Critical Analysis of Factorial Experiments and Orthogonal Fractions

Conclusions drawn from unreplicated factorial and fractional factorial experiments can be quite misleading when the data include one or more spurious values or when two results have been erroneously interchanged. The recognition of such occurrences may reduce the residual mean square to one‐tenth of its previous value and markedly change the estimated size and significance of the factor effects. A procedure for identifying spurious values is described. Each response value in turn is treated as missing and an empirical significance test is applied to the least of the residual mean squares. The procedure is repeated in a search for further spurious values and is followed by a search for interchanged results. In certain cases an aberrant cell may only be partially indentifiable. The whole critical analysis is embodied in a computer program, which includes analysis of variance before and after amendments to the data and lists individual residuals. Any orthogonal experimental design can be accommodated and the user has control over the model which is fitted: missing values are also permitted. Two examples of the critical analysis are described in detail and a summary is given of the result of applying the method to 23 sets of data in the statistical literature.