24D Page 123
(i), (ii) are exact in the limiting cases δ = 0, δ = 1 respectively.
Using either method the scores for each pair of rows can be entered in a square, which however is symmetrical, so that half of it suffices. This is the flag.
The score in the cell (i,j) measures the evidence that ΔΧ2(i) + ΔΧ2(j) is a dot: thus the flag square behaves like a rectangle. In particular it may be converged: a correct convergence should give the same wheel along both sides.
A flag may be tested for significance (R2 p 92. R3 pp 8, 79, 81, 82).
To flag all the 31 scores of the rectangle by hand would take too much time. A special machine is feasible; for the attempted flagging on miles and Robinson see Appendix 95.
Three abbreviated methods of flagging are described in the ensuing paragraphs (b), (c), (d).
(c) 9 x 9 flag.
For each row find the sum of entries ignoring their signs (sum of moduli).
Take the 9 best rows and flag them (by Scalar products).
There may be an obvious start: if not, converge the flag. To save time divide by 10 and ignore fractions.
Note: If chi 2 lim is expected, flagging is applied, not to 9 rows, but to 11 columns.
(d) Skeleton. (See R2 p 4.)
Make a skeleton of the rectangle: if, for example, the depth is 7 this means: take sums of ±7 as ±2, ±5 and ±3 as ±1, ±1 as 0. This reduces the arithmetic substantially: it is practicable to flag many more rows.
Note: These are written in the rectangle as dots and crosses with two entries in a cell for ±7.
A skeleton is unsatisfactory if the depth is even, e.g. if it is 6 the possible sums are ±6, ±4, ±2, 0, which cannot effectively be simplified without taking ±2 as 0, and this throws away too much evidence.
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