Statistical Analysis of Unreplicated Factorial Designs Using Contrasts

Factorial designs can have a large number of treatments due to the number of factors and the number of levels of each factor. The number of experimental units required for a researcher to conduct a $k$ factorial experiment is at least the number of treatments. For such an experiment, the total number of experimental units will also depend on the number of replicates for each treatment. The more experimental units used in a study the more the cost to the researcher. The minimum cost is associated with the case in which there is one experimental unit per treatment. That is, an unreplicated $k$ factorial experiment would be the least costly. In an unreplicated experiment, the researcher cannot use analysis of variance to analyze the data. We propose a method that analyzes the data using normal probability plot of estimated contrast of the main effects and interactions. This method is applied to data and compared with Tukey\u27s method that test for non-additivity. Our method is also discussed for use when the response is a multivariate set of measurements