Exercise 9.6.3 The missing value procedure that consists of analyzing the model (Y Z ) = X + e has been shown to give

Exercise 9.6.3 The missing value procedure that consists of analyzing the model (Y − Zγˆ ) = Xβ + e has been shown to give the correct SSE and BLUEs;

however, sums of squares explained by the model are biased upwards. For a randomized complete block design with a treatments and b blocks and the observation in the

c, d cell missing, show that the correct mean square for treatments is the naive

(biased) mean square treatments minus [y·d − (a − 1) ˆycd ]2/a(a − 1)2, where y·d is the sum of all actual observations in block

d, and ˆycd is the pseudo-observation (the nonzero element of Zγˆ ).