23J Page 95
23J FLOGGING THE EVIDENCE
(a) Impracticability of an exact formula.
No simple formula for weighing the evidence of a run can be exact. Evidence is derivable not only from the sheer magnitude of the bulges but also from having bulges on the right letters, or on a consistent group of letters (e.g. on all language letters); in other words it is unjust to take the message as a fair sample of itself, and necessary to include other messages.
This section gives only a brief crude account with a minimum of mathematics. For a more refined treatment see 23X.
(b) A primitive formula.
If it is assumed that the message is a fair sample of itself, the factor in favour of a setting due to a sigma-age is proportional to eδ2/2 [of 24X.]
It follows that the odds in favour of a settings with a sigma-age S, is about
The decibanage is 10 log10 of this [21(g)]. This is, essentially, the formula used to construct the table for decibanning wheel-setting runs.
(c) Combining the evidence of several runs.
If several runs are used to set the same wheel or wheels.
If there is no competition the decibanage is
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