Suppose that we use the same idea but instead of ordinary
In a two-way factorial, we have defined as the grand mean of the data, + I as the mean of the responses for the th level of factor A as the mean of the responses for the th level of factor B, and as the mean of the th factor-level combination. Show that this implies our zero-sum restrictions on the estimated effects.
Suppose that we use the same idea, but instead of ordinary averages we use weighted averages with as the weight for the th factor-level combination. Derive the new zero-sum restrictions for these weighted averages.
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