Repeated Measurement: Split-Plot Trend Analysis Versus Analysis of First Differences

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Abstract
For studies with repeated measurement of experimental units, ad hod claims (e.g., Box, 1950, Biometrics 6, 362-389) that analysis of increments of response is superior to trend analysis of the original data with a split-plot model are shown to be spurious. Reduction of interperiod correlation (by using first differences) does not necessarily eliminate problems with heterogeneity of the variance-covariance matrix over time. For the homogeneous condition, the expected variance of a simple trend contrast (between two treatments, for adjacent periods) is shown to be the same for either analysis, but the analysis of increments incurs a loss of degrees of freedom that can be critical in studies with few experimental units per treatment. An example from mammary physiology is given.

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