Yes, I've seen their stuff. Not interesting for a few reasons, including the one you mentioned. I was thinking about ordering one of their die sets to experiment with the crimper, though.
Match Ammo Lot Consistency over the Chronograph?
- Thread starter grauhanen
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Yes, I've seen their stuff. Not interesting for a few reasons, including the one you mentioned. I was thinking about ordering one of their die sets to experiment with the crimper, though.
Hi Shorty. Not quite, but close. A statistics correction is needed here to help clarify some of your points about SD and ES.
Standard Deviation (SD) proportions under the symmetrical bell curve of the Normal Distribution (ND) are on both sides of the mean. (And it has to be a ND, otherwise the SD is not valid - more on that later. Assume for now, for sake of description, that the data is distributed in a ND).
1 SD = 34.1%. 1 SD (the 1st SD) exists on both sides of the "mean" (average), or the central high point of the bell curve, so it accounts for double, or 64.2% of the variation around the mean (under the bell curve).
This can be confusing (34.1% or 64.2%). These are both "1 SD" values depending on what your question is. (I know, I know, the Statistician gods have made stats not very user friendly!)
A computer program spits out the 1 SD value for one side of the mean. e.g. for muzzle velocity, say if a sample's 1 SD = 10 fps, that is 10fps on each side of the mean. Therefore 34.1% of the sample was less than the mean, and 34.1% of the sample was greater than the mean. Therefore 68.2% of the rounds are within 1 SD of the mean. Translated to the example, that means that the round fired will have 20 fps variation 68% of the time, because the variation is random around the mean on both sides.
In other words, when using 1 SD to predict, you have to use the combined both sides of the mean under the curve, not just one side, since by random chance the muzzle velocity will land on either side of the mean. So you always have to double the 1 SD to make your prediction for the next shot when using that 1 SD proportion.
2 SD = 13.6% on one side of the mean, beyond the 1st SD on each side. Therefore the 2nd SD accounts for 27.2% of the variation. 1 SD + 2 SD = 95.4% of the sample's variance.
3 SD = 2.1% on one side of the mean out on the far tails of the curve, or 4.2% on both sides. Therefore 1 SD + 2 SD + 3 SD accounts for 99.6% of the variation around the mean.
Because of rounding decimals, the three percentages of 1 to 3 SD's are rounded to 68% - 95% - 99.7%.
RE comments on ES being predictive or not: In fact a sample's ES has strong predictive power when used with the sample's SD....by definition, because the bell curve's tails are defined by the ES. Based on your sample for that same lot of ammo, when you take the next shot, you can predict the muzzle velocity of that next shot has a 68% chance of being in the middle of the ES, and 32% chance of it being faster or slower than that out towards either tail of the bell curve.
For follow-up clarification, this Wikipedia page has a good summary of Standard Deviation, and the Normal Distribution:
https://en.wikipedia.org/wiki/Standard_deviation
Image of the Normal Distribution and SD's from that same link: (Creative Commons license, author credit: M.W. Toews).
I got those numbers from here, with respect to shooting. Pretty sure they're right. Not that yours are wrong, but rather, yours don't apply to this.
http://ballistipedia.com/index.php?title=FAQ
http://ballistipedia.com/index.php?title=FAQ
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Thanks _Shorty for that Link to Ballistipedia and the Rayleigh Distribution. That is new math and statistics for me, so I did alot of reading and followed many of the links (that go on forever into very deep statistics). Very interesting! And very helpful, I learned alot. The level and depth of the math and stats is well beyond my primitive level, but I think I get the gist.
The distribution, and associated stats (SD %'s etc) you are referring to apply to distribution of impacts on a target, which has a left-right and up-down variance in 2 dimensions. Therefore each POI is an X and Y coordinate. The coordinate of 0 is the center of the bullseye. This distribution is bivariate.
In contrast, the distribution of muzzle velocities is a 1-dimensional distribution. Values can never be 0. There are no X,Y coordinates. There is no center that exists until its generated by the data. When sample size is large enough, it will tend to fit the normal distribution, with the 68%-95%-99.7% SD's.
So I agree that you are correct that the ballisticians and statisticians have found that in target shooting, (generating a bivariate distribution) that the Rayleigh distribution better describes the distribution of POI's on target and generates those different SD's you cited (39%-86%-99%). The POI does not necessarily disperse symmetrically around center either, and that's where the complicated skewness of curves in 2 dimensions, and more complicated stats are required.
I noticed your target measurement program "Extended Target Data" outputs different stats than those SD's, showing the CEP's for 50%, 90% and 95%. I like these percentages because they are easy to understand. Are these user-defined in your setup, or are these standard with that program?
We have all experienced that when enough rounds are shot on a bullseye paper target with the same point of aim at dead center (no wind effects), that the center of the target will get shot out, and around the center the impact density gets thinner and thinner the farther they get from the center. This is a skewed distribution from the center in both X and Y dimensions, i.e. more impacts to the left of the median, less rounds to the right of the median in either dimension.
Wikipedia shows this graph of the "Probability distribution function for 'Rayleigh distribution'", where you can see all the SD's and 50% SD skewed left. The longer tail to the right is the fewer and fewer hits the further away from the central point of aim. And note that they all start at point 0. (Creative commons license. Author: Krishnavedala).
The distribution, and associated stats (SD %'s etc) you are referring to apply to distribution of impacts on a target, which has a left-right and up-down variance in 2 dimensions. Therefore each POI is an X and Y coordinate. The coordinate of 0 is the center of the bullseye. This distribution is bivariate.
In contrast, the distribution of muzzle velocities is a 1-dimensional distribution. Values can never be 0. There are no X,Y coordinates. There is no center that exists until its generated by the data. When sample size is large enough, it will tend to fit the normal distribution, with the 68%-95%-99.7% SD's.
So I agree that you are correct that the ballisticians and statisticians have found that in target shooting, (generating a bivariate distribution) that the Rayleigh distribution better describes the distribution of POI's on target and generates those different SD's you cited (39%-86%-99%). The POI does not necessarily disperse symmetrically around center either, and that's where the complicated skewness of curves in 2 dimensions, and more complicated stats are required.
I noticed your target measurement program "Extended Target Data" outputs different stats than those SD's, showing the CEP's for 50%, 90% and 95%. I like these percentages because they are easy to understand. Are these user-defined in your setup, or are these standard with that program?
We have all experienced that when enough rounds are shot on a bullseye paper target with the same point of aim at dead center (no wind effects), that the center of the target will get shot out, and around the center the impact density gets thinner and thinner the farther they get from the center. This is a skewed distribution from the center in both X and Y dimensions, i.e. more impacts to the left of the median, less rounds to the right of the median in either dimension.
Wikipedia shows this graph of the "Probability distribution function for 'Rayleigh distribution'", where you can see all the SD's and 50% SD skewed left. The longer tail to the right is the fewer and fewer hits the further away from the central point of aim. And note that they all start at point 0. (Creative commons license. Author: Krishnavedala).
Ah, it applies to POI because that gets treated as two variables. So 68/95/99.7 for single variables. Gotcha! As for ES and SD versus predictions, I thought that SD and the mean defined the scope of the distribution, not the SD and ES. And the ES just tells you what you happened to see during your data collection. You don't agree? Frankly, all I understand with any of that stuff is what I managed to glean on my own, hehe. Never studied stats in school, so my knowledge of it is thin. More or less only learned whatever little I needed to apply to any given task at hand. 
And that website I gave was relied upon heavily.
That program is called OnTarget TDS. Never met the guy that wrote it, but I'm acquainted with him a little bit. He's a fellow silhouette shooter, and earlier in its development I helped test and gave some suggestions. I could be mistaken, but I think we crossed paths over on steelchickens when discussing testing ammo, and he mentioned the program he was working on. It doesn't let you set up your own calculations, no. Just gives you what you see there. Some of the things it will display vary depending on which target you've used, too. You can use any target you want and then scan it and tag bullet holes, but it does more for you when you use one of its targets. I typically use one that is basically a practice version of the ARA target, with 25 bulls and some sighters squeezed closer together to fit onto an 8.5x11 sheet. You don't have to limit yourself to one shot per bull, but if you do then you can just scan the target and let it find all the bullet holes for you. This is obviously quicker than having to manually tag all the holes yourself, but you can do that if you decide to shoot more than one hole per bull. It then gives you an optimal ARA score as if you didn't have any scope zero error, and shows you how much scope error you had, too. And scores from a few other target types. And for some reason the printouts for the extra data actually contain more info than what you are shown on screen. For example, you also get CTC measurements for five 5-shot groups, where it treats each row as a group, in addition to the CTC for the 25-shot group from the entire target. My 100-shot data is four targets combined.
And that website I gave was relied upon heavily.That program is called OnTarget TDS. Never met the guy that wrote it, but I'm acquainted with him a little bit. He's a fellow silhouette shooter, and earlier in its development I helped test and gave some suggestions. I could be mistaken, but I think we crossed paths over on steelchickens when discussing testing ammo, and he mentioned the program he was working on. It doesn't let you set up your own calculations, no. Just gives you what you see there. Some of the things it will display vary depending on which target you've used, too. You can use any target you want and then scan it and tag bullet holes, but it does more for you when you use one of its targets. I typically use one that is basically a practice version of the ARA target, with 25 bulls and some sighters squeezed closer together to fit onto an 8.5x11 sheet. You don't have to limit yourself to one shot per bull, but if you do then you can just scan the target and let it find all the bullet holes for you. This is obviously quicker than having to manually tag all the holes yourself, but you can do that if you decide to shoot more than one hole per bull. It then gives you an optimal ARA score as if you didn't have any scope zero error, and shows you how much scope error you had, too. And scores from a few other target types. And for some reason the printouts for the extra data actually contain more info than what you are shown on screen. For example, you also get CTC measurements for five 5-shot groups, where it treats each row as a group, in addition to the CTC for the 25-shot group from the entire target. My 100-shot data is four targets combined.
