General Report on Tunny
24X Page 141
In order to estimate this factor, the simplest method is as follows:
Let sigma-age observed be s.
Let sigma-age expected for a given value of δ be s1.
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and the factor in favour of a particular value of δ rather than δ = 0 is, if we assume σ independent of δ,
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| Therefore natural banage is |  |
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The factor in favour of δ > δ0, rather than δ < δ0, assuming a uniform prior distribution for δ for positive δ (and no chance if δ < 0), is
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| If s2 = N, k = 3, δ = .08 this reduces to | |
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| = .15. |
Thus with N = 10168 a zero score on the significance test implies a factor of about 6 against the rectangle being significant.
The original discussion of 'significance test 0', given in the black file, makes no assumptions about distributions and is a direct application of Bayes' theorem. We proceed now to give an account of this with simplification and correction of the original argument. It is not assumed that the length N of the message is necessarily a multiple of 1271.
Let us assume some definite value of δ and suppose that the depth of the rectangle in a particular cell is k. Then the probability that there will be an entry of Θ in the cell (where Θ and k are integers
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