Efficiency of 35-p Fractional Factorial Designs Determined Using Additional Information on the Spatial Variability of the Experimental Field

The paper presents estimates of the relative efficiency (RE) of the 3^5‐1 (V) and 3^5‐2 (III) fractional factorial designs. Three variants of each fractional design were generated from a one‐replicated 3⁵ full factorial design applied in field experiments with pea (Pisum sativum L.). Plant height and seed yield were determined in the study. Additional measurements of soil properties (pH, P, K, Mg) and plant traits determined on the alleys between experimental strips, sown with a single cultivar, were performed in regular nets of sampling points. Geostatistical methods were used to estimate the spatial variation of the experimental field. Information on spatial variation was included in the statistical analysis. It was found that in the 3^5‐1 (V) fractional designs most of the significant effects were the same as in the 3⁵ full factorial design. Information from these two types of design was similar, although there was a distinct tendency to higher values of the coefficient of determination R² for linear models of the 3^5‐1(V) designs. The 3^5‐2 (III) fractional designs were more variable in detecting significant effects. Generally, mean RE was higher in the 3^5‐2 (III) design than in the 3^5‐1 (V) design, but at the same time the standard error of the latter one was distinctly lower. It was also demonstrated that in agricultural field experiments factorial fractional designs are a very good alternative to full factorial designs as concerns the estimation of main and two‐factor interaction effects in the case of the 3^5‐1 (V) designs and main effects in that of the 3^5‐2 (III) designs. Even if the designs have a highly reduced number of treatments to be tested they are equally or more effective than the original 3⁵ design from which they were generated, provided that the generator is chosen very carefully and the spatial variation of the experimental field is considered in statistical analysis of the experimental data.