Analysis of Sequential Observations with Applications to Experiments on Grazing Animals and Perennial Plants

Experiments on grazing animals and perennisl plants typically yield long sequences of observations on each experimental unit or plot. These data have usually been analysed by a splitplot 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 analysing their coefficients separately in a series of ANOVAs (Rowell and Walters 1976). Since agricultural data are rarely homogeneous and the number of times generally exceeds the error degrees offreedom theirst two methods can rarely be used. The third method has nor been widely accepted by agricultural scientists probably because high-order coefticients are difticult to interpret. But this paper illustrates that only low-order polynomial coefficients may be needed to fiit diffierences between sequences defined by treatment contrasts, and emphasizes that these coefticients need to be analysed together by MANOVA (Grizzle and Allen 1969) as they are correlated between experimental units. This apparently complicated procedure can be simpliCfied 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 as well as to the familiar growth curves.