Covariance Used to Analyze the Relation between Corn Yield and Acreage1

The relation between corn yield and the number of acres in corn on Iowa farms isa matter of considerable interest. If technical and economic conditions were uniform, the presumption wouldbe that corn acreage wouldvary with the productive capacity of the soil. The very existence of different type-of-farming areas in the state, however, indicates non-uniform conditions. The questions arise as to whether any relation of yield to corn acreage on individual farms exists within these type-of-farming areas, and if so, whether the relation is the same in one area as in another. Recent findings indieating that there is greater erosion on small farms lend additional interest to the inquiry.2 This problem was first attacked by Schultz using the technique of analysis of variance. At the time, however,he was handicapped by the fact that no method was available for handling disproportionate subclass numbers. He was compelled to make a random choiceof only part of the available data in order to keep his subclass numbers proportional. Later, Snedecor and Cox~ examined a similar set of data, using the newly developed techniques appropriate to disproportionate subclass numbers. The solution was still inconclusive because in dealing with disproportionate subclass numbers there must beset up somehypothesis about the population from which the sample is drawn. Usually, the exact form of the hypothesis is unessential, but in this ease the 'result obtained seemed to bea consequence of the hypothesis chosen. Meanwhile, the analysis of covariance as originally presented by Fisher has been expanded and perfected by him and his coworkers.li In its extended form, it lends itself admirably to the solution of the yield-acreage problem. In addition, further sur-