Error Mean Squares of Protein Yield of Alfalfa‐Grass Mixtures Computed by Five Methods 1

The purpose of this statistical study was to compare the error mean squares of herbage protein yields per hectare computed in five different ways. Herbage yield and protein percentage data were obtained from an alfalfa ( Medicago sativa L.)‐grass mixture trial conducted at Arlington, Wisconsin. These comparisons were made to determine the precision of protein analyses made on herbage from a limited number of replications with that based on all four replications. Method A, using protein percentages and herbage yields from all plots of four replications, gave an unbiased estimate of experimental error for protein yields per hectare. Protein yield by method B was computed from the weighted average percentage protein of replicates 1 and 2 and of 3 and 4, and the herbage yields from all plots of replicates 1 and 2 and of 3 and 4, respectively. Protein yield by method C was computed by using the protein percentages and herbage yields of replicates 1 and 3 and the weighted average protein percentage of replicates 1 and 3 for all plots of replications 2 and 4. Methods B and C were biased and underestimated the experimental error of method A, but the underestimation was small. Protein yield by method D was computed from the weighted average percentage protein and herbage yields of replicates 1 and 2 and of replicates 3 and 4. By method E, protein yield was computed for each plot in replications 1 and 3 as described for method A. These two methods have only one‐third as many degrees of freedom to estimate experimental error as the other methods in the four‐replication experiment. As compared with method A, methods D and E have a larger standard error of the mean.