Question: 6. Let , i, ()ij, ( )ijk, etc., be the terms in the decomposition (11.3.1), and let k = k, k i = ik

6. Let μ, αi, (αβ)ij, (αβγ )ijk, etc., be the terms in the decomposition (11.3.1), and let

μk = μ··k, αk i = μi·k − μk,

βk j = μ·jk − μk, (αβ)k ij = μijk − μk − αk i − βk j , be the terms in the decomposition (11.3.4) when the level of factor C is held fixed at k. Verify the following relations between the terms of the two decompositions.

(a) μk = γk + μ.

(b) αk i = αi + (αγ )ik.

(c) βk j = βj + (βγ )jk.

(d) Relation (11.3.5), that is, (αβ)k ij = (αβ)ij + (αβγ )ijk.

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