9.2 Designs with One Categorical Factor
Experimentation is to create a specific condition and investigate its effect on a specific outcome. We may be interested in how a surface treatment affects the properties of a material, how a solvent affects the yield of a synthesis or how a drug treatment affects a medical condition. The input variables are then called categorical factors, since they describe states that can be labeled but not ordered with respect to each other: we either use one treatment or another, or possibly none at all. In such cases, the hypothesis tests introduced in the last chapter can be used to analyze the results.
If the natural variation in the measured variable is large and the samples are small, it may be difficult to discern the effect of the treatment from the noise in the data. In such cases it is often necessary to design the experiment with noise and background factors in mind. This need is common in medical studies, for example, since patients are affected by a wealth of social, environmental and other background factors that are not under the experimenter's control.
The most common method for avoiding background effects is to make controlled experiments. This means that two groups are compared, where one is exposed to the experimental treatment and the other does not receive any treatment at all. If the experimental group shows an effect and the control group fails to do so, this indicates that the effect is due to the treatment. A background factor ...