Design & Factor Selection
Design Types & Categories
When two or more factors or interactions are confounded (aka aliased), the confounded factors or their interactions cannot be estimated independently with the current design. Usually this means that there are not enough of the proper runs to form the required estimates or that an interaction has been repeated. Confounding may result when runs are removed from a design without changing the requirements.
During an analysis based on individual (non-grouped) runs, confounding is found whenever there are not enough of the proper runs to support an estimate of each factor and interaction specified in the Interaction requirements. The absolute minimum number of runs required is one more than the number of parameters to be estimated.
When an analysis is made of subgroups, the number of subgroups is smaller than the original number of data. The maximum number of linear parameters (rows of the interaction list) that may be estimated is one less than the number of subgroups formed for the analysis.
During a regression, it may be necessary to determine if there are interactions confounded with those specified. It is often advisable to look for possible interactions between any significant interaction and the interactions of significant factors. It may make more sense to substitute a confounded interaction between significant main factors for one between non-significant factors. Interactions between significant factors should be introduced into the regression whenever they can be estimated. Adding an estimable interaction between significant factors will sometimes remove significance from a formerly significant interaction between non-significant factors.
When interactions are added to an analysis, an extended design may be generated to add runs to eliminate the confounding.
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