• Asymptotic test;
  • Chi square distribution;
  • Eigenvector;
  • Mixture distribution;
  • Principal component

Summary. Constants of allometric growth are commonly estimated by the first eigenvector of the covariance matrix of log measurements. Hills (1982, in Encyclopedia of Statistical Sciences, 48–54) defines a model of allometric extension for two related species by the conditions that (a) the constants of allometric growth are identical for both species and (b) the vector of mean differences is proportional to the common first eigenvector of both covariance matrices. We give a test for allometric extension and discuss estimation of the parameters of the allometric extension model, including standard errors.