Factors, Blocks, and Randomization

We'll refer to the components that might affect compressive strength as factors. In general, a factor is a variable that can affect the response variable of interest. Factors might be categorical or numerical. The strategy in a screening experiment is to test a number of factors in order to discover which ones have the greatest impact on the response variable. When we design an experiment, we ideally take into account all potential sources of variation in the response variable. We generally do this in several ways within an experiment.

• We deliberately manipulate—that is, set the values of—some factors (sometimes called treatments) that we believe affect the response variable.

• We control other factors by holding them constant. For instance, because we understand that the strength of concrete depends on the temperature at which it cures, we might test all combinations at the same temperature.

• We often repeat, or replicate, measurements of the response variable for a given treatment condition through a series of experimental runs. We do this to gauge and control for measurement error.

• We might block some runs to account for expected similarities among runs. We block when we have good reason to expect that some measurements will tend to be similar due to the shared factor being blocked.

• We randomize experimental runs to account for those factors that we cannot control, block, or manipulate. Thus, if we expect that changes in barometric pressure could affect the outcome, we randomly assign the sequence of testing different formulations.