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 March 10, 2010, 11:40 AM #1 l98ster Senior Member   Join Date: March 1, 2010 Location: Hopewell Junction, NY Posts: 454 What is the signifigance of Standard Deviation?? Hi everyone, Got my hands on a chronograph yesterday to test some new loads. One of the features that it gives is Standard Deviation. Most of my 10 shot strings for most of my loads fell between 12.8 - 3.1 standard deviation. Im not sure what this means. Can anyone help???? Thanks!!! -George ps: the chrono i used was a friends Competition electronics with the infrared setup. worked flawlessly, even with rapid fire strings!!!!
 March 10, 2010, 11:51 AM #2 Edward429451 Junior member   Join Date: November 12, 2000 Location: Colorado Springs, Colorado Posts: 9,494 tag
 March 10, 2010, 12:01 PM #3 Brian Pfleuger Moderator Emeritus   Join Date: June 25, 2008 Location: Austin, CO Posts: 19,410 The way I think of Standard Deviation is essentially the average amount that the average shot deviates from the average. Confused? In complex terms: http://en.wikipedia.org/wiki/Standard_deviation In simple terms: You might have muzzle velocities of: 2800 2805 2810 2790 2800 for an average (mean) of 2801 and a standard deviation of 7.4162. or, you might have muzzle velocities of: 800, 2805, 2810, 2790, 4800 for an average (mean) of 2801 but a standard deviation of 1414.23 In other words, more or less, the "average" shot of the first string is "off" the average (mean) by an "average" of 7.41fps while in the second string, the "average" shot is "off" the average (mean) by 1414.23fps. This is not the truest mathematical explanation, but it is essentially what the SD means to "average" people.... How much can I expect any given shot to deviate from the average. __________________ Nobody plans to screw up their lives... ...they just don't plan not to. -Andy Stanley
March 10, 2010, 12:06 PM   #4
XD Gunner
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Quote:
 How much can I expect any given shot to deviate from the average.
That's the golden statement!
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 March 10, 2010, 12:25 PM #5 zippy13 Senior Member   Join Date: August 23, 2008 Location: SoCal Posts: 6,442 We studied standard deviations in a university statistics course, and never used it again -- if you're not a statistician, don't worry about it. Here's a site with a great explanation (I like the animated graphic) link.
 March 10, 2010, 12:38 PM #6 mapsjanhere Senior Member   Join Date: August 6, 2009 Location: Albuquerque Posts: 2,806 In a reloading situation you're trying to minimize your SD. A big SD can show that you're not reloading consistently or you're having issues with pressure jumps, for example due to inconsistent ignition using standard primer where magnum is indicated. __________________ I used to love being able to hit hard at 1000 yards. As I get older I find hitting a mini ram at 200 yards with the 22 oddly more satisfying.
March 10, 2010, 12:51 PM   #7
BillCA
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Quote:
 How much can I expect any given shot to deviate from the average.
Pretty close.
The difference in velocity from shot to shot is your "deviation". Usually measured with a string of 5 shots (sometimes a few more). SD gives you a measurement of how much each of your shots varies. A SD of zero would indicate you did everything exactly the same between cartridges (unlikely). If your SD is a low number, you'll have consistency from shot to shot.

A "good" SD vs. "bad" SD varies from cartridge to cartridge and between rifle and handgun rounds. It can even vary between brands of brass (some have smaller volumes than others).

Clear as mud?
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 March 10, 2010, 01:16 PM #8 alfack Senior Member   Join Date: March 4, 2009 Location: Marysville, Washington Posts: 195 Under a standard bell shaped curve, where most of your shots occur at the apex of the curve, SD is a measure of how far off from the apex of the curve you can expect your shot to be. For example, 1 standard deviation brackets a small area on both sides of the apex, while 2 standard deviations brackets a larger area etc.. The lower the number, the better off you are, as far as consistency goes.
 March 10, 2010, 03:46 PM #9 Slamfire Senior Member   Join Date: May 27, 2007 Posts: 5,261 Wiki has a good explanation. http://en.wikipedia.org/wiki/Standard_deviation In theory, if what you are doing follows a bell curve (and not all things do!), then 68% or the time the velocity should be one standard deviation from the average. In a practical sense, comparing SD of loads is not as important as on target accuracy. Also, I consider the extreme spreads to be important in sorting out powders. For handguns, when you get extreme spreads in terms of high 100’s, 200’s, or god forbid more, the powder is inappropriate for the application.
 March 10, 2010, 08:57 PM #11 Tex S Senior Member   Join Date: November 12, 2008 Location: Fort Worth, TEXAS Posts: 875 Good info, Nick. What do benchrest shooters consider an acceptable SD?
 March 11, 2010, 09:38 AM #13 brotus2 Senior Member   Join Date: November 8, 2009 Location: Panama City Beach Posts: 269 I think I'll Standard Deviate some 270's today.
 March 11, 2010, 12:55 PM #14 Unclenick Staff   Join Date: March 4, 2005 Location: Ohio Posts: 15,246 TexS, It depends on the range, but they like it as small as possible. The guys going for 600 yards and out try to stay within an SD of 10 fps if they can manage it? Nick __________________ Gunsite Orange Hat Family Member CMP Certified GSM Master Instructor NRA Certified Rifle Instructor NRA Benefactor Member and Golden Eagle
 April 3, 2010, 06:27 PM #17 bignz Senior Member   Join Date: February 17, 2009 Location: North Texas Posts: 196 SD is a useful statistic. Things that are +- 1 SD are statistical outliers (or rare events), especially if they are +-2 SD. If you were to shoot thousand and thousands of rounds (and I hope you do) and measured all velocities (I hope you don't) and charted them you would have a distribution resembling a normal bell curve around the mean. Around 68% of all cases exist +- 1 SD. About 95% of all cases would exist +- 2 SD. Small SDs indicate that you are being very precise with your reloading method. Big SDs may indicate a problem. If for instance I were to find that my SDs were larger with WIN brass and they were smaller with RP brass - - - well I would prefer to buy RP brass... Same with primers.... Same with powder... Bullets... It is about making a predictable, repeatable, process. So yes I think SD is very important.\ ps: and now that I'm done typing this I read mongoose's post - - which is spot on.
 April 3, 2010, 08:30 PM #18 Unclenick Staff   Join Date: March 4, 2005 Location: Ohio Posts: 15,246 Actually, 1 SD is only about 80% of average deviation, owing to the root mean square finding part of the calculation (squaring to be rid of signs, finding the average of those squares, then taking the square root of that average). Where the area under the Gaussian bell curve is 100% of the the population of an infinite number of samples, the portion of the population under the curve inside the SD limits to two decimal places is: Within 1 SD of the mean, the area under the curve will be 68.27% of measured velocities Within 2 SD of the mean, the area under the curve will be 95.45% of measured velocities Within 3 SD of the mean, the area under the curve will be 99.73% of measured velocities Within 4 SD of the mean, the area under the curve will be 99.99% of measured velocities Because of the few extreme outliers (the bell curve goes from minus infinity to plus infinity) the average deviation (mean deviation (MD)) either side of the mean is just over 1.25 standard deviations. The portion of the population under the bell curve lying inside the MD boundaries is: Within 1 MD of the mean, the area under the curve will be 78.99% of measured velocities Half the population: Within 0.6745 SD of the mean, the area under the curve will be 50.00% of measured velocities All that assumes the shot distribution fits the Gaussian bell curve of normal distribution, and there aren't some non-random boundary conditions like mixing two different loads into the sampling. __________________ Gunsite Orange Hat Family Member CMP Certified GSM Master Instructor NRA Certified Rifle Instructor NRA Benefactor Member and Golden Eagle
 April 12, 2010, 10:26 AM #19 ccchas Junior Member   Join Date: April 3, 2010 Posts: 4 Thanks for the suggestions. I have purchased a Redding profile crimp die. their reputation is to put a really firm hold on the bullet. I read in 45 ACP bullseye discussions that an 0.469 crimp is good so I'll try that first. I also bought a 45 ACP case length gauge. For subsequent chrono work I'll sort the brass and only use the cases that are on spec. Lastly I have some Federal 150 primers. My S&W 625 "Miculek" revolver will double action light-strike on some primers; I've not had that problem with "150" primers. Regarding the statistics I've been trying to so some homework but mostly I've just beat my head against a wall of complicated theory. I want to understand what sample size is needed for this application to generate a good SD. I've read that 30 observations will work. There must be underlying assumptions leading to that value "30." Perhaps the number of observations needed is a function of the variability (although it is the variability that I am trying to measure). Maybe this is an iterative process.
April 12, 2010, 11:54 AM   #20
mongoose33
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Join Date: June 23, 2009
Location: Wisconsin
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Quote:
 Thanks for the suggestions. I have purchased a Redding profile crimp die. their reputation is to put a really firm hold on the bullet. I read in 45 ACP bullseye discussions that an 0.469 crimp is good so I'll try that first. I also bought a 45 ACP case length gauge. For subsequent chrono work I'll sort the brass and only use the cases that are on spec. Lastly I have some Federal 150 primers. My S&W 625 "Miculek" revolver will double action light-strike on some primers; I've not had that problem with "150" primers. Regarding the statistics I've been trying to so some homework but mostly I've just beat my head against a wall of complicated theory. I want to understand what sample size is needed for this application to generate a good SD. I've read that 30 observations will work. There must be underlying assumptions leading to that value "30." Perhaps the number of observations needed is a function of the variability (although it is the variability that I am trying to measure). Maybe this is an iterative process.
The number 30 is arbitrary. It comes from an idea that if a sample is "large" enough, one doesn't need to substitute the "t" distribution for a "z" distribution.

If you're really interested in laying this out statistically, consider using a confidence interval for the mean velocity.

I teach statistics. I evaluate my handloads using a chrono, and I consider 10 rounds to be enough of a sample to give me a good idea what a particular load is doing.

To me, a chrono tells me where a particular load tends to center in terms of velocity. If the standard deviation is very large, it tells me the mean velocity is not particularly stable, i.e., my estimate from the average is based on some pretty wildly-disparate observations.

Which statistic, or which method you wish to use to evaluate the consistency of your ammo depends on what you're trying to accomplish.

When I use my chrono for working up loads, my initial rounds through it (usually no more than 5 for a starting load) are simply to establish that I'm in a velocity (pressure!) range that I'm comfortable with.

Then, as I add more combinations (again, in the lower end of the loads, 5 rounds is usually it), I'm checking to see how velocity/pressure is doing.

If you're careful in how much powder is going into each case, and careful as to maintaining OAL, I don't believe you need more than 5. You're simply establishing safety parameters.

But as I get closer to max or what I think will be my production load, I'll load up 10 (maybe 15), and shoot those. I think 10 is just fine for establishing how the round performs, more or less. If i have a weird flyer (something that expands the ES a lot), I'll consider it bad brass or something else. But mostly that doesn't occur.

Think of it this way: If I work up a load with 5.7 grains of W231 powder at 1.225 overall length and produce velocities of 857 846 832 864 859 849 852 848 791, it's easy to see that the last velocity is not typical. If I want to describe what a 5.7 grain load of W231 does, is it reasonable for me to exclude the 791 and say that I'm around 850 fps?

That is, BTW, my load for Hornady XTP 230grain hollow points. And I see it as an 850fps load, something that mimics the velocity that the original .45 ACP was designed to produce, even though none of the data points are exactly on 850fps, and there was an odd one that was low. The low data point doesn't invalidate the general trend, which is that a 5.7gr load of W231 at 1.225 oal can be expected to produce about 850 fps.

I also evaluate the spread of the data, including the standard deviation. If I've got a lot of spread, then it suggests there is a lot of variability in my reloading--could be the powder measure is dropping inconsistent loads, the bullets may not all be the same weights, may be seated to different depths, etc.

I'm looking for standard deviation numbers in pistol that are no more than 2 percent of the average for a string of 10 shots, and less than 1 percent of the average for rifle. (I re-use brass for pistol, and it's not as consistent as I'd like, but the price is good.).

If I get numbers like that, I consider the averages to be pretty stable.

I think you may be placing too much emphasis on SD as a measure of quality, and ignoring accuracy in the process. Consistency is important, but so, too, is accuracy.

 April 12, 2010, 01:57 PM #21 Unclenick Staff   Join Date: March 4, 2005 Location: Ohio Posts: 15,246 The statistician I used to work with always claimed it took about 30 samples to have what he considered reasonable confidence the bell curve was symmetrical, though under some circumstances he would use 21. I've forgotten when? SAAMI procedures calls for 10 samples in pressure testing to prove a prospective charge for production. It seems to work most of the time, though, once in awhile an overly warm load is approved and the lot is later recalled. We don't know how many low pressure lots get through, since they don't recall those? I'd expect them to be greater in number because most commercial makers seem to have an internal extra safety margin they toss in; particularly for older chamberings. Military ammo is loaded to within both upper and lower performance and pressure limits, though, with the result you find more surplus military ammo that's inadvertently too hot than you do commercial ammunition. Obviously, if you fire enough rounds in load work up, that improves confidence your top load is not going to be producing unexpected extremes. I think that's what you were describing with your sets of 5? I like Dan Newberry's round robin approach for finding sweet spot loads, in part for that reason. You only fire 3 of each load level, but you've typically run through 21-30 in total and at least 9 that hover immediately around any charge that's a candidate for selection. __________________ Gunsite Orange Hat Family Member CMP Certified GSM Master Instructor NRA Certified Rifle Instructor NRA Benefactor Member and Golden Eagle
 April 14, 2010, 10:12 AM #22 ccchas Junior Member   Join Date: April 3, 2010 Posts: 4 A reloading objective is knowing that I'm satisfying the IDPA 45 ACP power factor requirement. Fortunately their testing for that requirement seems in light of the statistics we've been discussing to be quite generous. Three cartridges are selected and two of those have to make the power factor. Should that fail then three more are selected and tested. Two of three is just the minus 1 sigma level. I'm getting better looking chrono numbers now presumably from culling out short cases, setting a slightly shorter OAL (1.250) and making a tighter crimp (Redding profile at 0.469). After these adjustments the same loadings show around 25 fps faster average velocities. Power factor 165,000 needs 718 fps for a 230g bullet. My latest WST test loading, 10 rounds, measured in at 759 mean, 37 ES, 14 SD or 1.84 CV (Coefficient of Variability? i.e. the SD expressed as a percentage of the mean). That would still make power factor down at the minus 3 sigma, 99% level. With apparently two SD's of PF cushion this load seems sufficiently calibrated.

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