• 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.

• 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.

• 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.

• 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.

• 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.

• International Journal of Computer Science & Network Security
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• v.24 no.4
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• pp.44-50
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• 2024

This paper offers an overview of matrix formation and calculation techniques within the framework of General Linear Models (GLMs). It takes a sequential approach, beginning with a detailed exploration of matrix formation and calculation methods in regression analysis and univariate analysis of variance (ANOVA). Subsequently, it extends the discussion to cover multivariate analysis of variance (MANOVA). The primary objective of this study was to provide a clear and accessible explanation of the underlying matrices that play a crucial role in GLMs. Through linking, essentially different statistical methods, by fundamental principles and algebraic foundations that underpin the GLM estimation. Insights presented here aim to assist researchers, statisticians, and data analysts in enhancing their understanding of GLMs and their practical implementation in diverse research domains. This paper contributes to a better comprehension of the matrix-based techniques that can be extended to GLMs.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.405-414
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• 2002

We consider the problem of estimating the error variance of in a two-way mixed-effects ANOVA model using noninformative priors. First, we derive Jeffreys' prior, a reference prior, and matching priors. We then provide marginal posterior distributions under those noninformative priors. Finally, we provide graphs of marginal posterior densities of the error variance and credible intervals for the error variance in two real data set and compare these credible intervals.

• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.1008-1011
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• 2001

The purpose of this paper is to evaluate the chip breakability during turning using the experimental equation, which is developed by an orthogonal array method. The chip breaking index(CB), non-dimensional parameter is used in the evaluation of chip breakability. The analysis of variance(ANOVA)-test has been used to check the significance of cutting parameters. And using the result of ANOVA-test, the experimental equation of chip breakability, which consists of significant cutting parameters, has been developed.

• 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.