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In experimental design when two interactions, or a main effect and an interaction, share the same column, and so cannot be individually analyzed then their effects are aliased.
In the 23-1 design the factor C is aliased with the interaction AB:
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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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When the design is analyzed it is not possible to distinguish between the effects of changes in the settings of factor C or the effects of an interaction between factors A and C. Thus this design would only be useful if you believed, from other information, that interactions between A and C would not be significant.
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