Contents of Grubbs' monograph "Statistical measures of accuracy for riflemen ..."April 27 2011 at 1:18 PM
|Herb1836 (Login Herb1836)|
Does anyone have a copy of either the 1964 version (34 pages) or the 1991 version (52 pages) of Frank Ephraim Grubbs' monograph "Statistical measures of accuracy for riflemen and missile engineers"?
I'm trying to figure out what tables to create for group sizes by Monte Carlo simulation or numeric integration. I'd like what would be essentially a good table of contents for both versions.
I know that there is a paper by Taylor and Grubs that gives the expected value and standard deviation for groups sizes. In table 2 they also give various confidence intervals. This paper assumes that you know the "true" group size. It essentially assumes that the average group size is for an infinite number of N-shot groups. See:
Taylor and Grubbs, 1975
APPROXIMATE PROBABILITY DISTRIBUTIONS FOR THE EXTREME SPREAD
In reality of course the "true" group size is an unknown. All you can measure is an "estimated" group size based on some number of observations.
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I'm curious as to exactly what tables are in the Grubbs monograph to see how far Grubbs carried the idea, and if my notion on how to expand the tables agrees with his.
One thing is fairly certain - Assuming that the group size has a normal distribution with a mean and a standard deviation is a poor assumption. The assumption would only be true for very large group sizes (ie very poor group sizes) and when you have a lot more data than anyone normally collects.
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|This message has been edited by Herb1836 on Apr 27, 2011 6:11 PM|
This message has been edited by Herb1836 on Apr 27, 2011 2:06 PM
This message has been edited by Herb1836 on Apr 27, 2011 2:03 PM
Not sure, Herb...
|April 27 2011, 3:34 PM |
Thanks, but I have that one...
|April 27 2011, 5:54 PM |
Thanks for trying to help...
The Grubbs monograph is mentioned by a number of authors. Don't know if all of them have actually read the publication of if they are just citing it as a source. Grubbs certainly had the right idea, but when he first published in 1964 computers were expensive to play with. Not much memory in core and storage was relatively expensive too.
Now computer memory has gotten cheap, and storage cheaper yet. My idea is simply to brute force the problem by using the CDF of the normal distribution. So for every 0.0001 from 0.0001 to 0.9999 find how many sigmas away from mean that value is. Then copy file for both X and Y. Open X and Y files for reading. You'd read X file once and Y file 9999 times. Calculate the "product" at each point which is written into a fourth file. Read fourth file to get histogram and CDF. I think this would actually be a lot better than Monte Carlo simulation for the tails.
The other thing of course is how much precision do we need? +/-1% ought to be fine. Not many shooters will actually blast enough targets to be able to find a 1% difference between two different factors. You'd need thousands of groups.
You'd also have to calculate a bunch of other such tables to really get what is needed. For example given that you are going to average the group size from two targets, what is the expected distribution?
Another table would be for essentially Chi^2 distribution. Let's assume that we're using 5-shot groups. We want to throw out extreme values of the 5-shot group size to the 4-shot group size. So we simulate a bunch of 5-shot groups, get ratio of 5-shot to 4-shot (throwing out shot that results in largest group size) and figure out where -2.5% limit and +2.5% limit is. Now we can create a test for flyers of 5-shot groups at the 95% CI.
Whole thing goes on and on of course.
Herb I think I now have a way of defining / identifying the true fliers.
|April 28 2011, 12:36 AM |
If so, it will cut the stats to bare bones ....... To my satisfaction that is
........ Time will tell. ...... Best regards, Harry.
Certainly makes me curious...
|April 28 2011, 2:22 AM |
as to what kind of test you're considering.
A flyer of course is just a shot which has been labeled as "statistically abnormal."
In general I'd guess that the tendency is to look at say 4 clustered shots as the good ones and a shot that is "off" as a "flyer" in a quest to get an unrealistically good group size. It is of course really impossible to tell unless you have some notion of how good the group is expected to be.
A point of view .... and some discussion:
|April 28 2011, 6:18 AM |
Fliers may or may not present as statistically abnormal data points.
Yes, statistically a shot that is not in the otherwise representative group is an "outlier". If it unpredictably lands outside the otherwise representative group and was not "called" by the shooter, as resulting from error of aim, it is generally also identified as a "flier". Statistically that flier is also an outlier. So far so good. ...
However, a pellet which flew unpredictably but that landed in the centre of the group could not be identified as a statistical outlier. It is none-the-less a true "flier"... There are at least two such classes of shots. One results from a shot which was "called" because of poor aim but then landed well into the main group; and one that was aimed well but, though it flew erratically, somehow it found its way back to the middle of the group. Statistically these two shots would not be considered as outliers, but they may both be called "fliers". ...
The data we decide to include in the group/s analysis is dependent upon the purpose of the study. It has little to do with seeking unrealistic group sizes. As I think you suggest, for the most part, shooters tend to look at the results from a total system's viewpoint that includes rifle, pellet, shooter and environment. However, when we go beyond that to look, for example, at the rifle in isolation, we have to be more discriminating in the data that we may accept and yes, it is possible to eliminate much data that may be irrelevant to the particular group set we wish to analyze .....
More later perhaps. ..... Kind regards, Harry.
|April 28 2011, 2:42 PM |
I totally agree with all your remarks. You also are absolutely right that a "flyer" which hits the POA should still be discarded - but not too many shooters would want to throw out a "good" shot!
From a different point of view the idea behind discarding flyers is to improve the overall measure of group size. Group size is very susceptible to a "wild" shot. But if you throw out +/-2.5% tails you don't perturb the measure of average. So a statistical method of analysis would expect to discard some data which is "truly" representative in order to protect against data which is not.
Of course this still doesn't do anything to explain why the flyer occurred, nor what you can do to prevent them.
It also doesn't really help if you're shooting in a competition for points. You don't get do-overs. Same thing when taking a shot hunting. "Hey God, that was an oops. Please reposition the rabbit and let me try again..."
As you reduce the probability of a flyer, it will be harder and harder to prevent them. Think of a quality control type situation. You're sampling pellets to determine if they are good or not. the best you can really expect is to increase the probability that the pellets which pass the tests are good.
The measure of average may not be much perturbed by throwing out +/- 2.5% of tails
|April 28 2011, 6:50 PM |
in a perfect curve, but not throwing out one tail can shift the picture when specifically targeting one aspect of the overall system eg., the rifle itself. ... More later. ... best regards, Harry.
|April 28 2011, 11:03 AM |
Shot a few last night.....
had a bitchin' 4 shot one holer going... and pulled the 5th. Admittedly, I had the post about 5th shot curse in my head when it happened, and I was expecting it. Ha d acouple of other good groups (though not as tight, took a few shots to stop laughing at my self...), and knew every time the flier happened, cuz you can see whre the sight was pointed when the gun discharges.
Im starting to come around to "fliers" are the result of the shooter. Exception to that is some radical variance between pellets that are shot in the same group, but inspection, wieghing and sorting should eliminate most of that.....
dr_subsonic's pneumatic research lab
the Lunatic Fringe of American Airgunning
Southwest Montana's headquarters for Airgunning Supremecy
Source of flyers
|April 28 2011, 1:12 PM |
No doubt that the shooter can be a source. Pellets could be a source too of course as you pointed out.
Recognizing a flyer, and try to experimentally determine what caused the flyer are two different aspects of the process.
As I implied, the outliers due to shooter errors in aiming
|April 28 2011, 6:32 PM |
and during firing are not the kind of "fliers" that concern me. They can be "called" shots as Dan has indicated.
..."Recognizing a flyer, and try to experimentally determine what caused the flyer are two different aspects of the process. " ..... Yes, "process" singular.
Perhaps I shall follow up with other posts as I process my most recent data.
... Kind regards, Harry.
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