Exact F Tests for the Method of Unweighted Means in a 2 k Experiment

The analysis of a general k-factor factorial experiment having unequal numbers of observations per cell is complex.For the special case of a 2 k experiment with unequal numbers of observations per cell, the method of unweighted means provides a simple vehicle for analysis that requires no matrix inversion and can be used with existing software programs for the analysis of balanced data.All numerator sums of squares for testing main effects and interactions are .2 with one degree of freedom.In addition, for tests having one degree of freedom in any factorial experiment, the method of unweighted means may be modified to yield exact tests.