@article { ISI:000255532900018,
	title = {Hypothesis testing in comparative and experimental studies of function-valued traits},
	journal = {EVOLUTION},
	volume = {62},
	number = {5},
	year = {2008},
	month = {MAY},
	pages = {1229-1242},
	publisher = {BLACKWELL PUBLISHING},
	type = {Article},
	address = {9600 GARSINGTON RD, OXFORD OX4 2DQ, OXON, ENGLAND},
	abstract = {Many traits of evolutionary interest, when placed in their developmental, physiological, or environmental contexts, are function-valued. For instance, gene expression during development is typically a function of the age of an organism and physiological processes are often a function of environment. In comparative and experimental studies, a fundamental question is whether the function-valued trait of one group is different from another. To address this question, evolutionary biologists have several statistical methods available. These methods can be classified into one of two types: multivariate and functional. Multivariate methods, including univariate repeated-measures analysis of variance (ANOVA), treat each trait as a finite list of data. Functional methods, such as repeated-measures regression, view the data as a sample of points drawn from an underlying function. A key difference between multivariate and functional methods is that functional methods retain information about the ordering and spacing of a set of data values, information that is discarded by multivariate methods. In this study, we evaluated the importance of that discarded information in statistical analyses of function-valued traits. Our results indicate that functional methods tend to have substantially greater statistical power than multivariate approaches to detect differences in a function-valued trait between groups.},
	keywords = {Functional data analysis, multivariate analysis, phenotype, power, repeated-measures ANOVA, repeated-measures regression},
	issn = {0014-3820},
	doi = {10.1111/j.1558-5646.2008.00340.x},
	author = {Griswold, Cortland K. and Gomulkiewicz, Richard and Heckman, Nancy}
}
@article { ISI:000252359600010,
	title = {On tests for multivariate normality and associated simulation studies},
	journal = {JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION},
	volume = {77},
	number = {11-12},
	year = {2007},
	month = {NOV-DEC},
	pages = {1053-1068},
	publisher = {TAYLOR \& FRANCIS LTD},
	type = {Article},
	address = {4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND},
	abstract = {We study the empirical size and power of some recently proposed tests for multivariate normality (MVN) and compare them with the existing proposals that performed best in previously published studies. We show that the Royston{\textquoteright}s [Royston, J.P., 1983b, Some techniques for assessing multivariate normality based on the Shapiro-Wilk W. Applied Statistics, 32,121-133.] extension to the Shapiro and Wilk [Shapiro, S.S. and Wilk, M.B., 1965, An analysis of variance test for normality (complete samples). Biometrika, 52, 591-611.] test is unable to achieve the nominal significance level, and consider a subsequent extension proposed by Royston [Royston, J.P., 1992, Approximating the Shapiro-Wilk W-Test for non-normality. Statistics and Computing, 2, 117-119.] to correct this problem, which earlier studies appear to have ignored. A consistent and invariant test proposed by Henze and Zirkler [Henze, N. and Zirkler, B., 1990, A class of invariant consistent tests for multivariate normality. Communications in Statistics- Theory and Methods, 19, 3595-3617.] is found to have good power properties, particularly for sample sizes of 75 or more, while an approach suggested by Royston [Royston, J.P, 1992, Approximating the Shapiro-Wilk W-Test for non-normality. Statistics and Computing, 2, 117-119.] performs effectively at detecting departures from MVN for smaller sample sizes. We also compare our results to those of previous simulation studies, and discuss the challenges associated with generating multivariate data for such investigations.},
	keywords = {consistent tests, goodness-of-fit, invariant test, multivariate normality, power, size},
	issn = {0094-9655},
	doi = {10.1080/10629360600878449},
	author = {Farrell, Patrick J. and Salibian-Barrera, Mat{\'\i}as and Naczk, Katarzyna}
}
@article {perlman_emperors_1999,
	title = {The Emperor{\textquoteright}s new tests},
	journal = {Statistical Science},
	volume = {14},
	number = {4},
	year = {1999},
	month = {nov},
	pages = {355{\textendash}369},
	abstract = {In the past two decades, striking examples of allegedly inferior likelihood ratio tests (LRT) have appeared in the statistical literature. These examples, which arise in multiparameter hypothesis testing problems, have several common features. In each case the null hypothesis is composite, the size LRT is not similar and hence biased, and competing size tests can be constructed that are less biased, or even unbiased, and that dominate the LRT in the sense of being everywhere more powerful. It is therefore asserted that in these examples and, by implication, many other testing problems, the LR criterion produces {\textquoteleft}{\textquoteleft}inferior,{\textquoteright}{\textquoteright} {\textquoteleft}{\textquoteleft}deficient,{\textquoteright}{\textquoteright} {\textquoteleft}{\textquoteleft} undesirable,{\textquoteright}{\textquoteright} or {\textquoteleft}{\textquoteleft}flawed{\textquoteright}{\textquoteright} statistical procedures. This message, which appears to be proliferating, is wrong. In each example it is the allegedly superior test that is flawed, not the LRT. At worst, the {\textquoteleft}{\textquoteleft}superior{\textquoteright}{\textquoteright} tests provide unwarranted and inappropriate inferences and have been deemed scientifically unacceptable by applied statisticians. This reinforces the well-documented but oft-neglected fact that the Neyman-Pearson theory desideratum of a more or most powerful size test may be scientifically inappropriate; the same is true for the criteria of unbiasedness and -admissibility. Although the LR criterion is not infallible, we believe that it remains a generally reasonable first option for non-Bayesian parametric hypothesis-testing problems.},
	keywords = {a-admissibility, bioequivalence problem, d-admissibility, Fisher-Neyman debate, Hypothesis test, likelihood ratio test, multiple endpoints in clinical trials, multivariate one-sided alternatives, order-restricted hypotheses, power, significance test, size test, test for qualitative interactions, unbiased test},
	issn = {0883-4237, 2168-8745},
	doi = {10.1214/ss/1009212517},
	url = {http://projecteuclid.org/euclid.ss/1009212517},
	author = {Perlman, Michael D. and WU, LANG}
}
