Design of agronomic experiments for plots differentiated in fertility by past treatments
With the increase in agricultural field trials in recent years, the question of the use of former sites of concluded experiments is becoming of ever increasing importance. It was the aim of the present study to define the possible methods by which areas which have been differentially treated in past experiments may be effectively utilized in new experiments and to determine the efficiency of the various methods.
Methods of design were tested using the yields from a field which formed a portion of a rotation and fertilizer experiment conducted at the Iowa Agricultural Experiment Station since 1915.
The possible methods of design were grouped under two heads: (a) Those in which all the treatments in the new experiment could be planted on each of the original plots; and (b) those in which the block of the new experiment comprised a number of the original plots.
Reduction of the error was attempted in two ways: (a) By the grouping together of plots from different parts of the field on the basis of equal fertility (as indicated by the previous yield) to form the block of the new trial; and (b) by the application of a covariance treatment to blocks formed by the grouping of adjacent plots, using the results of the original trial as concomitant information.
The efficiency of the various methods in reducing the error variance was evaluated. It was shown that on the average equal fertility grouping was little better than adjacent plot grouping. The use of covariance on the adjacent plot grouping on the basis of one year's previous yield was twice as efficient as adjacent plot grouping alone. Multiple covariance on the basis of 2 previous years' results was over three times as efficient in reducing the error variance. The relationship of these methods to the variable influences affecting the yield from year to year and the manner in which each did or did not utilize the available information are discussed.
It was concluded that the most satisfactory method of design was to ignore the previous treatments and to form the blocks from adjacent plots in the normal manner. When the results come to hand at the end of the season the covariance adjustment should be used, supplying its own test as to its efficiency in reducing the error variance.
An experiment designed so that each treatment was represented on each of the original plots was superimposed on the fertilizer trial during 1936. Three top-cross varieties of corn were tested at two rates of planting (three and four plants per hill) each of these six possible treatments being tested with normal planting as against spaced planting.
The yields showed: (a) that the variety, Inbred 75 on Krug, gave the highest yields; (b) that under the dry seasonal conditions of 1936, the lower rate of planting gave the higher yield and (c) that spaced planting gave only .7 of a bushel per acre greater yield than normal planting. The error variances, both in this trial and in the case where covariance adjustments were applied to adjacent plot grouping, were comparable with the errors obtained from experiments placed on normal uniform sites, and very small differences between treatments were shown to be significant.
It was shown that in certain of the suggested designs it is impossible to separate the interaction of the new treatments with the differential fertility of the original plots from the error variance and therefore such interactions may play an important part in increasing the error. In cases such as the one studied, where a variety trial was superimposed on a fertilizer trial, it is evident that this interaction, though significant, will not increase the error variance unduly.
It may frequently be desirable to continue the original fertilizer trial because of its "permanent" nature. The bearing of the various designs on this matter is discussed and it is shown that with certain designs, the validity of the comparison of the total yields of the original plots is not disturbed by the new treatments.