Experimenters are often interested in systems that are multifactorial. A multi-factorial system is one whose output is believed or known to be dependent on the particular settings of several inputs, or factors. We can think of these factors as defining a space, with each point in this space corresponding to a particular set of factor settings. Experimenting can be thought of as exploring this space - finding out how the response of the system changes as factor settings are changed. There are several challenges in this exploration, among which are deciding what region to explore, designing an experiment that explores it most effectively, and describing the results of the exploration. This paper deals principally with the last of these; it shows how the factorial model can be used to describe how the response of the system changes as factor settings are changed. A strength of the factorial model is that it treats the factors as causes of change in the system's response and focuses on relations among these causes. In particular, the factorial model focuses on whether causes act independently on the system (in a sense to be explained below), or whether they interact. This is important because the experimenter generally seeks to control the system, and because control based on causes that act independently of other causes is relatively simple, whereas control based on causes that interact is more challenging. Also, mapping the space - finding out how the response of the system changes as factor settings are changed - will require less work if, during the exploration, it can be determined which of the causes act independently.
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