Heterogeneity, plot shape effect and optimum plot size

Abstract

By introducing heterogeneity indices, an empirical equation is proposed for characterizing the heterogeneity of non-isotropic fields. The formula is an extension of Fairfield Smith's (1938) empirical law describing heterogeneity in isotropic fields. Based on these indices, criteria are provided for choosing optimum plot shapes in terms of minimizing the sample variance and cost. Sample plots having their largest dimension in the direction with the largest index will give more accurate results (less variable) than plots with other shapes. Relations between the optimum plot size and relative cost versus variogram parameters are given for several variogram models. These relations indicate that variograms with small effective ranges have a very profound effect on the optimum plot sizes.

Tamanho de parcelas em experimentos com trigo irrigado sob plantio direto e convencional

“…Resultados semelhantes foram obtidos por Vallejo & Mendoza (1992), Zhang et al (1994), Ortiz (1995) e Viana et al (2002).…”

“…Diversos autores têm ressaltado a influência do tamanho das parcelas na precisão dos experimentos (Hatheway, 1961;Le Clerg, 1967;Steel et al, 1997), mostrando a existência de relação inversa entre o tamanho da parcela e o erro experimental (Vallejo & Mendoza, 1992;Zhang et al, 1994;Ortiz, 1995).…”

Effects of inter-varietal diversity, biotic stresses and environmental productivity on grain yield of spring barley variety mixtures

“…Last, the observed disease levels may have been biased by interplot interference, a well-studied phenomenon in which neighbouring plots as well as whole-trial plot diversity affect the spread of disease. Interplot interference is generally higher with smaller plots (Zhang et al 1994;de Oliveira et al 2005), potentially making the results from field trials less representative of largescale farming situations. In a field trial study of leaf rust resistance in barley varieties, Parlevliet and van Ommeren (1984) found the resistance of susceptible varieties to be generally overestimated and the resistance of partially resistant varieties to be greatly underestimated.…”

Minimum number of common bean plants per plot to assess field resistance to white mold

“…Additionally, the plot size is directly related to the cost of conducting experiments and evaluations; the optimal plot size is determined by the balance between cost and accuracy (Zhang et al 1994, Storck et al 2006 (Zanon and Storck 2000). The different methods are based on the observed relationship between plot size and residual variation, and differ in many aspects; an increase in plot size reduces plot variation, however, this decrease is finite.…”