The ANOVA analysis model is based on specified Interactions. When feasible, the total error is partitioned into its components: pure error and the error due to lack of fit. The ANOVA model is displayed as a Summary of the source of variation attributable to each parameter.
Associated with each ANOVA term are its degrees of freedom (df). For an ANOVA analysis, the degrees of freedom for each parameter and group of parameters depends on the number of levels associated with each parameter or group. When the number of levels for a factor is more than 2, the required number of df increases rapidly. For example, for a complete factorial design (CFD), 3 factors having 2 levels, requiring an 8 run design, requires 8 df for an ANOVA; 2 factors having 3 levels, requiring a 9 run CFD design, requires 49 df. Each factor requires (number of levels-1) df. An interaction requires the product of the df for each of its factors. Each df requires one data run. Additional runs to satisfy an ANOVA model may be generated by replicating the design as many times as is required to obtain sufficient runs. CFD for 2-level designs will always support an ANOVA model, 3-level and up; mixed-level designs will support ANOVAs only when the design has many more runs than is required to estimate the parameters. When there are not enough unique runs to support the requirements for an ANOVA based on the model, the model is reduced for purposes of the ANOVA to the linear factors only.