Design of Experiments: Blocking, Confounding and Interactions

September 27th, 2013

In a previous post we considered some general points about experimental design. In this post we will look at some other common considerations when planning an experiment, specifically blocking, confounding and interactions.

Blocking: The idea behind blocking is to reduce the impact of uncontrolled variations on the experimental units. There are various examples of blocks including experiments on different machines, different operators or multiple days of the week. We would want to allocate our treatments across these nuisance factors or it may not be possible to directly compare our treatments because the differences cannot be separated from the effect of the nuisance factors.

Confounding: The term confounding is related to blocking as it describes the situation where the effect of two factors cannot be separated from each other. In the design this can be seen by them always varying together. In the simple case of a two level factorial experiment where each factor can be set at a low or high value then if the factors appear together only at low/low or high/high then they would be confounded as we cannot separate out which factor is causing any change.

Interactions: The term interaction refers to the joint effect of two (or more) factors on the output of a system. Here we cannot consider the main effects of the factors separately as the main effects and interaction need to be considered as a whole to describe the relationship between input and outputs.

These issues are reasonably straightforward to visualise for small designs but it rapidly becomes more complex as the number of factors increases.

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