Block Size and Orientation, and Allowance for Positional Effects, in Field Experiments

Warren, James A.; Méndez, Ignacio

doi:10.1017/s0014479700011182

Cited by 8 publications

(7 citation statements)

References 7 publications

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“…Variance inflation for blocks with 35 to 42 plots was more than 2X than of blocks of five to seven plots in 27% of these trials, but less than 1.2X in 41%. A similar pattern in sensitivity to block size and other influences was observed by Warren and Mendez (1981) in a study of 13 uniformity trials. In three trials classified as highly sensitive to choice of blocks, there were few choices that did not inflate variances seri-ou~ly relative to blocks of two plots each.…”

supporting

confidence: 80%

“…Both numerical and visual methods have been proposed for this diagnostic purpose. Warren and Mendez (1981) proposed that computer based analyses of block designs supply both the customary experimental error variance and an estimate of background variation suitable for diagnostic purposes. Corrective analyses would be undertaken when the customary experimental error showed unacceptably high inflation.…”

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confidence: 99%

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Methods for Estimating Background Variation in Field Experiments¹

Warren¹,

Méndez

1982

Agronomy Journal

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A widely useful method for estimating background variation in field experiments would provide experimenters with a diagnostic tool that could be used to reveal trials for which customary design‐based analyses are inadequate. Such a diagnostic tool would provide reassurance for cases suited for customary analyses and would signal a need for corrective analyses when plot to plot variation has not been properly accounted for. This paper is an early step in the search for such a widely useful diagnostic tool. It examines the performance of a number of methods that have been proposed for describing plot to plot variation and explores the effectiveness of these methods over widely different data sets from uniformity trials. Methods were assessed primarily on the basis of consistency of providing residual mean squares usable as a diagnostic measure of background variation. In addition, methods were compared in terms of how well they described plot to plot variation (R2 for estimated and observed responses). Results obtained made it clear that the suitability of a method forestimating background variation must be evaluated over a number of different trials, including trials sensitive to block size and orientation. Most methods performed well in at least one or two trials. Few were generally effective. Preliminary indications were that the Best Blocks of Two Method was most generally useful and that Polynomial Regressions and the Modified Papadakis method were promising. The versions used of the following methods were not consistently effective in estimating background variation: Rows and Columns, Ordinary Papadakis, Fourier Analysis and Inverse Polynomial.

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Methods for Estimating Background Variation in Field Experiments¹

Warren¹,

Méndez

1982

Agronomy Journal

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“…For decades, blocks have been widely used as an efficient tool for local control and to reduce experimental error (Cochran and Cox, 1957; Casler, 2015). Blocking effectiveness depends on block size (i.e., number of plots per replication), shape, and orientation (Warren and Mendez, 1981). In particular, randomized complete block designs (RCBDs) are the most commonly used experiments in agriculture, especially those with a small number of treatments (Piepho et al, 2015).…”

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confidence: 99%

Mega‐Environmental Design: Using Genotype × Environment Interaction to Optimize Resources for Cultivar Testing

2019

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The efficient use of testing resources is one of the key factors for successful plant breeding programs. Controlling micro‐ and macro‐environmental variability is an effective way of improving the testing efficiency and the selection of superior genotypes. Common experimental designs in genotypic testing usually use replicated or augmented experiments at each location, but they are balanced across locations. Some studies suggest that the increase in population size even at the expense of balanced experiments might be beneficial if genotype × environment interaction (GEI) is modeled. The objective of this study was to compare strategies for micro and macro‐environmental variability control that include GEI information to optimize resource allocation in multi‐environment trials (METs). Six experimental designs combined with four spatial correction models were compared for efficiency under three experimental sizes using simulations under a real yield variability map. Additionally, six resource allocation strategies were evaluated in terms of accuracy and the expected response to selection. The α‐lattice (ALPHA) experimental design was the best one at controlling micro‐environmental variability. The moderate mega‐environmental design (MED) strategy had the largest response to selection. This strategy uses historical mega‐environments (MEs) to unbalance genotypic testing within MEs while modeling GEI. The MED was the best resource allocation strategy and could potentially increase selection response up to 43% in breeding programs when genotypes are evaluated in METs.

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“…Larger blocks, in complete or incomplete block designs, tend to contain groups of units that are more heterogeneous than small blocks (Briggs and Shebeski, 1968;Lin and Binns, 1984). The sensitivity of a field experiment to changes in block size is extremely variable (Warren and Mendez, 1981), suggesting that conclusions from a uniformity experiment may apply strictly to the particular crop-site combination on which the experiment was based (Wuest et al, 1994). Warren and Mendez Abbreviations: IVDMD, in vitro dry matter digestibility; N, number of plots per strip; NDF, neutral-detergent fiber; P, plot size; RIS, Replicates within Sets design; S, number of strips; S/ R, Sets within Replicates design; Vw, pooled variance within incomplete blocks.…”

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Experimental Design Factors Affecting Error Variation in Orchardgrass

Casler

Tageldin²

1996

Agronomy Journal

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Several experimental design factors over which the researcher has control may affect the precision of field experiments. The objective of this experiment was to identify the effects of changing plot size, incomplete block size, and incomplete block shape on precision of forage yield and quality estimates in orchardgrass (Dactylis glomerata L.). Orchardgrass seed was planted uniformly into 288 plots of various sizes. Forage yield, in vitro dry matter digestibility (IVDMD), and neutral‐detergent fiber (NDF) were determined over a 2‐yr period. Error variances (Vw) were computed for variously sized incomplete blocks (in one or three strips and from 1 to 12 plots strip−1) within each plot size and expressed as log(Vw). Values of log(Vw) for IVDMD and NDF concentration were unaffected by experimental design factors. Values of log(Vw) for forage yield increased with increasing number of plots per strip, but these effects varied among plot sizes and for one‐ vs. three‐strip blocks. Three‐strip blocks had a mean log(Vw) 71% greater than one‐strip blocks, an effect that could be offset only by doubling the number of replicates in a field test. To obtain maximum precision in cases where a large number of replicates impossible or impractical, orchardgrass field experiments should employ incomplete block designs, particularly when limited seed stocks or land requires a plot size near 1.4 m2. Incomplete block designs with this plot size should not contain multiple strips within incomplete blocks.

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Block Size and Orientation, and Allowance for Positional Effects, in Field Experiments

Cited by 8 publications

References 7 publications

Methods for Estimating Background Variation in Field Experiments¹

Methods for Estimating Background Variation in Field Experiments¹

Mega‐Environmental Design: Using Genotype × Environment Interaction to Optimize Resources for Cultivar Testing

Experimental Design Factors Affecting Error Variation in Orchardgrass

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Block Size and Orientation, and Allowance for Positional Effects, in Field Experiments

Cited by 8 publications

References 7 publications

Methods for Estimating Background Variation in Field Experiments1

Methods for Estimating Background Variation in Field Experiments1

Mega‐Environmental Design: Using Genotype × Environment Interaction to Optimize Resources for Cultivar Testing

Experimental Design Factors Affecting Error Variation in Orchardgrass

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Product

Resources

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Methods for Estimating Background Variation in Field Experiments¹

Methods for Estimating Background Variation in Field Experiments¹