Orthogonal Arrays in Market Research

June 24, 2009 by Gregg Larson

While Orthogonal Arrays have been around since the 1940’s, it was Genichi Taguchi who popularized them by making them easier for engineers to execute valid experiments.  It is for this reason that orthogonal arrays have incorrectly been termed “Taguchi Arrays”.  His first contribution of the linear graph made it easy for engineers to understand.  His second contribution was the creation of triangular tables that made it easy to create alias structures for any design .  The strength of these designs is in their ability to take a large number of factors and determine the “critical few” with as few tests as possible.  Researchers can design an orthogonal array relatively easily by assigning factors to a column and then matching the levels within each factor to the different designations within the array. The goal of the designs is to have as much resolution as possible, as long as the number of runs can be justified.   The reason for this is that as you increase the resolution of the design, the more interactions you separate from the main effects.  If your experiment can only perform a limited number of runs, such as in my case, the design may not be able to separate all interactions, and therefore you will begin to introduce confounding into the design.  Understanding this, the designer can limit the effects of confounding by properly assigning the factors to the correct columns of the array. Table 5 is an example of an Orthogonal Array: an L16 (215) design. The use of the ‘L’ in the identification of the array is linked to the origin of the Orthogonal Array, because it is actually an extension of the Latin Square fractional factorial design . Run 1    A=1    B=1    C=1    D=1    E=1    F=1    G=1 Run 2    A=1    B=1    C=1    D=2    E=2    F=2    G=2 Run 3    A=1    B=1    C=2    D=1    E=1    F=2    G=2 Run 4    A=1    B=1    C=2    D=2    E=2    F=1    G=1 Run 5    A=1    B=2    C=1    D=1    E=2    F=1    G=2 Run 6    A=1    B=2    C=1    D=2    E=1    F=2    G=1 Run 7    A=1    B=2    C=2    D=1    E=2    F=2    G=1 Run 8    A=1    B=2    C=2    D=2    E=1    F=1    G=2 Run 9    A=2    B=1    C=1    D=1    E=2    F=2    G=1 Run 10    A=2    B=1    C=1    D=2    E=1    F=1    G=2 Run 11    A=2    B=1    C=2    D=1    E=2    F=1    G=2 Run 12    A=2    B=1    C=2    D=2    E=1    F=2    G=1 Run 13    A=2    B=2    C=1    D=1    E=1    F=2    G=2 Run 14    A=2    B=2    C=1    D=2    E=2    F=1    G=1 Run 15    A=2    B=2    C=2    D=1    E=1    F=1    G=1 Run 16    A=2    B=2    C=2    D=2    E=2    F=2    G=2 Table 5: L16 Orthogonal Array

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