A monte carlo study of alternative procedures for testing the hypothesis of parallelism for complete and incomplete growth curve data

Abstract

Data collected over time on the same experimental unit, frequently called growth curve data, is typical of many clinical, biological, medical and agricultural studies. Such data is usually highly correlated and may be difficult to analyze if there are missing observations. Monte Carlo simulations using a broad spectrum of dispersion structures are used to compare for significance level and power of various procedures for testing the parallelism of the response curves for both complete and incomplete growth curve data. The various analysis methods used are (1) the split-plot; (2) Hotelling's T-square; (3) analysis of the estimated regression coefficients for each experimental unit by Hotelling's T-square; (4) successive differences; and (5) estimation of missing data then using the procedures 1 through 4; and (6), adjusting these procedures using the Geisser-Greenhouse correction as appropriate. Of these methods, for complete data the split-plot analysis using the Geisser-Greenhouse correction was most satisfactory with four multivariate but with eight multivariate responses, Hotelling's T-square on the estimated regression coefficients for each subject was best. For incomplete data the split-plot analysis using the Geisser-Greenhouse correction from the smoothed dispersion matrix was most satisfactory.