Hypothesis testing in comparative and experimental studies of function-valued traits

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Hypothesis testing in comparative and experimental studies of function-valued traits

TitleHypothesis testing in comparative and experimental studies of function-valued traits
Publication TypeJournal Article
Year of Publication2008
AuthorsGriswold, CK, Gomulkiewicz, R, Heckman, N
Date PublishedMAY
Type of ArticleArticle
KeywordsFunctional data analysis, multivariate analysis, phenotype, power, repeated-measures ANOVA, repeated-measures regression
AbstractMany 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.