• 지질공학
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• 제25권3호
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• pp.331-337
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• 2015

본 연구에서는 화강암 풍화토와 편마암 풍화토를 대상으로 모형시험 수행 중 획득한 간극수압, 함수비 데이터를 대상으로 Hotelling의 T² 분석을 실시하여 사면의 이상거동을 감지할 수 있는 기법을 개발하였다. 각 시험에서는 간극수압 3개와 함수비 3개가 동시에 측정되며, 이들의 상관관계를 이용하여 신뢰구간 95.0%와 90.0%를 기준으로 T² 통계량을 계산하였다. 분석결과에 의하면 모형사면 내의 국부적인 붕괴는 센서 위치에 따라 감지하지 못하는 경우가 있으며, 사면 전체붕괴의 경우 수백 초에서 수천 초 전에 T² 통계량이 신뢰구간 90%를 초과하여 이상거동을 감지할 수 있었다. Hotelling의 T² 분석은 동일 사면 내 다양한 측정치 간의 상관성을 분석할 수 있어 유일한 관리기준치를 설정할 수 있으며, 신뢰도 수준에 따라 단계적인 예경보 기준설정이 가능하다.

• 응용통계연구
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• 제23권2호
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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.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.305-312
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• 2005

In the cluster analysis, Hotelling's $T^2$ can be used to estimate the unknown number of clusters based on the idea of multiple comparison procedure. Especially, its threshold is obtained according to the probability of committing the type one error. Examples are used to compare Hotelling's $T^2$ with other classical location test statistics such as Sum-of-Squared Error and Wilks' $\Lambda$ The hierarchical clustering is used to reveal the underlying structure of the data. Also related criteria are reviewed in view of both the between variance and the within variance.

• Asian Pacific Journal of Cancer Prevention
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• 제14권3호
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• pp.1629-1633
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• 2013

Background: Gene set analysis (GSA) incorporates biological with statistical knowledge to identify gene sets which are differentially expressed that between two or more phenotypes. Materials and Methods: In this paper gene sets differentially expressed between acute lymphoblastic leukaemia (ALL) with BCR-ABL and those with no observed cytogenetic abnormalities were determined by GSA methods. The BCR-ABL is an abnormal gene found in some people with ALL. Results: The results of two GSAs showed that the Category test identified 30 gene sets differentially expressed between two phenotypes, while the Hotelling's $T^2$ could discover just 19 gene sets. On the other hand, assessment of common genes among significant gene sets showed that there were high agreement between the results of GSA and the findings of biologists. In addition, the performance of these methods was compared by simulated and ALL data. Conclusions: The results on simulated data indicated decrease in the type I error rate and increase the power in multivariate (Hotelling's $T^2$) test as increasing the correlation between gene pairs in contrast to the univariate (Category) test.

• 응용통계연구
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• 제22권6호
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• pp.1355-1364
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• 2009

본 논문에서는 다변량 자료의 위치모수에 대한 로버스트 검정 방법으로 유사등변성과 고붕괴성을 만족하는 MVE와 MCD 추정량에 근거한 로버스트 검정방법을 제안하였다. 일반적으로 이들 추정방법은 낮은 효율성으로 인하여 통계적 추론보다는 잠재적 이상치의 발견과 같은 탐색적분석에서 사용된다. 우리는 검정력을 높이기 위하여 MVE와 MCD 추정량에 근거한 일단계 재가중절차를 사용했는데, 가중치 선정과 관련된 임계값을 조절함으로써 현실적으로 사용가능한 높은 효율성과 정확성을 갖춘 검정방법을 제시하였다. 모의실험 결과 본 연구에서 제안한 검정법은 모분포에 관계없이 모두 명목유의수준을 제대로 유지하고 검정력도 높게 나타났으며, 이상치를 포함하고 있는 사례를 이용하여 실제로 모평균에 대한 가설검정을 수행한 결과 기존 방법과는 달리 영향을 받지 않았다.

• Communications for Statistical Applications and Methods
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• 제22권2호
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• pp.121-135
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• 2015

We consider testing equality of mean functions from two samples of functional data. A novel test based on the adaptive Neyman methodology applied to the Hotelling's T-squared statistic is proposed. Under the enlarged null hypothesis that the distributions of the two populations are the same, randomization methods are proposed to find a null distribution which gives accurate significance levels. An extensive simulation study is presented which shows that the proposed test works very well in comparison with several other methods under a variety of alternatives and is one of the best methods for all alternatives, whereas the other methods all show weak power at some alternatives. An application to a real-world data set demonstrates the applicability of the method.

• 문화기술의 융합
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• 제7권1호
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• pp.223-233
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• 2021

본 연구는 디자인씽킹을 활용한 수업에서의 창의적 문제해결 경험을 살펴보기 위해 서울의 A대학에서 2018년 2학기 정규수업으로 개설된 공학제품 설계 수업에 등록한 1학년 학생 37명(남 27명, 여 10명)을 대상으로 실시되었다. 본 연구에서 창의적 문제해결력은 창의적 성향과 문제해결력으로 나누어 살펴보았으며, Hotelling's T-square test와 t-test를 통해 사전-사후의 창의적 문제해결력 차이를 살펴본 결과, 창의적 성향 중 인내와 열정, 유머, 호기심, 진취적 성향이, 문제해결력 중 문제해결 행동이 유의미하게 증가된 것으로 나타났다. 이어, 성찰일지를 통해 창의적 문제해결의 과정을 살펴본 결과, 디자인씽킹의 공감하기와 프로토타입 및 테스트 단계에서는 문제해결을 위한 활동이 보다 많이 나타나고, 정의하기/발상하기와 아이디어 내기 단계에서는 창의적 활동이 보다 많이 나타나는 것을 확인해 볼 수 있었다. 본 연구의 결과는 디자인씽킹을 통해 창의적 문제해결력이 항상될 수 있음을 나타내주며, 효과적인 디자인씽킹 활용 수업을 위한 교수적 지원이 뒷받침되어야 함을 시사해 준다.

• Quantitative Bio-Science
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• 제36권1호
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• pp.23-31
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• 2017

Datasets from DNA microarray experiments, which are in the form of large matrices of expression levels of genes, often have missing values. However, the existing statistical methods including the principle components analysis (PCA) and Hotelling's t-test are not directly applicable for the datasets having missing values due to the fact that they assume the observed dataset is complete in general. Many methods have been proposed in previous literature to impute the missing in the observed data. Troyanskaya et al. [1] study the k-nearest neighbor (kNN) imputation, Kim et al. [2] propose the local least squares (LLS) method and Rubin [3] propose the multiple imputation (MI) for missing values. To identify differentially expressed genes, we propose a new testing procedure when the missing exists in the observed data. The proposed procedure uses the Stouffer's z-scores and combines the test results of individual imputed samples, which are dependent to each other. We numerically show that the proposed test procedure based on MI performs better than the existing test procedures based on single imputation (SI) by comparing their ROC curves. We apply the proposed method to analyzing a public microarray data.

• Genomics & Informatics
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• 제14권4호
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• pp.187-195
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• 2016

In genetic association studies with high-dimensional genomic data, multiple group testing procedures are often required in order to identify disease/trait-related genes or genetic regions, where multiple genetic sites or variants are located within the same gene or genetic region. However, statistical testing procedures based on an individual test suffer from multiple testing issues such as the control of family-wise error rate and dependent tests. Moreover, detecting only a few of genes associated with a phenotype outcome among tens of thousands of genes is of main interest in genetic association studies. In this reason regularization procedures, where a phenotype outcome regresses on all genomic markers and then regression coefficients are estimated based on a penalized likelihood, have been considered as a good alternative approach to analysis of high-dimensional genomic data. But, selection performance of regularization procedures has been rarely compared with that of statistical group testing procedures. In this article, we performed extensive simulation studies where commonly used group testing procedures such as principal component analysis, Hotelling's $T^2$ test, and permutation test are compared with group lasso (least absolute selection and shrinkage operator) in terms of true positive selection. Also, we applied all methods considered in simulation studies to identify genes associated with ovarian cancer from over 20,000 genetic sites generated from Illumina Infinium HumanMethylation27K Beadchip. We found a big discrepancy of selected genes between multiple group testing procedures and group lasso.