• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.111-120
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• 2006

In a two-stage two-level balanced nested design, type I error rates for the parametric tests and the rank transformed tests for the main effects and the nested effects are in overall similar to each other. Furthermore, powers for the rank transformed statistic for the main effects and the nested effects in a two-stage two-level balanced nested design are generally superior to powers for the parametric statistic When the effect size and the sample size are increased, we can find that powers increase for the parametric statistic and the rank transformed statistic are dramatically improved. Especially for the case of the fixed effects in the asymmetric distributions such as an exponential distribution, powers for the rank transformed tests are quite high rather than powers for the parametric tests.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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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.

• Journal of the Korea Safety Management & Science
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• v.12 no.1
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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.

• Journal of the Korea Safety Management & Science
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• v.10 no.3
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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.

• Journal of Korean Society of Forest Science
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• v.97 no.6
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• pp.565-569
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• 2008

Geographic variation of characteristics of cone, seed and bract morphology were examined in 8 populations of rare endemic Abies nephrolepis (Trautv.) Maxim and A. koreana Wilson. Additionally we studied classification index to distinguish between the species by the method of discriminant analysis. Nested ANOVA showed that there were statistically significant differences among populations as well as among individuals within populations in all 13 morphological traits. In the seed length, seed index, bract width, and bract index of A. nephrolepis and the bract width and index of A. koreana, variance components among populations were larger than those among individuals within populations. In discriminant analysis, three traits (cone width, length of seed wing, and bract length) were found to be useful in discriminating A. nephrolepis from A. koreana. The optimal classification results of stepwise selection were discriminated length of seed wing and bract length.

• East Asian mathematical journal
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• v.5 no.1
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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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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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.

• IE interfaces
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• v.18 no.4
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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.

• Proceedings of the Safety Management and Science Conference
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• 2012.04a
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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.

• Journal of the Ergonomics Society of Korea
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• v.32 no.6
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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.