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