Spatial variation from soil and related factors o en a ects the outcome of agronomic eld experiments. e randomized complete block (RCB) is the most prevalent design despite ine ciencies that can result in in ated error terms. Experimental designs such as the Latin square (LS) allow for bidirectional blocking and o er the potential to account for spatial variability better. e objectives of this research were to investigate the occurrence of two-way gradients in agronomic eld trials and compare the estimated relative e ciency (ERE) of a LS to a RCB. irty LS trials were evaluated in 10 states during 2013 across the midwestern United States investigating crop yields of corn (Zea mays L.), soybean [Glycine max (L.) Merr.], and sorghum [Sorghum bicolor (L.) Moench]. e results show that 47% of the trials exhibited a two-way gradient, indicating this characteristic is widespread across a large geographic region. Overall, the ERE was increased in 70% of the trials by using the LS design. A lower ERE occurred in 7% of the trials conducted using a LS. Multiple gradients appear common in agronomic eld plot trials and enough variation existed between the two blocking directions to justify the use of a LS design. Our data indicate the LS o ers a low risk, high reward option of experimental design for controlling spatial heterogeneity and increasing precision. When possible, the LS design should be used in eld experiments where the trial area appears uniform and gradients to block against are not obvious.

Plot size has an important impact on variation among plots in agronomic field trials, but is rarely considered during the design process. Uniformity trials can inform a researcher about underlying variance, but are seldom used due to their laborious nature. The objective of this research was to describe variation in maize field trials among field plots of varying size and develop a tool to optimize field-trial design using uniformity-trial statistics. Six uniformity trials were conducted in 2015–2016 in conjunction with Iowa State University and WinField United. All six uniformity trials exhibited a negative asymptotic relationship between variance and plot size. Variance per unit area was reduced over 50% with plots 41.8 m2 in size and over 75% when using a plot size >111.5 m2 compared to a 13.9 m2 plot. Plot shape within a fixed plot size did not influence variance. The data illustrated fewer replicates were needed as plot size increased, since larger plots reduced variability. Use of a Shiny web application is demonstrated that allows a researcher to upload a yield map and consider uniformity-trial statistics to inform plot size and replicate decisions.