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Old April 8, 2012, 11:31 AM   #1
Edward429451
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Can someone tell me my Standard Deviation for this Load?

Can someone with a ballistics program run this load for me and tell me my SD and perhaps calculated pressure is?

44 Magnum
245 gr (429421) (actual weight 253 gr /.430)
19.4 gr 2400
Midway Brass
Fed 150 LP Primer
1.690 OAL

1361 FPS
8 FPS AVG DEV
28 FPS ES

44 Mag/7.5"/SBH

Thanks!
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Old April 8, 2012, 02:03 PM   #2
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if you are refering to standard deviation you are going to need more than one shot to determine that and that would be preferably at least 10 shots. the SD for one shot would be zero
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Old April 8, 2012, 02:37 PM   #3
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http://easycalculation.com/statistic...-deviation.php

QL can guesstimate pressure, but fireformed H2O capcity is needed.
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Old April 8, 2012, 04:03 PM   #4
Edward429451
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Above is 10 shot average. Do you need the exact info from the 10 shots?

I don't have the water capacity. I processed the brass already.
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Old April 8, 2012, 04:22 PM   #5
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Quote:
Above is 10 shot average. Do you need the exact info from the 10 shots?
Yep, you need the datum from each individual shot. That will tell you how much the shot deviated from the standard (standard deviation). Ten shots is good, fifty shots is better, a hundred shots would give you information you could use.

The computer you're typing this on will give you the numbers you need. Plug them into any standard Excel-type program and it'll crunch the numbers for you, or you can do it yourself.
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Old April 8, 2012, 04:22 PM   #6
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NOTE: I was composing when you answered the shot count number was 10. You can find it on the table below. I'll leave that table up as the ratios for shot counts hold for anyone.

Once you get the arguments correct, the ballistics program repeats the calculation the same way each time, getting the same result each time, so it's standard deviation is alway zero, too, no matter how many times you run that calculation. It uses a mathematical model to attempt to find your average or mean value.

Velocity standard deviation is a measure of how irregular your velocities are that lets you predict what percentage of all future shots you take with that load will have what velocities. Since that irregularity depends your primer seating technique, your powder throw consistency, your crimp consistency, and upon how settled fouling in your barrel is, upon whether or not your cases are the same brand and have the same reloading history (number and pressure of reloads) so the hardness of the brass is the same, upon your cylinder's chambers being exactly the same size and aligned equally well with the bore, etc., we have no way to know that from a computer calculation for an idealized gun with perfect load consistency, which is what the computer calculation represents.

On a bell curve, average deviation is about 1.25 times bigger than standard deviation, so if you have 8 fps average deviation you'd expect standard deviation to be about 6.4 fps if the sample size is extremely large. If it's not very large, then, based on the extreme spread of 28 fps and different numbers of shots involved in getting that ES, estimates for more practical numbers of shots would be:

Code:
shots fired	ES	    SD Estimate
2		28		24.8
3		28		16.5
4		28		13.6
5		28		12.0
6		28		11.1
7		28		10.4
8		28		9.8
9		28		9.4
10		28		9.1
11		28		8.8
12		28		8.6
13		28		8.4
14		28		8.2
15		28		8.1
16		28		7.9
17		28		7.8
18		28		7.7
19		28		7.6
20		28		7.5
21		28		7.4
22		28		7.3
23		28		7.3
24		28		7.2
25		28		7.1
 		28		6.4
The reason the number gets smaller as you fire more shots is your extreme spread pair has more chance of being a larger and less likely deviation on the bell curve. For 10 shots the 9.1 ES estimate is probably about as good as you'll get.

Estimating pressure is tough. Alliant doesn't tell you about the 7.5" barrel length they claim for their two recipe loads with 250 grain Keith style LSWC's. It is not a standard pressure barrel length for .44 Mag, according to the SAAMI documents. If it is a single-shot barrel, then it's measured from the breech of the gun, so it includes the chamber. If it's a revolver it's measured from the start of the forcing cone, after the chamber. Not knowing which they used affects the pressure estimate by about 30%.

For your SRH, Lyman's old and new data for 2400 with your bullet is quite different. Comparing the two allows that you may be anywhere from about 26,000 psi to about 37,000 psi. That would agree with Alliant's recipe for the 250 grain Keith, which is 20 grains under CCI 300 primer. My guess from your velocities is that you are nearer the low side, but for safety you should assume the high side.
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Old April 8, 2012, 09:28 PM   #7
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If you have a spreadsheet, just plug in your shot data in a list ...
1200
1250
1230
1400
1210
...

then in a cell do =STDEV(A1:A40) and you have it. What is nice is you can eyeball your data and threw out (if needed) an obvious 'error' such as the 1400 in the above list of values. STD does require at least 10 shoots for valid STD. More of course is always better. You do need to read up on the subject to get the most from STD.....

Here is one place. Good tutorial. You do have to have at least 10 posts in the forum to get to the library I think.

http://rugerforum.net/library/35296-...deviation.html

Here is another ....

http://riflemansjournal.blogspot.com...-shooters.html
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Old April 8, 2012, 09:41 PM   #8
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Agree with Uncle Nick.
In the short run typical of hobbyist chronographing, the Standard Deviation is close to 1/3 the Extreme Spread.

Since Standard Deviation is a smaller number than Extreme Spread, it is more commonly used for bragging purposes even when actual statistical analysis is not being done. But if you are shooting at a physical target at long range, Extreme Spread really matters. Plow your high and low velocity shots into a ballistics chart or program and see the difference in elevation.
Consistent velocity is one big reason that a BPCR like .45-70 can be so accurate as to amaze owners of "modern" rifles.
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Old April 9, 2012, 12:04 AM   #9
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Quote:
In the short run typical of hobbyist chronographing, the Standard Deviation is close to 1/3 the Extreme Spread.
Just checked agianst the ~250 revolver load tests in my spread sheet that I've done and this is 'roughly' true. (9,35), (10,30), (23, 75), (15,47), (5, 14), (6,23), (33, 103), (28, 115) .... Never really paid attention to that little detail....
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Old April 9, 2012, 12:15 AM   #10
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I think I'm on the lower side of the pressure also, though your caution is well noted. This load shoots really good, I'm hesitant to load it up any further because my velocity is there, minimal leading, and I can hold it to 3" @ 50 yds which is superb for me. (Irons!)

I looked and could not locate the datum from that string. Apparently I did the calcs and recorded the avg vel/avg dev/es only, so I will have to generate more this spring when our mountains finally thaw out. I can load 100 and get nice sampling. I just casted up a bunch of Keith boolits

Hey this is good info and good reading, thanks to all who responded.
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Old April 9, 2012, 12:21 AM   #11
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One mathematically unsophisticated writer decreed that Standard Deviation WAS 1/3 the Extreme Spread.

A mathematically sophisticated scientist who got into shooting suggested that Coefficient of Variation, the SD as a percentage of the Average, was a better measure of consistency. He found that 1% pistol ammunition was about what could be done with careful use of normal reloading gear; CoV 1% = 8 fps SD on an 800 fps load.

But your highest velocity shot and your lowest velocity shot will normally shoot the fartherest apart in elevation at long range, so those are what you need to know. (Unless you shoot the fabled match conditioned SMLE which "compensates" at 600 yards.)
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Old April 9, 2012, 09:42 AM   #12
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Quote:
run this load for me and tell me my SD and perhaps calculated pressure is?
Unless you shoot the load in your gun, the standard deviation you would get is just a "guesstimate". There are too many unknown variables like how tight your cylinders are, how much crimp was applied, exact seating depth, how small the brass was sized, how much neck tension on the bullet (how springy the brass- new or older brass).
The only way to get the real SD is to fire the rounds in your gun and chronograph each shot.
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Old April 9, 2012, 09:49 AM   #13
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I should have added that the numbers I calculated came from tables in Denton Bramwell's article, The Perverse Nature of Standard Deviation, and from Dennis Marshall's tables in his article Statistics for Handloaders in Lyman #46 (pp 140-147). The idea is that because the bell curve is taller in the center, each shot has a higher probability of occurring neat the average than at higher deviations, so when you fire just a few shots you probably haven't got a good representation of ES for all future such loads, whereas a larger group's ES is more representative. That's why 1/3 works at 9 shots (actually from about 8-11 shots closely enough), but is too small for smaller numbers of shots and is too large for bigger group numbers, being about 1/4 by the time you get to a 25 shot group. By that time you don't need a multiplier as the standard calculation is working well enough by then.

Denton Bramwell suggests that for data up to 7 shots the multiplying tables are actually more accurate than the standard calculations which tend to underestimate population SD. One other reason in addition to probability of low shot counts under-representing ES is that as the sample size gets smaller the average value it gives you is less likely to accurately represent population average for all examples of that load in the future. The tables allow for both factors where the standard calculation assumes the average error is adequately allowed for by substituting n-1 for n in computing the root mean square of the deviations (SD rather than σ).

For whatever normal distribution you might have, the ES multipliers for different sample sizes, based on the number of samples, n, from these tables are below, though you can get them from the above table by ratio dividing by 28.

Code:
For n samples, multiply ES by the coefficient in the second column
or divide by the coefficient in the third column to get estimated SD.

n	SD Est.	1/SD Est
2	0.887	1.128
3	0.591	1.692
4	0.486	2.058
5	0.430	2.326
6	0.395	2.532
7	0.370	2.703
8	0.351	2.849
9	0.337	2.967
10	0.325	3.077
11	0.315	3.175
12	0.307	3.257
13	0.299	3.344
14	0.293	3.413
15	0.288	3.472
16	0.283	3.534
17	0.279	3.584
18	0.275	3.636
19	0.272	3.676
20	0.268	3.731
21	0.265	3.774
22	0.262	3.817
23	0.260	3.846
24	0.257	3.891
25	0.254	3.937
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Old April 9, 2012, 10:41 AM   #14
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Quote:
The tables allow for both factors where the standard calculation assumes the average error is adequately allowed for by substituting n-1 for n in computing the root mean square of the deviations (SD rather than σ).
The shots that you've recorded and have data for comprise a sample drawn from a much larger population of all shots you theoretically could have taken with all the variables held constant. It's possible to calculate both the standard deviation (SD) of the sample, which can be done exactly, and the SD of the population, which can only be estimated. Statisticians use n in the divisor when calculating sample SD and n-1 when calculating population SD. The statistic of interest in most scientific applications, as well as for shooters, is the population SD, so n-1 is the appropriate choice.
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Old April 9, 2012, 01:12 PM   #15
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FlyFish,

You have that stated backwards. The divisor is n for the population standard deviation (σ) and n-1 for sample standard deviation (SD). SD is an estimate of σ, but in small samples tends to underestimate it, which gives value to the fact n-1, a smaller divisor, makes the result of the estimate bigger (though I understand its real purpose is just to make the math in Fisher's ANOVA methodology work out; I've not been through his Statistical Methods for Research Workers myself, but it is the foundation of modern statistical methods). The estimate improvement is therefore a bonus, not that any estimate from a small sample made by any means can be expected to provide a lot of precision.
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Old April 9, 2012, 02:23 PM   #16
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Quote:
You have that stated backwards. The divisor is n for the population standard deviation (σ) and n-1 for sample standard deviation (SD).
Ah yes. Brain cramp - you are correct, and thanks for noticing my error. The larger point I was trying to make is that the stat of interest is the population SD, not that of the sample.

I've been running ANOVAs for many years and have never heard that the purpose of using n-1 is related to making ANOVA "work out." Not saying it's not true, just that I've never heard statisticians refer to it that way. The way I learned it is that the sample SD is a biased (low) estimator of the population SD and using n-1 corrects (somewhat) for small sample sizes, somewhat analogous to the way that Student's t "corrects" z-scores for small samples.
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Old April 9, 2012, 02:52 PM   #17
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Pressure:
I don't have QuickLoad and comments by some of the users here don't give me a lot of confidence in it for straight pistol cases anyhow.

Does it help you to know that your load of 19.5 gr 2400 + 429421 is right in the middle of Lymans load range where
.44 Magnum 429421
18.5 gr 2400 = 30,300 CUP
20.6 gr 2400 = 37,200 CUP

Probably not linear but if it were, you are about 34,000.

So what does that tell you and what will you do about it?
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Old April 9, 2012, 03:44 PM   #18
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Quote:
Originally Posted by FlyFish
Ah yes. Brain cramp - you are correct, and thanks for noticing my error. The larger point I was trying to make is that the stat of interest is the population SD, not that of the sample.
Still not right unless the ten rounds he fired are all he's ever going to fire and are therefore the whole population. Otherwise, the best he can hope to do is estimate what the final population (all he ever will fire of that same load from that same gun) standard deviation is going to turn out to be by finding the sample standard deviation. So, he wants to find the sample standard deviation either by calculation or, better yet for small samples, from the lookup table. Calculating the population standard deviation will give him the smallest number and the most likely erroneous.

Symbols:
Code:
                          Population             Sample
                                                    _
Mean (Average)                 μ                    x                  
Standard Deviation             σ                   SD

Quote:
Originally Posted by FlyFish
I've been running ANOVAs for many years and have never heard that the purpose of using n-1 is related to making ANOVA "work out."
I first heard mention of this in a textbook from long ago that said, rather cryptically, it was for "technical reasons." Denton Bramwell, who makes his living off this stuff, was the one who mentioned it's there to make the math come out right. He says actually both the n and n-1 denominator versions of the calculation will tend to underestimate population standard deviation when the samples are small; hence the tables.

Denton says in a footnote to his article:

Quote:
" Before 1925, everybody divided by n, but, then, Fischer came out with his book on ANOVA. n-1 makes the math in ANOVA work cleanly, and the influence of ANOVA on the science of statistics was profound. After 1925, the world pretty much switched to n-1. The choice of n or n-1 is simply a matter of convenience, anyway, and does not spring from some great, secret truth, known only to statisticians."

Denton Bramwell

Note: For those not familiar with the acronym, ANOVA, stands for Analysis Of Variance and refers to Fisher's method, specifically.
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Old April 9, 2012, 05:54 PM   #19
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Quote:
Still not right unless the ten rounds he fired are all he's ever going to fire and are therefore the whole population. Otherwise, the best he can hope to do is estimate what the final population (all he ever will fire of that same load from that same gun) standard deviation is going to turn out to be by finding the sample standard deviation. So, he wants to find the sample standard deviation either by calculation or, better yet for small samples, from the lookup table. Calculating the population standard deviation will give him the smallest number and the most likely erroneous.
I think we’re talking past each other a bit and if we were sitting across a table we’d realize we agree about this – it’s just difficult to communicate this way.

I see now that we’re looking at the same problem in different ways and it’s the terminology that’s the issue – and I was also correct in my original post on this, just I didn’t explain it as well as I might have. Let me try again.

We start from the understanding that however many shots we chronograph they are only a sample of the theoretically infinite number of shots that we could have taken with the same load under the same conditions. That theoretically infinite number of shots is the population and it’s the statistics of that population that are of interest, not the statistics of the sample itself (except in the unusual circumstance where those are all the shots of that load we ever will shoot and, in effect, the sample equals the population). So, what we are doing is estimating the population variance from the sample variance, and that’s what I meant by using n-1 to calculate the population variance – what would have been better wording is to say that you use n-1 to calculate (estimate) the population variance from the sample data (or the sample sum of squares). If in fact the population and the sample are the same thing – as I said, an unusual circumstance - then the correct divisor is n.
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Old April 9, 2012, 09:08 PM   #20
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SD with a low sample size is virtually useless. Any statistical modeling depends on large sample sizes, or populations, to provide meaningful information. SD on a 10 shot string says nothing. The ES is much more helpful. Take a stat course and the virtues of large populations vs. the vice of small will be hammered home in the first class.
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Old April 9, 2012, 09:47 PM   #21
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FishFry,

Now I see what you were saying. I wasn't parsing the syntax successfully. Welcome to computers.


Moxie,

If you use the table to get your SD from ES, then it's just as good, for comparative purposes, as the ES itself is, as it's then just a constant factor you apply. You'll want a table of confidence coefficients to go with it for smaller sample sizes so you don't read more into it than it actually means.

Denton Bramwell has offered that he considers the usual calculation to be more useful for shooters starting at about 15 shots. He thinks SAAMI, in requiring only 10 shots for pressure and velocity testing of ammunition, is erring on the easy side, but that's all a member manufacturer uses to be compliant with the SAAMI/ANSI standard. On the other hand, he points out SAAMI's prescribed method has a generous variance allowance, so they seem to be trying to compensate some that way. Nevertheless, the occasion lot of hot ammunition gets out on the market, particularly when copper crushers are used to test pressure, so I suspect 15 would be wiser.

In the end, whether a sample size is useful or not really depends what you are trying to know. If you're just trying to verify an AR passes the government criterion for barrel life by staying inside of 7" at 100 yards, and your first three are inside an inch, then you've proved it with reasonable confidence. If your first three make a 4" group, though, you'd better keep shooting because almost 10" is still within 95% confidence for 3 shots with that ES. You'd need shots that stayed within 4" to get 95% inside 7", though.
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Old April 10, 2012, 06:28 PM   #22
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Quote:
So what does that tell you and what will you do about it?
That's a good question. It tells me that my velocity is higher than my target velocity and so I could trim it back some, still do everything I need it to do, and do it with less pressure than I even have now...If it's something different than that, enlighten me.

At 19.0 grains I'm at 1344 fps/13 AD/49 ES and that is not bad no matter how you slice it. I can't help but think that you're trying to tell me something and I'm not getting it.
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Old April 10, 2012, 07:48 PM   #23
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Averaging the velocity of each shot fired will tell you if it is faster or slower than your "target velocity". S.D. of the velocities will usually indicate if your load is potentially accurate or not. Small S.D. usually means accurate load.
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Old April 11, 2012, 10:15 AM   #24
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Quote:
Originally Posted by Edward
At 19.0 grains I'm at 1344 fps/13 AD/49 ES and that is not bad no matter how you slice it. I can't help but think that you're trying to tell me something and I'm not getting it.
Well, your ES has gone up a lot. That suggests ignition is now less consistent. That could be difference in your crimping consistency, primer seating pressure consistency, or some other loading factor, but it also can happen just because you had the powder forward in the case for some shots and lying back over the primer for others. It's also a little easier for the powder to burn consistently at higher pressure.

If your sample is still ten rounds, from your data for the 19 grain load the table says SD is 15.9 fps. Using that to estimate confidence limits, at your average velocity, that means your muzzle energy will have a +4.8%/-4.7% range 95% of the time, and +7.2%/-7.0% 99.7% of the time. A rule of thumb is anything over about 10% difference in energy is noticed as being different by nerve endings. Your range is under that and so you are probably good to go as far as perceived consistency on the receiving end goes.

Using a G1 BC of 0.210 for that bullet, the resulting drop tables show about 1" vertical stringing at 100 yards, and 3.5" at 200 yards (in case you shoot silhouettes). That assumes the gun locked in a machine rest, though, and in the hand slight differences in the recoil moment can compensate at one specific range, altering it at others. So you'd have to try it see what you really get on targets.
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Old April 11, 2012, 11:32 PM   #25
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Funny you should mention crimp. That batch got crimped differently at 19.0 gr. I have a FCD and have been using it but when I loaded that load I absent mindedly started crimping with the roll crimp and finished the whole batch like that since I had already started.

So next I load 100 rounds at 19.0 but use the FCD, and put them all over the chrony, and then we will be able to glean something useful perhaps.

muzzle energy will have a +4.8%/-4.7% range 95% of the time, and +7.2%/-7.0% 99.7% of the time. That sounds good. Now I'm anxious to see if I can get those numbers down a little more. I know I can't drop this load lower than 19.0 gr because the ES really deteriorates bad at lower pressure than 19.0 gr gives.

That's good info, thanks.
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