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STATISTICS

Validity and Efficiency of Neighbor Analyses in Comparison with Classical Complete and Incomplete Block Analyses of Field Experiments

^a Nanjing Agricultural University, Nanjing, China
^b Dep. of Plant Science, McGill University, Macdonald Campus, 21,111 Lakeshore Rd., Ste-Anne-de-Bellevue, QC, Canada H9X 3V9

cydp{at}musica.mcgill.ca

Received for publication May 21, 1997. In classical block analysis, the assumption of independence between observations from neighboring plots within a block is violated when spatial autocorrelation is present, resulting in incorrect treatment effect estimates and an inflated error variance estimate. Before recommending any neighbor analysis designed to account for spatial autocorrelation, its validity in estimation and testing and its efficiency must be examined. Our main objective was to assess the validity and efficiency of five neighbor analyses in comparison with complete and incomplete block analyses, using 50 pseudo-experiments for each of 50 data sets derived from two uniformity trials for soybean and wheat. The neighbor models were first difference with (FD-EV) or without (FD) errors in variables, second difference with (SD-EV) or without (SD) errors in variables, and first-order autoregressive errors. Geostatistical analysis based on the normalized semivariance detected spatially structured variation at different degrees in the data sets. The first and second differences were effective in removing spatial trends and autocorrelation. Our simulation study showed that FD-EV provided valid estimates of the error variance in all and SD-EV in most of the data sets. On average, the observed significance level was slightly beyond the theoretical level for both analyses. The other neighbor analyses underestimated the error variance. Excluding SD, neighbor analyses had similar efficiency and were more efficient than complete and incomplete block analyses, with average relative efficiencies of about 300 and 130%, respectively. Relative efficiency tended to increase with decreasing normalized nugget effect (NC₀) and increasing CV. When spatially structured variation is strong (i.e., NC₀ < 10%), highly rectangular plots must be preferred to nearly square plots in incomplete block and neighbor analyses. Considering validity and efficiency, the best method was FD-EV, which is thus a reliable alternative to classical block analysis when spatial autocorrelation is present.

Abbreviations: CB, complete block • FD, first difference • FD-EV, first difference with errors in variables • Emp, average empirical variance • GLS, generalized least squares • IB, incomplete block • Pre, average predicted variance • RCB, randomized complete block • REML, restricted maximum likelihood • SD, second difference • SD-EV, second difference with errors in variables

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