The Comparison of the 3k Full Factorial and 3k-p Confounded Design for the assessment of Wheat Production

Abstract

The purpose of an irrigation experiment is to increase food security during the dry season; thus, it is crucial to select an experimental design that can effectively and efficiently assess the effects of various irrigation techniques on crop productivity. A complete factorial design and a confounded design are two possible designs that may be employed. Hence, this study compared the performance of the 3³ full factorial and 3^3-p confounded design for the dry season irrigation experiment.  The objectives of the study include: to group the treatment in a 3³ full factorial experiment into various blocks using confounding; to test the significance of main effects and the interaction effects not confounded and to calculate the gain in precision when the 3³ full factorial design is confounded. The data for this study were secondary data obtained from the Anambra State River Basin Authority (ARBA) in Anambra State. The findings of the study showed that factor B (row spacing) has a significant impact on the design using the full factorial design while the no effect and interactions were found to insignificantly impact on the confounded design. It was found that the full factorial 3³ experiment minimizes the average variance of the parameter estimates and minimizes the maximum variance of all possible normalized linear combinations of parameter estimates than the confounded experiment which was found to relatively maximize the information matrix than the confounded experiment but the confounded experiment which relatively maximizes the information matrix than the full factorial experiment. The full factorial design provides an increase in precision of about 13% when employed instead of the confounded design, and it was found that the full factorial design comparatively optimizes the information matrix compared to the confounded design with a value of 0.94, which is close to 1. As a result, it was shown that confounding a full factorial design does not always result in a more efficient design since some information is lost when specific effects are confounded with blocks.