categorical data fitted to all possible three dimensional log-linear models, one might identify whether $2{\times}2{\times}k$ or $2{\times}3{\times}K$ tables are collapsible over the third variable.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.997-1005
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• 2003

We can use the logistic model for categorical data when the response variables are binary data. In this paper we consider the problem of constructing the confidence intervals for logistic model in I${\times}$J${\times}$2 contingency table. These constructions are simplified by applying logit transformation. This transforms the problem to consider linear form which called the logit model. After obtaining the confidence intervals for the logit model, the reverse transform is applied to obtain the confidence intervals for the logistic model.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.753-762
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• 2009

A measure of agreement H in$2{\times}2$ contingency table was proposed by Park and Park (2007) to resolve the two paradoxes of k. In this study, we generalize H to where the number of categories is greater than two and derive its asymptotic large-sample variance. We also explain the relationships between k's paradoxes and marginal distributions. Using some examples of $3{\times}3$ contingency tables, the behaviors of H and other measures of agreement are compared.

• The Korean Journal of Applied Statistics
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• v.23 no.4
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• pp.777-781
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• 2010

Yates' continuity correction of the chi-squared test for testing the homogeneity of two binomial proportions in $2{\times}2$ contingency tables is developed to lower the value of the test statistic slightly. The effect of continuity correction is expected to decrease as the sample size increases. However, in extremely unbalanced $2{\times}2$ contingency tables, we find some cases where the effect of continuity correction is eccentric and is larger than expected. In such cases, we conclude that the chi-squared test with continuity correction should not be employed as a test statistic in both asymptotic tests and exact tests.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.479-496
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• 2003

We investigate logit confidence intervals for the odds ratio based on the delta method. These intervals are constructed using pseudo-Bayes estimators. The Gart method and Agresti method smooth the observed counts toward the model of equiprobability and independence, respectively. We obtain better coverage probability by smoothing the observed counts toward the pseudo-Bayes estimators in 2$\times$2 table. We also improve legit confidence intervals in 2$\times$2$\times$K tables by generalizing these ideas. Utilizing pseudo-Bayes estimators, we obtain better coverage probability by smoothing the observed counts toward the conditional independence model, no three-factor interaction model and saturated model in 2$\times$2$\times$K tables.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.457-464
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• 1999

In this paper, we propose an overlapped mosaic plot which proposed by Hartigan and Kleiner(1981) represents the counts in $2{\times}2$ contingency table directly by tiles whose area is proportional to the cell frequency. Overlapped mosaic plot provides some measurements of association including dynamic graphics for mosaic plots. Dynamic graphics for mosaic plots give some useful informations when one gets some measurements of association and selects a model, and current statistical software does not provide this feature. We can see the deviations between observation and estimate of independence from overlapped mosaic plot. This dynamic graphics give some useful informations how far this data are apart from independence.

• 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.

• Korean Journal of Veterinary Research
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• v.36 no.4
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• pp.941-948
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• 1996

The accuracy of rectal palpation and ultrasonography for predicting the presence of a functional corpus luteum in subestrous dairy cows was investigated, using the result of a radioimmunoassay for progesterone in plasma. Luteal status (high or low progesterone concentrations) was diagnosed in 820 cows, using rectal palpation and B-mode transrectal ultrasonography, and the results of rectal palpation and ultrasonography were compared in $2{\times}2$ contingency table with plasma progesterone concentrations. A $2{\times}2$ contingency table analysis allowed the calculation of sensitivity, specificity and predictive values for rectal palpation and ultrasonography. The sensitivity, specificity, predictive value of a positive test and predictive value of a negative test were 81.9%, 67.5%, 79.0% and 71.4% for rectal palpation, and 96.3%, 88.8%, 94.5% and 92.4% for ultrasonography, respectively. The percentages of observed agreement and expected agreement between rectal palpation and ultrasonography were 71.8% and 57.1%, respectively. An evaluation of agreement between rectal palpation and ultrasonography, the value of Kappa was 0.34. It was concluded that a ultrasonography was more sensitive and specific than rectal palpation in predicting the presence of a functional corpus luteum. Therefore, ultrasonographic examination is a reliable method for assessing the functional status of ovarian structures in subestrous dairy cows.

• School Mathematics
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• v.19 no.3
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• pp.461-480
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• 2017

The aim of this study was to analyze characteristics of teachers' knowledge about correlation with data presented in $2{\times}2$ tables. In order to achieve the aim, this study conducted didactical analysis about two-way tables through examining previous researches and developed a questionnaire with reference to the results of the analysis. The questionnaire was given to 53 middle and high school teachers and qualitative methods were used to analyze the data obtained from the written responses by the participants. This study also elaborated the framework descriptors for interpreting the teachers' responses in the light of the didactical analysis and the data was elucidated in terms of this framework. The specific features of teachers' knowledge about correlation with data presented in $2{\times}2$ tables were categorized into three types as a result. This study raised several implications for teachers' professional development for effective mathematics instruction about correlation and related concepts dealt with in probability and statistics.