• Title, Summary, Keyword: Variance analysis(ANOVA)

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Why do we get Negative Variance Components in ANOVA

  • Lee, Jang-Taek
    • Communications for Statistical Applications and Methods
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    • v.8 no.3
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    • pp.667-675
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    • 2001
  • The usefulness of analysis of variance(ANOVA) estimates of variance components is impaired by the frequent occurrence of negative values. The probability of such an occurrence is therefore of interest. In this paper, we investigate a variety of reasons for negative estimates under one way random effects model. It can be shown, through simulation, that this probability increases when the number of treatments is too small for fixed total observations, unbalancedness of data is severe, ratio of variance components is too small, and data may contain many outliers.

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The Application of Analysis of Variance (ANOVA) (분산분석)

  • Pak, Son-Il;Oh, Tae-Ho
    • Journal of Veterinary Clinics
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    • v.27 no.1
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    • pp.71-78
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    • 2010
  • Analysis of variance (ANOVA) is a method to analyze the data from the experimental designs comparing two or more groups or treatments at the same time, and is the most effective tool of analyzing more complex data sets with different source of variations. This article describes the logic of ANOVA, the application of the method to the analysis of a simple data set, and the methods available for performing planned or post hoc multiple comparisons between the treatments means. In addition, the common misuse of the techniques is also discussed to emphasize that an inappropriate statistical analysis is potentially far more harmful than poorly conducted research. Lastly, an example is given for illustration purposes.

ON THE ADMISSIBILITY OF HIERARCHICAL BAYES ESTIMATORS

  • Kim Byung-Hwee;Chang In-Hong
    • Journal of the Korean Statistical Society
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    • v.35 no.3
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    • pp.317-329
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    • 2006
  • In the problem of estimating the error variance in the balanced fixed- effects one-way analysis of variance (ANOVA) model, Ghosh (1994) proposed hierarchical Bayes estimators and raised a conjecture for which all of his hierarchical Bayes estimators are admissible. In this paper we prove this conjecture is true by representing one-way ANOVA model to the distributional form of a multiparameter exponential family.

Reference Priors in a Two-Way Mixed-Effects Analysis of Variance Model

  • Chang, In-Hong;Kim, Byung-Hwee
    • Journal of the Korean Data and Information Science Society
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    • v.13 no.2
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    • pp.317-328
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    • 2002
  • We first derive group ordering reference priors in a two-way mixed-effects analysis of variance (ANOVA) model. We show that posterior distributions are proper and provide marginal posterior distributions under reference priors. We also examine whether the reference priors satisfy the probability matching criterion. Finally, the reference prior satisfying the probability matching criterion is shown to be good in the sense of frequentist coverage probability of the posterior quantile.

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Hierarchical Bayes Estimators of the Error Variance in Two-Way ANOVA Models

  • Chang, In Hong;Kim, Byung Hwee
    • Communications for Statistical Applications and Methods
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    • v.9 no.2
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    • pp.315-324
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    • 2002
  • For estimating the error variance under the relative squared error loss in two-way analysis of variance models, we provide a class of hierarchical Bayes estimators and then derive a subclass of the hierarchical Bayes estimators, each member of which dominates the best multiple of the error sum of squares which is known to be minimax. We also identify a subclass of non-minimax hierarchical Bayes estimators.

Statistical Analysis of a Loop Designed Microarray Experiment Data (되돌림설계를 이용한 마이크로어레이 실험 자료의 분석)

  • 이선호
    • The Korean Journal of Applied Statistics
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    • v.17 no.3
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    • pp.419-430
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    • 2004
  • Since cDNA microarray experiments can monitor expression levels for thousands of genes simultaneously, the experimental designs and their analyzing methods are very important for successful analysis of microarray data. The loop design is discussed for selecting differentially expressed genes among several treatments and the analysis of variance method is introduced to normalize microarray data and provide estimates of the interesting quantities. MA-ANOVA is used to illustrate this method on a recently collected loop designed microarray data at Cancer Metastasis Research Center, Yonsei University.

Process Optimization of Thermal-sprayed STS316 Coating (STS316 용사코팅의 최적 공정 설계)

  • Kim, Kyun-Tak;Kim, Yeong-Sik
    • Journal of Ocean Engineering and Technology
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    • v.24 no.1
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    • pp.161-165
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    • 2010
  • In the present study, process optimization for thermal-sprayed STS316 coating has been performed using $L_9(3^4)$ orthogonal array and analysis of variance (ANOVA). STS316 coatings were fabricated by flame spray process on steel substrate, and the hardness test and microstructure observation of the coatings were studied. The results of hardness test were analyzed by ANOVA. The ANOVA results showed that the spray distance had the greatest effect on hardness of the coating, on the other hands, the effects of oxygen gas flow and spray distance were ignorable. From these results, the optimal combination of the flame spray parameters could be derived, and confirmation experiment was carried out to verify these derived results. The calculated hardness of the coatings by ANOVA was found to approximately close to that of confirmation experimental result. Thus, it was considered that design of experiments using orthogonal array and ANOVA was effective for process optimization of thermal-sprayed STS316 coating.

Power Algorithms for Analysis of Variance Tests

  • Hur, Seong-Pil
    • Journal of the military operations research society of Korea
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    • v.13 no.1
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    • pp.45-64
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    • 1987
  • Power algorithms for analysis of variance tests are presented. In experimental design of operational tests and evaluations the selection of design parameters so as to attain an experiment with desired power is a difficult and important problem. An interactive computer program is presented which uses the power algorithms for ANOVA tests and creates graphical presentations which can be used to assist decision makers in statistical design. ANOVA tests and associated parameters (such as sample size, types and levels of treatments, and alpha-level)are examined.

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Unbalanced ANOVA for Testing Shape Variability in Statistical Shape Analysis

  • Kim, Jong-Geon;Choi, Yong-Seok;Lee, Nae-Young
    • The Korean Journal of Applied Statistics
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    • v.23 no.2
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    • pp.317-323
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    • 2010
  • Measures are very useful tools for comparing the shape variability in statistical shape analysis. For examples, the Procrustes statistic(PS) is isolated measure, and the mean Procrustes statistic(MPS) and the root mean square measure(RMS) are overall measures. But these measures are very subjective, complicated and moreover these measures are not statistical for comparing the shape variability. Therefore we need to study some tests. It is well known that the Hotelling's $T^2$ test is used for testing shape variability of two independent samples. And for testing shape variabilities of several independent samples, instead of the Hotelling's $T^2$ test, one way analysis of variance(ANOVA) can be applied. In fact, this one way ANOVA is based on the balanced samples of equal size which is called as BANOVA. However, If we have unbalanced samples with unequal size, we can not use BANOVA. Therefore we propose the unbalanced analysis of variance(UNBANOVA) for testing shape variabilities of several independent samples of unequal size.

Optimum seat design for the quadruple offset butterfly valve by analysis of variance with orthogonal array

  • Lee, Sang-Beom;Lee, Dong-Myung
    • Journal of the Korean Society of Marine Engineering
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    • v.38 no.8
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    • pp.961-967
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    • 2014
  • In onshore and offshore plant engineering, a broad use of pipe system have been achieved and accordingly related technologies has been developed especially in the field of flow control valves. The aim of this study is to suggest the quadruple offset butterfly valve for bi-directional applications which show equivalent operating torque characteristics of the triple offset butterfly valve. Seat design parameters for the quadruple offset butterfly valve are determined by the proposed method utilizing both ANOVA (analysis of variance) and the orthogonal array. Through additive model considering the effect of design parameters on seating torque, mean estimation is performed and thus its optimization results are verified by design of experiment results. The insight obtained from the present study is beneficial for valve design engineers to develop reliable and integrated design of the quadruple offset butterfly valve.