ANALYSIS OF SEQUENTIAL OBSERVATIONS WITH APPLICATIONS TO EXPERIMENTS ON GRAZING ANIMALS AND PERENNIAL PLANTS

Experiments on grazing animals and perennial plants typically yield long sequences of observations on each experimental unit or plot. These data have usually been analyzed by a split-plot in time ANOVA, or by a repeated-measurements MANOVA when the variances or covariances are heterogeneous between times, or by fitting polynomial equations to the sequences and analyzing their coefficients separately in a series of ANOVA. Since agricultural data are rarely homogeneous and the number of times generally exceeds the error degrees of freedom the first 2 methods can rarely be used. The 3rd method has not been widely accepted by agricultural scientists probably because high-order coefficients are difficult to interpret. Only low-order polynomial coefficients may be needed to fit differences between sequences defined by treatment contrasts. These coefficients may need to be analyzed together by MANOVA as they are correlated between experimental units. This apparently complicated procedure can be simplified greatly in practice and the sequential variation in treatment contrasts readily graphed and interpreted. Data from a grazing trial are treated by these methods to illustrate their applicability to periodic sequences and to the familiar growth curves.