An Incomplete Five Factor Analysis

When we come to five factor analyses the number of different types of incomplete analysis is considerable. We will discuss only one type( ), but from such a viewpoint that it is hoped that the general method of treatment will be clear. 

A complicated example dealing with glass manufacture is described by C. E. Gould and W. M. Hampton Supplement to Journal of the Royal Statistical Society, Vol. Ill, page 137, 1936. See particularly E. S. Pearson s contribution to the discussion, page 156. This example is also discussed by Tippett, Methods of Statistics, Section 10, 31, and by Kendall, The Advanced Theory of Statistics, Vol. II, page 202, -where he treats it as a complete analysis. 

Blend Numbers Pair Numbers Mix Numbers Mix Totals Pair Totals m n i TohiU 

In the table the first two figures 11 and 16 are the duplicate determinations of quality on Mi 1 Pair 1 Blend 1, first truck. The 27 is the total of 11 and 16. The next pair of fibres 17 and 16 are the determinations on the second truck of mix 1, and the 33 following is their total. The last figure in the row is the mix total. The second row is for the second mix and is precisely identical. The third row has 27 as the total for the first truck, 60 as the total for the second truck, and 87 as the pair total. The same follows for the second pair for blend 1, with the addition of 145 as the blend total. 

Prima fo(ie this is a five factor analysis, the factors being Blends (B), Pairs (P), Mixes (M), Trucks (T) and Determination of Quality (A). It is immediately apparent that it is not a complete five factor analysis, however, as A is obviously a simple replication there is no distinction between all the first determinations as compared with the second. Further, there is nothing special to distinguish the first pairs from the second pairs, so the pair main effect P will not exist and we will have a Between Pairs within Blends effect formed by pooling the siuns of squares and degrees of freedom of the P and B X P terms. 

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