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Defining Relationship

The defining relationship defines the aliasing structure in a fractional factorial design. The 24-1 design shown below has the defining relationship 'ABCD':

 A BCD B ACD C ABD AB CD AC BD BC AD D ABC 1 -1 -1 -1 1 1 1 -1 2 1 -1 -1 -1 -1 1 1 3 -1 1 -1 -1 1 -1 1 4 1 1 -1 1 -1 -1 -1 5 -1 -1 1 1 -1 -1 1 6 1 -1 1 -1 1 -1 -1 7 -1 1 1 -1 -1 1 -1 8 1 1 1 1 1 1 1

The table shows the aliased terms for each column.  Notice that the aliased terms all combine to make the defining relationship.

Refer to the Design of Experiments for other terms.

 The Design of Experiments is covered in the MiC Quality basic Design of Experiments course and Advanced Design of Experiments course. Try out our courses by taking the first module of the Primer in Statistics free of charge.
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