9.10 Summary

• It is often necessary to design experiments with noise and background factors in mind to ensure that measured effects are due to the treatments of the experiment.
• One way to avoid background effects is to make randomized controlled experiments. These compare the experimental group to a control group, which is not manipulated. In medical studies the control group receives a placebo. As a further precaution such studies should be blinded or double-blinded.
• In a crossover experiment, the subjects receive a sequence of at least two treatments, one of which may be a control. After receiving one treatment they are crossed over to the other. Different groups receive the treatments in different order. The precision in the data increases as compared to randomized controlled experiments, as each individual is his or her own control.
• Several categorical factors can be tested simultaneously in full factorial experiments. They consist of orthogonal test matrices where all factors are varied simultaneously while still allowing complete separation of their effects. In particular, the two-level full factorial design tests all possible combinations of factor settings at two levels. These types of experiments also detect factor interactions.
• If factor interactions are present, the response to a change in one factor depends on the setting of another. This is a common situation, as many phenomena rely on appropriate combinations of factors.
• Fractional factorial experiments have reduced numbers of treatments compared to full factorial experiments. They are based on confounding one or several factors with high order interactions. A side effect is that other interactions or factors are confounded also. These designs are typically used for factor screening, since they provide less information than full factorial designs. The resolution describes the degree of confounding.
• Plackett–Burman designs constitute another class of screening design. The number of treatments is a multiple of four. When the number of factors increases, this makes it easier to find a test plan of suitable size, compared to fractional factorials. Since the main effects and two-way interactions are confounded in these designs they should be applied with caution.
• Continuous, numerical factors may produce curvature in the response. Center points can be added to two-level factorial designs to detect curvature but several additional treatments are required to fit a second-degree regression model to the data.
• Response surface methods combine design of experiments and regression modeling. Designs suited for such methods include central composite designs and Box–Behnken designs.