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An experimental design is orthogonal if each factor can be evaluated independently of all the other factors. In a two level factorial design, this is achieved by matching each level of each factor with an equal number of each level of the other factors.
For example, in the array the '+1' level of Factor A (runs 2 and 4) is matched with one instance of Factor B at '-1' and one at '+1'. If any two columns are compared, the same thing will be found for both factor levels.
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Treatment
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A
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B
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AB + C
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1
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-1
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-1
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+1
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2
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+1
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-1
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-1
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3
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-1
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+1
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-1
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4
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+1
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+1
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+1
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The term 'orthogonal array' is often used in the context of Taguchi designs; 'Taguchi Orthogonal Arrays'.
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