Sample size for estimation of direct effects in path analysis of corn.
The objective of this study was to assess the sample size required for estimating the direct effects of explanatory variables on the grain yield of corn in the combinations formed by three types of hybrids x two harvests x nine scenarios of explanatory variables x two types of path analyses x four levels of accuracy. A total of 6340 plants were evaluated (361, 373, and 416 plants from single-, triple-, and double-cross hybrids in the 2008/2009 harvest, respectively, and 1777, 1693, and 1720 plants from single-, triple-, and double-cross hybrids in the 2009/2010 harvest, respectively). Eleven explanatory variables were measured in each plant: plant height, ear insertion height, ear weight, number of grain rows per ear, ear length and diameter, cob weight and diameter, 100-grain mass, number of grains per ear, grain length and, the main variable, grain yield. Thus, nine scenarios were planned (scenarios 1, 2, 3, 4, 5, 6, 7, 8, and 9 with 0, 1, 2, 3, 4, 5, 6, 7, and 8 explanatory variables excluded, respectively) and two types of path analyses conducted (traditional and ridge path analyses). The sample size required for estimating the direct effect of each explanatory variable on grain yield was assessed using resampling with replacement at four accuracy levels [95% confidence interval ranges (95%CI) of 0.15, 0.25, 0.35, and 0.45]. The use of the ninth scenario of path analysis is recommended regardless of hybrid and harvest given the smaller sample size required compared to the previous scenarios. To estimate direct effects with the maximum 95%CI of 0.25, 10 to 530 plants are required depending on the type of hybrid, harvest, scenario, type of path analyses, and explanatory variables. To estimate the direct effects in the ninth scenario with a maximum 95%CI of 0.25, 120 plants suffice regardless of the type of hybrid, harvest, or type of path analyses.