Numerical comparison of some test procedures for determining model adequacy when fitting polynomial equations to sequences of observations

Abstract

A number of procedures for testing adequacy of polynomial approximations to growth curves based on Rao’s test for additional information, Grizzle and Allen’s test or univariate t-tests were compared using data simulated from quadratic models. Quadratic models were indicated as adequately fitting the data in 95.10± 0.10 percent of analyses when the degree of the approximating polynomial was determined by the lowest-order significant coefficient (P = 0.05) that was followed by two successive nonsignificant ones according to separate t-tests. Procedures based on the Grizzle and Allen test and modifications of it indicated quadratic models in 86.70 ± 0.41 to 95.34 ±0.21 percent of analyses depending on error structure, variance and the number of coefficients analysed together. The t-test would be preferred in practice as its performance did not depend on the error structure or variance.