Identifying and removing spatial correlation from yield experiments

In classical statistics, the effect of soil trends is compensated for by replication and randomization of treatments. Two field experiments were conducted at sites with significant soil trends to evaluate the use of semivariograms for identifying spatial correlation in plot yield, and evaluate the ability of nearest-neighbor analysis (NNA) in removing trend. The first experiment involved a P-fertilizer trial with winter wheat (Triticum destivum L.) on an eroded hillslope in eastern Washington. The second experiment involved a N- and P-fertilizer trial with cotton (Gossypium hirsutum L.) in Dera Ismail Khan, Pakistan. One of the difficulties in using semivariograms of plot-yield data to evaluate spatial correlation in experimental errors is that yield is affected by the presence of trends as well as by the pattern in treatment randomization and replication. To remove the influence of treatment randomization, the measured mean for each treatment was subtracted from the measured yield for that treatment in each plot. Semivariograms of these deviations in yield relative to the treatment mean showed significant structure for both experiments, indicating spatial correlation between plots resulting from soil trends. We used NNA to adjust measured plot yields for the effects of spatial correlation. Semivariograms of yield deviations after this adjustment exhibited no spatial structure, indicating removal of spatial correlation between plots. Analysis of variance (ANOVA) on measured yields before adjustment by NNA in both experiments showed nonsignificant treatment effects, while block effects were highly significant.