Multivariate Analysis as a Means of Comparing Growth in Fish

Abstract

The Hotelling's T² is described as a test for differences between like von Bertalanffy growth parameters estimated from two fish groups when these parameters are correlated. Equations to calculate T² are presented as are equations to modify T² to an F statistic for use in testing. Simultaneous confidence intervals and critical F values are described to separate effects of parameters on observed differences in growth. Assumptions made by the T² technique are discussed, as are ways in which any bias caused by violating these assumptions is lessened. Two numerical examples concerning growth differences among groups of Pacific ocean perch (Sebastes alutus) are provided. Growth of male and of female perch captured off the Columbia River is different with L_∞ being the most statistically significant parameter and t₀ the least. Growth of male perch captured off Vancouver Island and off the Columbia River is also different with only L_∞ statistically significant.Key words: Hotelling's T², multivariate statistics, Pacific ocean perch, von Bertalanffy, growth