"* = Nik. GENERAL STRUCTURE OF ANALYSIS OF DESIGNS 87 21. , v are linearly independent. , r }, n = ri + r2 + .... r0. 22. , ljkb), N' (c + r r'ln)''0 will satisfy the normal equations in intrablock analysis. Show further that the dispersion matrix of t is a2 [ (c -f- r r'/n) - 1 (rr' \ l c -f )L Ero/n] and the variance 28. £] (ii) In a connrcted design of equal block-size k where further N N' is non- singular, show that the intrablock, interblock and combined inter and intra- block estimates of the treatment contrast L' t are respectively L' I c + -- | * 0, L' (NN')~1 N B and L' froC + y NN' 1 _1 fwQ + y NB~j Use (i) to obtain the linear combination of the first two estimates having least variance and show that it is in general different from the third esti- mate.
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