• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.757-764
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• 2012

This research is for comparison of test statistics for homogeneity when the data is collected based on complex sample design. The survey data based on complex sample design does not satisfy the condition of independency which is required for the standard Pearson multinomial-based chi-squared test. Today, lots of data sets ara collected by complex sample designs, but the tests for categorical data are conducted using the standard Pearson chi-squared test. In this study, we compared the performance of three test statistics for homogeneity between two populations using data from the 2009 customer satisfaction evaluation survey to the service from Gyeongsangnam-do regional offices of education: the standard Pearson test, the unbiasedWald test, and the Pearsontype test with survey-based point estimates. Through empirical analyses, we fist showed that the standard Pearson test inflates the values of test statistics very much and the results are not reliable. Second, in the comparison of Wald test and Pearson-type test, we find that the test results are affected by the number of categories, the mean and standard deviation of the eigenvalues of design matrix.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.815-824
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• 2013

Traditional Pearson chi-squared test is not appropriate for the data collected by the complex sample design. When one uses the traditional Pearson chi-squared test to the complex sample categorical data, it may give wrong test results, and the error may occur not only due to the biased variance estimators but also due to the biased point estimators of cell proportions. In this study, the design based consistent Wald test statistics was derived for k-population homogeneity test, and the traditional Pearson chi-squared test statistics was partitioned into three parts according to the causes of error; the error due to the bias of variance estimator, the error due to the bias of cell proportion estimator, and the unseparated error due to the both bias of variance estimator and bias of cell proportion estimator. An analysis was conducted for empirical results of the relative size of each error component to the Pearson chi-squared test statistics. The second year data from the fourth Korean national health and nutrition examination survey (KNHANES, IV-2) was used for the analysis. The empirical results show that the relative size of error from the bias of variance estimator was relatively larger than the size of error from the bias of cell proportion estimator, but its degrees were different variable by variable.

• The Korean Journal of Applied Statistics
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• v.16 no.1
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• pp.151-167
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• 2003

Although there exist numerous measures of association, most of them are lacking in generality in that they do not intend to measure the association between heterogeneous type of random variables. On the other hand, many statistical analyzes dealing with complex data sets require a very sophisticate measure of association. In this note, the p-value of independence tests is utilized to obtain a measure of association. The proposed measure of association have some consistency in measuring association between various types of random variables.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.523-536
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• 2021

Although there exist numerous measures of association, most of them are lacking in generality in that they do not intend to measure the association between heterogeneous type of random variables. On the other hand, many statistical analyzes dealing with complex data sets require a very sophisticate measure of association. In this note, the p-value of independence tests is utilized to obtain a measure of association. The proposed measure of association have some consistency in measuring association between various types of random variables.

• Korean Journal of Food Science and Technology
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• v.50 no.2
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• pp.244-247
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• 2018

Quantitative analysis for non-host infection bacteriophage was conducted for their enumeration. Flow cytometry and epifluorescence microscopy (EPM) were selected as counting methods. Correlation analysis was performed based on the plaque assay method on the existing host infection and consisted of Pearson correlation statistical analysis, regression analysis, and difference analysis. Analyses of 12 samples with flow cytometry and plaque assay methods showed that there was a correlation of 96.7% with Pearson correlation value r=0.967, $R^2$ 0.9352, and difference value of 1.063. Analyses of 12 samples with EPM and plaque assay methods showed that there was a correlation of 99.0% with Pearson correlation value r=0.990, $R^2$ 0.9811, and difference value of 1.605. Therefore, flow cytometry and epifluorescence microscopy would be effective for enumeration of Weissella cibaria bacteriophage with plaque assay.

• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.455-467
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• 2003

There has been a long debate on the applicability of the chi-square approximation to statistics based on small sample size. Extending comparison results among Pearson chi-square Χ$^2$, generalized likelihood .ratio G$^2$, and the power divergence Ι(2/3) statistics suggested by Rudas(1986), recently developed disparity statistics (BWHD(1/9), BWCS(1/3), NED(4/3)) we compared and analyzed in this paper. By Monte Carlo studies about the independence model of two dimension contingency tables, the conditional model and one variable independence model of three dimensional tables, simulated 90 and 95 percentage points and approximate 95% confidence intervals for the true percentage points are obtained. It is found that the Χ$^2$, Ι(2/3), BWHD(1/9) test statistics have very similar behavior and there seem to be applcable for small sample sizes than others.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.149-150
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• 2003

소표본 분할표 자료에서 적합도 검정통계량들의 카이제곱 근사 적용 가능에 대하여 많은 연구가 진행되었다. 소표본에서 세 가지 검정 통계량(피어슨 카이제곱 $X^{2}$, 일반화 가능도비 $G^{2}$, 그리고 역발산 I(2/3) 검정통계량)에 관하여 비교한 Rudas(1986)의 연구를 확장하여, 최근에 제안된 차이측도(BWHD(1/9), BWCS(1/3), NED(4/3) 검정통계량)를 포함시켜 비교 분석하였다. 독립모형의 이차원 분할표, 조건부 독립모형과 한 변수 독립 모형을 따르는 삼차원 분할표에 대한 모의실험을 통하여 생성된 90과 95 백분위수와 이에 대응하는 95% 신뢰구간을 살펴보고 실제 백분위수와 비교하였다. 그 결과 $X^{2}$, I(2/3), 그리고 BWHD(1/9) 검정통계량이 유사한 결과를 나타내었고 이 통계량들이 기존에 제안된 검정통계량들보다 적은 표본크기에서도 카이제곱 근사방법에 적용 가능함을 발견하였다.

• The Science & Technology
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• v.18 no.6 s.193
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• pp.51-54
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• 1985

피어슨이 개발한 '카이제곱검정'은 그 자체로 본다면 하나의 사소한 사건이었으나 우리의 숫자세계를 해석하는 방법에서 하나의 전환을 구획하는 신호가 되었다. 오늘날 아이디어를 정책수립가들과 일반에게 제시하는 하나의 표준방법이 될 수 있을 것이다.

• The Korean Journal of Applied Statistics
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• v.17 no.2
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• pp.337-346
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• 2004

The Pearson chi-square goodness-of-fit test and the likelihood ratio tests are usually used for testing independence in two-way contingency tables under random sampling. But both of these tests may provide false results for the contingency table with clustered observations. In this case we consider the generalized linear mixed model which includes random effects of clustering in addition to the fixed effects of covariates. Both the heterogeneity between clusters and the dependency within a cluster can be explained via generalized linear mixed model. In this paper we introduce several types of generalized linear mixed model for testing independence in contingency tables with clustered observations. We also discuss the fitting of these models through a real dataset.

• The Korean Journal of Applied Statistics
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• v.26 no.6
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• pp.889-902
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• 2013

Several goodness-of-fit test statistics have been proposed for a multinomial logit regression model; however, the properties of the proposed tests were not adequately studied. This paper evaluates three different goodness-of-fit tests using grouping strategies, proposed by Fagerland et al. (2008), Bull (1994), and Pigeon and Heyse (1999). In addition, Pearson (1900)'s method is also examined as a reference. Simulation studies were conducted to evaluate the four methods in terms of null distribution and power. A real data example is presented to illustrate the methods.