TABLE OF CONTENTS We know from Chapter 1 that in the planning stages of an experiment, the experimenter must decide whether the levels of factors are to be set at fixed values or chosen at random from many possible levels. In the intervening chapters, except for Section 3.6, it has always been assumed that the factor levels were fixed. In practice it may be necessary to choose the levels of the factors at random, depending on the objectives of the experiment. Are the results to be judged for these levels alone, or are they to be extended to more levels, of which those in the experiment are but a random sample? In the case of some factors such as temperature, time, or pressure, it is usually desirable to pick fixed levels, often near the extremes and at some intermediate points, because a random choice might not cover the range in which the experimenter is interested. In such cases of fixed quantitative levels, we often feel safe in interpolating between the fixed levels chosen. Other factors such as operators, days, or batches may often be only a small sample of all possible operators, days, or batches. In such cases the particular operator, day, or batch may be less important than whether operators, days, or batches in general increase the variability of the experiment.
It is not reasonable to decide after the data have been collected whether the levels are to be considered fixed or random. This decision must be made prior to...
