scholarly journals Alternative Hypothesis Tests for the Covariance Matrix Based on Eigenvalues and Multivariate Normality

2012 ◽  
Vol 9 (1) ◽  
pp. 9-27
Author(s):  
Sueli Aparecida Mingoti ◽  
Letícia Pereira Pinto
Keyword(s):  
Covariance Matrix ◽  
Alternative Hypothesis ◽  
Multivariate Normality ◽  
Hypothesis Tests

Power Differences Between the Modified Brown-Forsythe and Mixed-Model Approaches in Repeated Measures Designs

Methodology ◽  
2007 ◽  
Vol 3 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Guillermo Vallejo ◽  
María P. Fernández ◽  
Pablo E. Livacic-Rojas
Keyword(s):  
Least Squares ◽  
Covariance Matrix ◽  
Interaction Effect ◽  
Repeated Measures ◽  
Mixed Model ◽  
Information Criterion ◽  
Generalized Least Squares ◽  
Superior Performance ◽  
Multivariate Normality ◽  
Repeated Measures Designs

Abstract. This article compares the sensibility of the modified Brown-Forsythe (MBF) approach developed by Vallejo and Ato (2006) and a modified empirical generalized least squares (EGLS) method adjusted by the Kenward-Roger solution available in the SAS Institute's (2002) Proc Mixed program to detect the presence of an interaction effect under departures from covariance homogeneity and multivariate normality. Although none of the approaches demonstrated superior performance in all situations, our results indicate that the so-called EGLS method, based on the Akaike's Information Criterion or based on always assuming a unstructured between-subjects heterogeneous covariance pattern, was the most powerful alternative. Results also indicate that little power can be achieved with the EGLS method if the covariance matrix is specified correctly.

The genus Relicinopsis is nested within Relicina (Parmeliaceae, Ascomycota)

2017 ◽  
Vol 49 (3) ◽  
pp. 189-197 ◽  
Author(s):  
Paul M. KIRIKA ◽  
Pradeep K. DIVAKAR ◽  
Steven D. LEAVITT ◽  
Kawinnat BUARUANG ◽  
Ana CRESPO ◽  
...  
Keyword(s):  
Ribosomal Dna ◽  
Dna Sequences ◽  
Alternative Hypothesis ◽  
Morphological Features ◽  
Evolutionary Relationships ◽  
New Combinations ◽  
Hypothesis Tests ◽  
Phylogenetic Framework ◽  
Phenotypic Features

AbstractMacro-morphological features traditionally used to segregate genera in Parmeliaceae have been shown to be highly plastic, placing limits on their taxonomic value. Here we aim to elucidate the evolutionary relationships of the genera Relicina and Relicinopsis and reassess the phenotypic features traditionally used to separate these genera. To this end, we gathered ribosomal DNA sequences of ITS, nuLSU and mtSSU and analyzed them in a phylogenetic framework. Relicina was recovered as paraphyletic, with Relicinopsis nested within, and three different clades were identified within Relicina. Alternative hypothesis tests significantly rejected the monophyly of Relicina. Our results indicate that the presence or absence of bulbate cilia is of limited taxonomic value in this clade. Based on differences in conidia, however, we propose to accept Relicinopsis as a subgenus within Relicina as Relicina subgen. Relicinopsis (Elix & Verdon) Kirika, Divakar & Lumbsch. It is proposed that five new combinations of species previously classified in Relicinopsis be placed in Relicina.

scholarly journals ON THE POWER OF INVARIANT TESTS FOR HYPOTHESES ON A COVARIANCE MATRIX

2015 ◽  
Vol 33 (1) ◽  
pp. 1-68
Author(s):  
David Preinerstorfer ◽  
Benedikt M. Pötscher
Keyword(s):  
Time Series ◽  
Covariance Matrix ◽  
Regression Models ◽  
General Framework ◽  
Alternative Hypothesis ◽  
Spatial Regression ◽  
Substantial Portion ◽  
Time Series Regression ◽  
Statistical Planning ◽  
Watson Test

The behavior of the power function of autocorrelation tests such as the Durbin–Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation becomes strong, Krämer (1985, Journal of Econometrics 28, 363–370.) (for the Durbin–Watson test) and Krämer (2005, Journal of Statistical Planning and Inference, 128, 489–496) (for the Cliff-Ord test) have shown that power can be very low, in fact can converge to zero, under certain circumstances. Motivated by these results, Martellosio (2010, Econometric Theory, 26, 152–186) set out to build a general theory that would explain these findings. Unfortunately, Martellosio (2010) does not achieve this goal, as a substantial portion of his results and proofs suffer from nontrivial flaws. The present paper now builds a theory as envisioned in Martellosio (2010) in an even more general framework, covering general invariant tests of a hypothesis on the disturbance covariance matrix in a linear regression model. The general results are then specialized to testing for spatial correlation and to autocorrelation testing in time series regression models. We also characterize the situation where the null and the alternative hypothesis are indistinguishable by invariant tests.

scholarly journals Using Simple Alternative Hypothesis to Increase Statistical Power in Sparse Categorical Data

2017 ◽  
Vol 6 (6) ◽  
pp. 158
Author(s):  
Louis Mutter ◽  
Steven B. Kim
Keyword(s):  
Sample Size ◽  
Categorical Data ◽  
Null Hypothesis ◽  
Statistical Power ◽  
Goodness Of Fit ◽  
Alternative Hypothesis ◽  
Small Sample ◽  
Statistical Hypothesis ◽  
Hypothesis Tests ◽  
Simple Alternative

There are numerous statistical hypothesis tests for categorical data including Pearson's Chi-Square goodness-of-fit test and other discrete versions of goodness-of-fit tests. For these hypothesis tests, the null hypothesis is simple, and the alternative hypothesis is composite which negates the simple null hypothesis. For power calculation, a researcher specifies a significance level, a sample size, a simple null hypothesis, and a simple alternative hypothesis. In practice, there are cases when an experienced researcher has deep and broad scientific knowledge, but the researcher may suffer from a lack of statistical power due to a small sample size being available. In such a case, we may formulate hypothesis testing based on a simple alternative hypothesis instead of the composite alternative hypothesis. In this article, we investigate how much statistical power can be gained via a correctly specified simple alternative hypothesis and how much statistical power can be lost under a misspecified alternative hypothesis, particularly when an available sample size is small.

scholarly journals ON HYPOTHESIS TESTS FOR COVARIANCE MATRICES UNDER MULTIVARIATE NORMALITY

2015 ◽  
Vol 35 (1) ◽  
pp. 123-142 ◽  
Author(s):  
Letícia Pereira Pinto ◽  
Sueli Aparecida Mingoti
Keyword(s):  
Covariance Matrices ◽  
Multivariate Normality ◽  
Hypothesis Tests

The use and abuse of hypothesis tests: how to present P values

2010 ◽  
Vol 25 (3) ◽  
pp. 107-112 ◽  
Author(s):  
C J Smith ◽  
Z V Fox
Keyword(s):  
Best Practice ◽  
Varicose Veins ◽  
Alternative Hypothesis ◽  
Hypothesis Test ◽  
P Value ◽  
Hypothesis Tests ◽  
Compression Stockings ◽  
P Values ◽  
Repeated Observations ◽  
Key Issues

This overview highlights some of the key issues involved in performing and interpreting hypothesis tests. We describe the general approach taken in performing a hypothesis test with a focus on how to state the null and alternative hypothesis, and why two-sided tests are usually more appropriate than one-sided tests. We describe best practice techniques in performing and presenting the results of hypothesis tests. We recommend that, alongside any p-values, authors should also present estimates of the size of any treatment effects and their confidence intervals. Furthermore, they should specify the exact p-value rather than using terms such as 'NS' or the commonly used asterix notation. We discuss other pitfalls that are encountered at the analysis stage such as the use of repeated observations on individuals, the use of multiple tests on the data and the erroneous use of parametric tests when data are not normally distributed and vice versa. We highlight these points using two different examples: one looking at the use of compression stockings for preventing the occurrence of DVT on long-haul flights and a second hypothetical study comparing laser versus surgery techniques for the removal of varicose veins.

Molecular data show that Topeliopsis (Ascomycota, Thelotremataceae) is polyphyletic

2008 ◽  
Vol 40 (1) ◽  
pp. 39-46 ◽  
Author(s):  
Armin MANGOLD ◽  
María P. MARTÍN ◽  
Klaus KALB ◽  
Robert LÜCKING ◽  
H. Thorsten LUMBSCH
Keyword(s):  
Dna Sequences ◽  
New Genus ◽  
Alternative Hypothesis ◽  
Large Subunit ◽  
Molecular Data ◽  
New Combination ◽  
Phylogenetic Study ◽  
Hypothesis Tests ◽  
Thin Walled

Abstract:A phylogenetic study using DNA sequences of the nuclear ribosomal large subunit from 38 species is used to infer the phylogeny of species currently placed in Topeliopsis. The genus is shown to be polyphyletic; monophyly of previous and current circumscriptions of the genus are rejected using two alternative hypothesis tests. Topeliopsis meridiensis is shown to be closer to Chapsa than Topeliopsis, but additional studies are necessary to understand the circumscription of Chapsa. The new genus Melanotopelia Lumbsch & Mangold is described to accommodate T. toensbergii and T. rugosa. These species were previously regarded as aberrant in Topeliopsis because of their thin-walled ascospores and dark pigmented proper exciple. The new combination Graphis mexicana (Hale) Kalb, Lücking & Lumbsch is proposed and Graphis muscicola and Topeliopsis globosa reduced to synonymy with this species.

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