• Communications for Statistical Applications and Methods
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• v.23 no.5
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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.

• Journal of Integrative Natural Science
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• v.5 no.4
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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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• v.16 no.2
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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.

• Korean System Dynamics Review
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• v.8 no.2
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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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• v.4 no.2
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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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• v.8 no.3
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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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• 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.

• Health Policy and Management
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• v.23 no.1
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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.

• Journal of the Korea institute for structural maintenance and inspection
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• v.18 no.4
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• pp.107-117
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• 2014

This study tests homogeneity and performs multiple comparison analysis among treatment levels of each factor group through t-test by materials and analysis of variance by structural type and service period. For that descriptive statistical analysis is performed for static and dynamic response characteristics and their ratios of calculated versus measured values based on a good many safety assessment reports for bridges. Homogeneity and post hoc test based on descriptive statistical analysis provide the measures for homogeneity identification among comparison groups in addition to the statistical reference values such as central tendency, variation and shape. This study is expected to be valuable for structural integrity assessment and design by comparing the measured and calculated values with the reference values for the homogeneous group identified, which can help the engineers review the adequacy of the values and put the group database to practical use.

• Laser Solutions
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• v.16 no.4
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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.