Repeated Measures in Randomized Block and Split Plot Experiments

Randomized block and split plot designs are among the most commonly used experimental designs in forest research. Measurements for plots in a block (or subplots in a whole plot) are correlated with each other, and these correlations must be taken into account when analyzing repeated measures data from blocked designs. The analysis is similar to repeated measures analysis for a completely randomized design, but test statistics must allow for random block x time effects, and standard errors for treatment means must also incorporate block-t<rblock variation and block x treatment interactions as well as variation among plots within a block. Two types of statistical analysis are often recommended for repeated measures data: analysis of contrasts of the repeated factor, and multivariate analysis of variance. A complete analysis of repeated measures should usually contain both of these components, just as in univariate analysis of variance it is often necessary to decompose the main effects into single degree of freedom contrasts to answer the research objectives. We demonstrate the multivariate analysis of variance and the analysis of contrasts in detail for two experiments. In addition, estimation of coefficients assuming a polynomial growth curve is discussed in detail for one of these experiments. The first experiment, a randomized complete block design, is a forest nutrition study of the long term effects of mid-rotation nitrogen and phosphorus fertilization on loblolly pine (Pinus taeda L.), and the second, a split plot design, is an air pollution study of the effects of ozone and acid precipitation on loblolly pine growth.