THE CHOICE OF CONFOUNDING IN A 3K FACTORIAL DESIGN

Abstract

When the numbers of treatments are greater than the available blocks in 3^k factorial experiments, confounding becomes very necessary. Confounding is necessary to reduce the block size as well as reduce the experimental errors. 3², 3³ and 3^k>3 factorial experiments were considered. In 3² experiments, the AB and AB² were recommended for confounding. Similarly, confounding ABC and ABC² are recommended since two main effects are found in a block which can be used for experimentation. Confounding ABC and AB²C is also recommended since two main effects are found in a block which can be used for experimentation. On the contrary confounding ABC² and AB²C² are not recommended since only one main effect is found in a block. Furthermore, in 3³ factorial experiment in 3² blocks using ABC, ABC², AB²C and AB²C² as defining contrast, ABC and AB²C² as well as ABC² and AB²C should not be confounded since they aliased with the main effects when used during fractional replication. However, in 3⁴ factorial experiments no main effect is aliased with (1) the lowest treatment. In generalized interactions, ABCD and ABCD² as well as ABCD and ABC²D are recommended for confounding since three main effects are seen in a block. In contrast, the following pairs of interactions are not recommended for confounding because only two main effects are found in a block: ABCD² and ABC²D; ABCD² and AB²CD; ABC²D and AB²CD.