Increasing Precision in Agronomic Field Trials Using Latin Square Designs

Abstract

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.

Beyond Latin Squares: A Brief Tour of Row‐Column Designs

“…In our experience, as well as that of other researchers (Williams, 1986; Kempton et al, 1994; Gilmour et al, 1997; Piepho and Williams, 2010; Bailey, 2012; Casler, 2015; Jones et al, 2015), the trial history of an experimental field, as well as the various operations necessary for the conduct of a planned experiment (i.e., plowing, seeding, fertilization, spraying, harvesting, etc.) typically are such that major heterogeneity can be expected both between columns and between rows.…”

“…Designs with one‐way blocking are still dominant in agricultural field experiments (Jones et al, 2015). The reasons for this dominance are manifold, including the better familiarity of many researchers with simple designs such as the RCBD, the emphasis of such designs in textbooks and courses on experimental design, and the flexibility in the placement of blocks in the field layout.…”

“…In a recent study, Jones et al (2015) reported on 30 field trials with soybean [ Glycine max (L.) Merr.] laid out according to Latin square designs with six treatments.…”

“…The use of Latin squares in practice is somewhat limited by the fact that the number of replications, the number of rows, the number of columns, and the number of treatments must all be equal (Casler, 2015; Jones et al, 2015). More flexibility can be introduced by allowing rows and/or columns to form incomplete blocks.…”

Automating Uniformity Trials to Optimize Precision of Agronomic Field Trials

“…Multistate field trials on corn (Zea mays L.), soybean (Glycine max (L.) Merr. ), and sorghum [Sorghum bicolor (L.) Moench] showed that multiple gradients were prevalent in field trials [25]. Plots squarer in shape provided a safeguard to the experimenter if the presence and direction of gradients was not known.…”