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Central Appalachian Hill Land Pasture Evaluation Using Cows and Calves. I. Ordinary and Generalized Least Squares Analysis for an Unbalanced Grazing Experiment¹

In formal grazing trials, especially those involving cow-calf test units, the land area needed and cost of initiation and operation limit the number of treatments simultaneously evaluated. Often it is desirable to terminate and add a new treatment or simply add a new treatment during the trial. The analysis of the resulting unbalanced data poses several difficulties. The objective of this paper was to evaluate a two-step statistical procedure to analyze cow-calf responses from an unbalanced grazing trial. Per animal and per hectare responses and pasture characteristics were obtained from a 6-year study conducted in the Appalachian hill land region. Soils ranged from a Typic Hapludult to a mixed, mesic Hapludult. Pastures were a mixture of Kentucky bluegrass (Poa pratensis L.), white clover (Trifolium repens L.), and orchardgrass (Ductylis glomerata L.) and 12 agronomic or animal management treatments were evaluated. Some of the original treatments were deleted and new ones added, but not always on fields already in the study or in equal replication. The full 6-year unbalanced data set contained two balanced subsets used to evaluate results from the two-step analysis. The statistical procedure involved a fist step of estimating variance components for year and field effects. These were applied in a second step as a weighted adjustment through a generalized least squares analysis. The variance components, treatment mean adjustments and associated standard deviations from the two-step analyses were compared with ordinary least squares (OLS) analyses where years were fixed effects and fields ignored (OLS₁) or year and field effects were both ignored (OLS₂). Year and field variances for cow and calf daily gains, pasture productivity estimates and pasture measurements from the 6-year unbalanced data had similar magnitude and structure from the two-step procedure compared with the two balanced data subsets. The residual error from OLS₁ and 0LS₂ compared with the twostep analysis were consistently larger. The two-step analysis (unbalanced data) gave biologically rational adjustments of treatment means and offers much potential for use in experiments requiring high resources and where unbalance is likely for maximum treatment evaluation.

Key Words: Daily gain • Pasture productivity • Pasture measurements • Year and field variance components • Error structure • Adjusted treatment means

² Plant physiologst, USDA ARS and professor of crop science; professor of statistics; professor of animal science, and associate professor of statistics, North Carolina State Univ., Raleigh, NC 27650.

Received for publication October 6, 1982.