• Communications for Statistical Applications and Methods
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• 제23권5호
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• pp.433-444
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• 2016

When we observe binary responses in a cluster (such as rat lab-subjects), they are usually correlated to each other. In clustered binomial counts, the independence assumption is violated and we encounter an extra-variation. In the presence of extra-variation, the ordinary statistical analyses of binomial data are inappropriate to apply. In testing the homogeneity of proportions between several treatment groups, the classical Pearson chi-squared test has a severe flaw in the control of Type I error rates. We focus on modifying the chi-squared statistic by incorporating variance inflation factors. We suggest a method to adjust data in terms of dispersion estimate based on a quasi-likelihood model. We explain the testing procedure via an illustrative example as well as compare the performance of a modified chi-squared test with competitive statistics through a Monte Carlo study.

• 통합자연과학논문집
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• 제5권4호
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• pp.241-245
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• 2012

Categorical data collected based on complex sample design is not proper for the standard Pearson multinomial-based chi-squared test because the observations are not independent and identically distributed. This study investigates effects of bias of point estimator of population proportion and its variance estimator to the standard Pearson chi-squared test statistics when the sample is collected based on complex sampling scheme. This study examines the effect under two population homogeneity test. The standard Pearson test statistic can be partitioned into two parts; the first part is the weighted sum of ${\chi}^2_1$ with eigenvalues of design matrix as their weights, and the additional second part which is added due to the biases of the point estimator and its variance estimator. Our empirical analysis shows that even though the bias of point estimator is small, Pearson test statistic is very much inflated due to underestimate the variance of point estimator. In the connection of design-based variance estimator and its design matrix, the bigger the average of eigenvalues of design matrix is, the larger relative size of which the first component part to Pearson test statistic is taking.

• Communications for Statistical Applications and Methods
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• 제16권2호
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• pp.389-396
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• 2009

Approximations for the null distribution of a test statistic arising in multivariate analysis to test homogeneity of variances and a mixture of two beta distributions by making use of a product of beta baseline density function and a polynomial adjustment, so called beta-polynomial density approximant, are discussed. Explicit representations of density and distribution approximants of interest in each case can easily be obtained. Beta-polynomial density approximants produce good approximation over the entire range of the test statistic and also accommodate even the bimodal distribution using an artificial example of a mixture of two beta distributions.

• 한국시스템다이내믹스연구
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• 제8권2호
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• pp.25-49
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• 2007

An important assumption of the classical linear regression model is that the disturbances appearing in the population regression function are homoskedastic; that is, they all have the same variance. If we persist in using the usual testing procedures despite heteroskedasticity, what ever conclusions we draw or inferences we make be very misleading. The contribution of this paper will be to the concrete procedure of the proper estimation when the heteroskedasticity does exist in the data, because the quality of dependent variable predictions, i.e., the estimated variance of the dependent variable, can be improved by giving consideration to the issues of regional homogeneity and/or heteroskedasticity across the research area. With respect to estimation, specific attention should be paid to the selection of the appropriate strategy in terms of the auxiliary regression model. The paper shows that by testing for heteroskedasticity, and by using robust methods in the presence of with and without heteroskedasticity, more efficient statistical inferences are provided.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.501-512
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• 1997

In multiple linear regression model we have presupposed assumptions (independence normality variance homogeneity and so on) on error term. When case weights are given because of variance heterogeneity we can estimate efficiently regression parameter using weighted least squares estimator. Unfortunately this estimator is sen-sitive to outliers like ordinary least squares estimator. Thus in this paper we proposed some statistics for detection of outliers in weighted least squares regression.

• Communications for Statistical Applications and Methods
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• 제8권3호
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• pp.603-613
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• 2001

A test based on score statistic is derived for detecting homoscedasticity of errors in unbalanced random effects linear model. A small simulation study is performed to investigate the finite sample behaviour of the test statistic which is known to have an asymptotic chi-square distribution under the null hypothesis.

• Journal of the Korean Data and Information Science Society
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• 제24권4호
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• pp.815-824
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• 2013

국가단위의 조사와 같은 대규모 표본조사에서는 표본의 대표성을 확보하기 위해 층화, 집락, 계통, 불균등확률추출 등을 종합적으로 사용하는 복합표본설계가 일반화되어 있다. 이러한 복합표본설계에 기초한 범주형 자료분석에서는 자료의 독립성과 다항분포를 가정하는 전통적인 피어슨검정이 왜곡된 검정결과를 가져올 수 있다. 본 연구는 복합표본설계에 의한 범주형조사자료의 k-모집단 동질성검정에서 설계기반 일치통계량인 Wald 검정통계량을 유도하고, 전통적인 피어슨검정통계량을 사용할 경우 발생할 수 있는 오차요인을 항목별로 분해하여, 분산의 편의에 의한 영향, 추정량의 편의에 의한 영향, 기타 분산의 편의와 추정량의 편의가 교락되어 미치는 영향으로 각각 분해하는 식을 도출하였다. 또한, 도출된 식의 각 항목이 피어슨 카이제곱검정통계량에 미치는 상대적 크기를 경험적으로 확인하기 위해 국민건강영양조사 제4기 2차년도 자료를 이용해 경험분석 하였다. 분석결과, 변수에 따른 차이는 있지만 대체로 분산의 편의가 미치는 영향이 추정량의 편의가 미치는 영향보다 크다는 것을 명확히 확인할 수 있었다.

• 보건행정학회지
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• 제23권1호
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• pp.44-51
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• 2013

Background: This study designed to evaluate the homogeneity of Korean diagnosis related group (KDRG) version 3.4 classification system. Methods: The total 5,921,873 claims data submitted to the Health Insurance Review and Assessment Service during 2010 were used. Both coefficient of variation (CV) and reduction in variance of cost were measured for evaluation. This analysis was divided into before and after trimming outliers at the level of adjacent DRG (ADRG), aged ADRG (AADRG) split by age, and DRG split by complication and comorbidity. Results: At the each three level of ADRG, AADRG, and DRG, there were 38.9%, 38.7%, and 30.0% of which had a CV > 100% in the untrimmed data and there were 1.4%, 1.4%, and 1.9% in the trimmed one. Before trimming outliers, ADRGs explained 52.5% of the variability in resource use, AADRGs did 53.1% and DRGs did 57.1%. The additional explanatory power by age and comorbidity and complication (CC) split were 0.6%p and 4.6%p for each, which were statistically significant. After trimming outliers, ADRGs explained 75.2% of the variability in resource use, AADRGs did 75.6%, and DRGs did 77.1%. The additional explanatory power were 0.4%p and 2.0%p for each, which were statistically significant too. Conclusion: The results demonstrated that KDRG showed high homogeneity within groups and performance after trimming outliers. But there were DRGs CV > 100% after age or CC split and the most contributing factor to high performance of KDRG was the ADRG rather than age or CC split. Therefore, it is recommended that the efforts for improving clinical homogeneity of KDRG such as review of the hierarchical structure of classification systems and classification variables.

• 한국구조물진단유지관리공학회 논문집
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• 제18권4호
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• pp.107-117
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• 2014

본 연구는 실제 구조진단 사례에 기초하여 재료와 형식 및 공용기간에 따라 교량의 응답, 충격계수, 고유진동수 및 각 특성의 해석값/계측값 비 등에 관한 기술통계를 분석하고 주재료에 따른 T-검정과 구조형식 및 공용기간에 따른 분산분석을 통해서 요인 부집단 수준 간동질성 검정 및 다중비교분석을 수행하였다. 본 연구 결과는 응답 분포의 중심값, 산포도, 대칭성 등 통계적 특성 및 비교분석 집단 간 동질성 식별을 위한 참조값을 제공하며, 이것은 내하력 평가 등 구조 진단과 설계에서 엔지니어들이 취득한 계산 또는 계측값의 타당성을 비교검토하고 데이터베이스를 활용하는 등의 공학적 판단을 하는데 실제적으로 유용한 정보를 제공할 것으로 기대된다.

• 한국레이저가공학회지
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• 제16권4호
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• pp.12-16
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• 2013

For mass production of electronic devices, the processing of the printing roll is one of the most important key technologies for printed electronics technology. A roll of printing process, the gravure printing that is used to print the electronic device is most often used. The indirect laser processing has been used in order to produce printing roll for gravure printing. It consists of the following processing that is coating of photo polymer or black lacquer on the surface of printing roll, pattering using a laser beam and etching process. In this study, we have carried out study on the coating and etching for $25{\mu}m$ line width on the printing roll. To do this goals, a $4{\mu}m$ coating thickness and 20% average coating thickness of the coating homogeneity of variance is performed. The factors to determine the thickness and homogeneity are a viscosity of coating solution, the liquid injection, the number of injection, feed rate, rotational speed, and the like. After the laser patterning, a line width of $25{\mu}m$ or less was confirmed to be processed through etching and the chromium plating process.