General Report on Tunny
24X Page 145
lying outside this interval, then φ(x/N) = 10 and the natural banage is
 |
or roughly 
decibans with an error of less than two decibans for the usual values of N.
The prior probability of any particular (differenced) wheel patterns (for a 1+2 rectangle) is 2-71 if the patterns obtained by reversing dots and crosses are regarded as equivalent to the original patterns. (This neglects wheel characteristics.) So particular wheel patterns are evens not allowing for competition, if
 . |
(Compare the argument this far with R3 p 40.)
If x2/N = 120 the wheel patterns are 41 decibans up, not allowing for competition. This is the justification for assuming x2 < N.120 in the argument above. If x2 ≥ 120N it is certain that the wheels are substantially right and inaccuracy in the odds does not matter.
We now go on to the problem of finding the odds that the wheels are substantially right. Clearly the result must depend on what is meant by wheel patterns being substantially correct, but it may not be very sensitive to variations in the definition, provided that the definition is a reasonable one.
Let x' be the double bulge on a typical pair of wheel patterns. Then whatever the definition of substantially correct, the factor in favour of the wheel patterns, obtained from the rectangle, being substantially correct is
 |
summed over all wheel patterns which are regarded as substantially equivalent to those of the rectangle. (The factor 1/3 corresponds to the -5 d.b. referred to above.)
If, for a typical pair of wheel patterns, y is the sum of the moduli of the scores of the characters that are changed in the rectangle patterns in order to get the new ones, then a good approximation is x' = x - 2y if the new patterns are too different from the old ones. Therefore the factor above is approximately equal to
 |
|
 |
Back to General Report on Tunny. Contents.