RE: "Extreme Spread is not only a statistically inefficient measure but also one frequently and easily abused."
The most frequent abuse of extreme spread is chasing the "best group size" (the smallest group). The smallest group size is absolutely meaningless. The valid estimator is the average group size. If you want a smaller group size, just shoot more groups. Sooner or later you'll get lucky and shoot yet an even smaller group by pure luck.
Danielson's 2-shot method is very inefficient. Assuming that horizontal and vertical deflection are both Gaussian and equal, and that the correlation coefficient is zero, then the gold standard is the radial standard deviation which is 100% efficient. In Danielson's 2-shot method he analyzed two different brands of ammo. He used 24 shots of each type, but only got 12 measurements per type. Combining all 24 shots for each type and analyzing using the Rayleigh model would be 100% efficient.
- I believe the example worked out in this spreadsheet shows how 2-shot samples can be transformed to provide an efficient sample set for the Rayleigh model. The only trick to note is that each pair represents two observations, not just one. Thus from 24 shots we have 24 radii measurements (though only 12 are unique) and this allows us to compute the Rayleigh MLE for a 24-shot sample. If there is an error in that math or example please note it. David (talk) 13:00, 15 May 2015 (EDT)
The "best" number of shots per group depends on the % of flyers. No flyers, 5-7 shots are about the same and are "best". A high % of flyers would mean that lower number of shots per group would be better.