A statistical procedure used to study the effects of process variables on a process and their collective effect on an independent variable. It is used when the effect of the combination of the variables is complex and involves the study of the various combinations of the variables. For example, temperature, pressure, and the concentration of reactants can have an effect on the yield of a desired product. By selecting high, medium, and low levels for each variable, the number of separate experiments that would be required to study fully the effects on the product would be 3³ = 27. These would be randomly sequenced and possibly repeated in duplicate or triplicate. The test results on yield would then be interpreted by a regression analysis and analysis of variance to determine the influence of each of the variables. Where there are many variables that give too many combinations to be practically considered, a fractional factorial experimental design is used. This allows for a fraction of the full factorial experimental design to be used that can lead to the same outcome, although the level of statistical uncertainty is correspondingly increased. See experimental design.