Estimating Spatial Variation in Analysis of Data from Yield Trials: A Comparison of Methods

Abstract

In large yield trials, variation in soil fertility (or, more generally, yield potential) can result in substantial heterogeneity within blocks and, thus, poor precision in treatment estimates. Precision may be improved using statistical analyses in which this spatial variation is accounted for in estimation of treatment or entry means. Three such types of spatial analysis are trend analysis, the Papadakis method, and analyses based on correlated errors models (which account for spatial variation through correlations between yields of neighboring plots). We reviewed the theory and empirical performance of these spatial analyses and compared them with the classical analyses. The classical analyses can be justified solely on the basis of randomization; spatial analyses depend on the model specified for the variation in yield potential. Performance depends on the polynomial used to describe yield potential in trend analysis, on the neighboring plots used to estimate fertility in the Papadakis analysis, and on the correlation structure in the correlated errors models. Empirical comparisons were based on data from 11 corn (Zea mays L.) yield trials and 1 soybean (Glycine max L.) trial, each showing evidence of heterogeneity within blocks. In comparison with the classical randomized blocks analysis, precision tended to be best for the trend and the trend plus correlated errors analyses, with the Papadakis method intermediate. Ranking of entries differed across analyses, because each analysis adjusts for spatial variation in a different way. Using a spatial analysis technique can improve precision, but selecting the most appropriate analysis for a given data set can be hard.

Alternativas experimentais na avaliação de famílias em programas de melhoramento genético do feijoeiro

“…Entre esses métodos, o de Papadakis (1937) e o de médias mó-veis (Townley-Smith & Hurd, 1973). Recentemente, em razão do interesse nesse tipo de análise, novas propostas surgiram (Bartlett, 1978;Wilkinson et al, 1983;Besag & Kempton, 1986;Samra et al, 1990;Vivaldi, 1990;Zimmerman & Harville, 1991;Ball et al, 1993;Brownie et al, 1993;Stroup et al, 1994;Helms et al, 1995;Anoshenko, 1996;Clarke & Baker, 1996). Em todos esses trabalhos foram evidenciadas as vantagens do uso da análise espacial.…”

Efficiency of an Incomplete Block Design Based on Geostatistics for Tillage Experiments

“…Agricultural and soil research usually involves 4 large plots or large numbers of treatments and, therefore, large blocks which are rarely uniform. In 5 such cases, soil heterogeneity can result in low efficiency of the randomized complete block design 6 due to a large error term (Mulla et al, 1990;Brownie et al, 1993). Likewise, when local 7 heterogeneity is spatially structured, randomization and replication alone do not ensure that all 8 treatment comparisons are made with equal precision (van Es and van Es, 1993).…”

“…Brownie et al 16 (1993) reviewed the properties, merits and drawbacks of both methods and described some 17 variations on each. Although improvement in precision has been reported when comparing these 18 methods with conventional designs (Samra et al, 1992;Brownie et al, 1993;Stroup et al, 1994), 19 they are not widely adopted. Another approach to increase precision is to reduce block size through 20 the use of incomplete block designs (Yates, 1936).…”

Statistical Challenges in Analyses of Chamber‐Based Soil CO 2 and N 2 O Emissions Data

“…Selection of best performing structure was conducted based on AIC values as above. As an additional criterion for assessing the efficiency of data analyses, we reported average standard errors for the differences of interest, that is, either differences between selected treatments within the same week or differences between different weeks of the same treatment (Zimmerman and Harville, 1991;Brownie et al, 1993).…”