Assessing sample size and variable number in multivariate data, with specific reference to cone morphology variation in a population of Picea sitchensis

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Abstract
A multivariate extension of univariate sample size estimation is outlined that enables one to determine sample size for a multivariate study. The procedure is presented and illustrated by application to intraindividual and interindividual variation of cone morphology in a population of Picea sitchensis (Bong.) Carr. The method involves the stabilization of a scalar estimate of the structure of the correlation matrix (the determinant) among variables for a given sample size. The sample-specific dependency of previously described methods is avoided by random selection of several replicates in nonstructured and structured (nested) models. The procedure is best applied in pilot studies where it can aid in the characterization of multivariate data prior to analysis. Additionally, repeatability estimates for cone scale morphology are presented.