Consequences of using estimated response values from negligible interactions in factorial designs

Abstract

This article analyzes the increase in the probability of committing type I and type II errors in assessing the significance of the effects when some properly selected runs have not been carried out, and their responses have been estimated from the interactions considered null from scratch. This is done by simulating the responses from known models that represent a wide variety of practical situations that the experimenter will encounter; the responses considered to be missing are then estimated, and the significance of the effects is assessed. Through comparison with the parameters of the model, the errors are then identified. To assess the significance of the effects when there are missing values, the Box‐Meyer method has been used. The conclusions are that one missing value in eight run designs, and up to three missing values in 16 run designs experiments can be estimated without hardly any notable increase in the probability of error when assessing the significance of the effects.