• 응용통계연구
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• 제19권1호
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• pp.111-120
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• 2006

이단계 이수준 균형지분모형에서 주효과 및 지분효과를 검정하기 위한 모수적 검정과 순위변환을 이용한 검정은 전반적으로 제1종 오류율이 상당히 유사하며, 주효과 및 지분효과를 검정하기 위한 순위변환통계량의 검정력은 모수적 통계량의 검정력보다 상대적으로 뛰어난 수준임을 보여준다. 한편 효과의 크기와 표본의 크기를 증가시킬수록 모수적 통계량과 순위변환 통계량의 검정력 증가량의 크기는 현저하게 향상되며, 특히 지수분포와 같은 비대칭분포하에서 모든 인자가 고정일때 순위변환 통계량의 검정력이 모수적 통계량의 검정력보다 월등히 높은 수준임을 나타낸다.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1059-1071
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• 2008

In a balanced factorial design with a nested factor where crossed factors as well as a nested factor exist simultaneously, powers of the rank transformed FR statistic for testing the main, nested and interaction effects are superior to those of the parametric F statistic. In heavy tailed distributions such as exponential and double exponential distributions, powers of the FR statistic show much higher level than those of the F statistic. Further powers of the F and FR statistic for testing the main effect show the highest level in an absolute size as compared with powers of the F and FR statistic for testing the nested and interaction effects. However powers of the FR statistic for testing the nested and interaction effects rather than the main effect are greater in a relative size than powers of F statistic for the all population distributions.

• 대한안전경영과학회지
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• 제12권1호
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• pp.199-205
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• 2010

The research proposes the three-factor random measurement models for estimating the precision about operator, part, tool, and various measurement environments. The combined model with crossed and nested factors is developed to analyze the approximate F test by degrees of freedom given by Satterthwaite and point estimation of precisions from expected mean square. The model developed in this paper can be extended to the three useful models according to the type of nested designs. The study also provides the three-step procedures to evaluate the measurement precisions using three indexes such as SNR(Signal-To-Noise Ratio), R&R TR(Reproducibility&Repeatability-To-Total Precision Ratio), and PTR(Precision-To-Tolerance Ratio), The procedures include the identification of resolution, the improvement of R&R reduction, and the evaluation of precision effect.

• 대한안전경영과학회지
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• 제10권3호
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• pp.245-251
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• 2008

The research proposes three ANOVA(Analysis of Variance) tests using expected mean square(EMS) algorithms in various split-plot designs. The variance tests consist of Never-Pool test, Sometimes-Pool test and Always-Pool test. This paper also presents two EMS algorithms such as standard method and easy method. These algorithms are useful to make a decision rule for pooling. Numerical examples are illustrated for various split-plot designs such as split-plot designs, split-split-plot designs, repetition split-plot designs, and nested designs. Pragmatically, the results are summarized and compared with popular ANOVA spreadsheets and data model equations.

• 한국산림과학회지
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• 제97권6호
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• pp.565-569
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• 2008

소멸위기수종인 분비나무와 구상나무 8개 천연집단의 지리적 위치에 따른 구과, 종자 및 포침의 형태적 특성에 대한 변이의 구명과 단계적 판별분석을 이용하여 이들 변수 중 수종간 식별에 도움을 주는 분류 지표를 선정하고자 하였다. Nested 분산분석 결과 구과, 종자 및 포침 특성 13가지 형질 모두에서 집단간 및 집단 내 개체 간에 유의적인 차이를 보였다. 분비나무는 종자길이, 종자지수, 포침폭 및 포침지수 특성에서, 구상나무는 포침폭과 포침지수 특성에서 총 분산 가운데 집단간 차지하는 비율이 집단내의 개체가 차지하는 비율보다 높게 나타났다. 분비나무와 구상나무의 식별을 위한 판별분석 결과 변별력을 갖는 주요 형질들은 구과폭, 종자날개의 폭 및 포침길이 특성으로 나타났으며, 최종적으로 변수증감법(stepdisc method)에 의한 단계적 판별분석에서 종자날개의 폭과 포침길이 인자의 최적결합으로 판별되었다.

• East Asian mathematical journal
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• 제5권1호
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• pp.95-110
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• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2005년도 춘계공동학술대회 발표논문
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• pp.975-982
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• 2005

The purpose of the Gage R&R study is to determine whether a measurement system is adequate for monitoring a process. If the measurement system variation is small relative to the process variation, then the measurement system is deemed 'adequate'. The sources of variation associated with the measurement system are compared using an analysis of variance (ANOVA) model, in general. A typical ANOVA model used in a standard Gage R&R study is the two-factor random effect model. Then, the ANOVA partitions the total variation into three categories: repeatability, reproducibility, part variation. However, if the process variation possesses the between group variation, within group variation, and within-part variation, these variations can cause the measurement system evaluation to provide misleading results. That is, in the standard Gage R&R study these variations affect the estimate of repeatability, reproducibility, or both. This paper presents a four-factor nested factorial ANOVA model which explicitly considers these variations for the Gage R&R study. The variance component estimates are derived by setting the EMS equations equal to the corresponding mean square from the ANOVA table and solving. And the proposed model is compared with the standard Gage R&R model.

• 산업공학
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• 제18권4호
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• pp.444-453
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• 2005

The purpose of the Gage R&R study is to determine whether a measurement system is adequate for monitoring a process. If the measurement system variation is small relative to the process variation, then the measurement system is deemed "adequate". The sources of variation associated with the measurement system are compared using an analysis of variance (ANOVA) model, in general. A typical ANOVA model used in a standard Gage R&R study is the two-factor random effect model. Then, the ANOVA partitions the total variation into three categories: repeatability, reproducibility, part variation. However, if the process variation possesses the between group variation, within group variation, and within part variation, these variations can cause the measurement system evaluation to provide misleading results. That is, in the standard Gage R&R study these variations affect the estimate of repeatability, reproducibility, or both. This paper presents a four-factor nested factorial ANOVA model which explicitly considers these variations for the Gage R&R study. The variance component estimators are derived by setting the EMS equations equal to the corresponding mean square from the ANOVA table and solving. And the proposed model is compared with the standard Gage R&R model.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2012년 춘계학술대회
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• pp.277-292
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• 2012

The research presents an application of Balanced ANOVA (BANOVA) by utilizing randomized orders for various Split-Plot Designs (SPDs) which include two cell designs, split-plot with one-way HTC (Hard to Control) factor, split-plot with two-way HTC factor, split-split-plot design and nested design. In addition, four MINITAB examples of 2-level split-plot designs based on the number of blocks and the type of whole-plots are presented for practitioners to obtain comprehensive understanding. Furthermore, the geometrical interrelated properties among three typical Designs of Experiments (DOE), such as Factorial Design (FD), Response Surface Design (RSD), and Mixture Design (MD) are discussed in this paper.

• 대한인간공학회지
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• 제32권6호
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• pp.529-534
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• 2013

Objective: This study determines which of two types of 2D menu is better on iPhone. Background: Menu systems have been important components in modern graphical user interfaces. Review of menu design studies for human-computer interaction suggests that menu design guidelines for smartphones need to be reappraised. Method: A nested factorial design was used. Twenty-four participants were divided into two groups. The subjects were nested within the menu type. Two types of menus are an overview menu and a text menu. Two different breadth levels are 16 and 64. The participants performed five tasks in each breadth level. A task is defined as locating a product or product class on the deepest level of the hierarchy. An Apple iPhone 2G was used. Results: The results for ANOVA indicated a lack of a significant difference for time to respond between the two types of 2D menus. The overview menu showed the better satisfaction score between the two menu types. Conclusion: Even though the differences were not significant, an overview menu tended to show better performance and preference scores than a text menu that required scrolling. Application: This study can provide menu design guidelines when 2D menus are considered for small displays in a high breadth level.