Search

The number of replications is assumed to interfere in the estimates of the path analysis coefficients. Thus, the objective of this work was to determine the sufficient number of replications for the path analysis of traits in maize cultivars. An experiment was conducted with 15 maize cultivars in a complete randomized block design with nine replications, and seven variables were measured. Then, 511 data files (matrices) formed by all combinations of the nine replications were organized, in groups of 1, 2, 3, 4, 5, 6, 7, 8 and 9 replications. In each matrix, containing the averages of 15 cultivars for the seven variables, Pearson's linear correlation coefficients were estimated, the multicollinearity diagnostics and path analysis were performed and dispersion diagrams were constructed. The sufficient number of replications for the path analysis was determined from the parameter estimates of the quadratic response plateau model. With the replications number increases, the accuracy of the path analysis coefficient estimates improves, but the gains in accuracy gradually decrease. Six replications are sufficient to perform the path analysis of agronomic traits of maize cultivars and can be used as a reference for designing future experiments.

The objectives of this work were to determine the sample size (number of plants) necessary to estimate the indicators of the of multicollinearity degree - condition number (CN), determinant of the correlation matrix (DET), and variance inflation factor (VIF) - in productive traits of rye and to verify the variability of the sample size between the indicators. Five and three uniformity trials were conducted with the cultivars BRS Progresso and Temprano, respectively, and seven productive traits were evaluated in 780 plants. Twenty-one cases were obtained from seven traits, combined five to five. In each case, 197 sample sizes were planned (20, 25, 30, ..., 1,000 plants) and in each size 2,000 resampling were performed, with replacement. For each resample the CN, DET and FIV were determined and the average among 2,000 estimates of each indicator of the multicollinearity degree was calculated. Then, for each case and indicator, the sample size was determined through three models: models of maximum modified curvature, segmented linear with plateau response, and segmented quadratic with plateau response. There was superiority the quadratic model segmented with plateau in adjusting the degree of multicollinearity according to the sample size for all indicators. There is a need greater sample size to detect multicollinearity when diagnosed by DET and for sizes larger than 101, 258 and 102 plants when diagnosing for the number of conditions, determinant and inflation factor performed, respectively.