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Given:

	Mg* =	the mean of any particular one of the the individual groups of measures
	Mr* =	the mean of the row to which that group belongs
	Mc* =	the mean of the column to which that group belongs
	MT =	the mean of the total array of data

If there is zero interaction between the row and column variables, then the difference between the mean of any particular group and the mean of the total array of data

Mg*—MT

should be equal to the simple additive combination of

	Mr*—MT	the difference between the mean of the row to which that group belongs and the mean of the total array of data
	andTT
	Mc*—MT	the difference between the mean of the column to which that group belongs and the mean of the total array of data

Thus on the null hypothesis expectation of zero interaction

	[null]Mg*—MT	= (Mr*—MT)+(Mc*—MT)
	[null]Mg*—MT	= Mr*+Mc*—2MT
	[null]Mg*	= Mr*+Mc*—MT

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