"Standard" Deviation For Standard Deviation ???

28 April 2002, 20:00

<.>

My Oehler 35 P gives me standard deviation. Yeah, I had to surf the net a bit and figure out what it means to me . . . I understand the bell curve and grading A - F.

SD for this chrono provides a figure in fps where 2/3 (66.66%) of the rounds will be within this velocity.

So . . . is there any percent of velocity that the standard deviation should fall into for accurate loads? 1% of velocity? Is that a good figure? 35 fps SD for 3500 fps?

Anyone done the math on this principle?

Thanks

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[This message has been edited by Genghis (edited 04-28-2002).]

29 April 2002, 02:55

<Don G>

For target loads in my 308 that might get used out to 1000 yards I try for SD of 7 or about 0.3% I try to keep ES less than 1%.

For a hunting load that will never get used past 300 yards this is not necessary. In a hunting rifle the ballistics change due to velocity variation is trivial. It is the barrel "harmonics" or barrel "whip" that matters. This will affect group size at ranges out to 300 yards a lot more than the SD or ES would predict in an external ballistics program.

Don

29 April 2002, 04:03

<MontanaMarine>

Am I wrong?

I usually:
1. Chrono 10 rounds.
2. Determine average velocity.
3. Determine the deviation of each round from the average velocity.
4. Total the 10 deviations and divide that number by 10.
5. The result is the standard deviation.

If I am off the mark, please school me.

Thanks, MM

29 April 2002, 04:17

<eldeguello>

As a general rule, we seem to believe that the lower the deviation between the velocity of a series of shots, the more accurate a load will be. This is the way "accuracy loads" are selected by the Lyman Handbook authors, for example. However, it doesn't always work out this way. Sometimes the most accurate load turns out to be one which does not show the lowest deviation, so we're back to finding our most accurate load by shooting holes in a target, rather than by looking at chronograph results.

29 April 2002, 04:35

Bob338

MM~
Standard deviation is defined in any dictionary. Basically, without getting into high math, it is the square root of the sum of the squares of a series of numbers. You truly need a calculator.

The SD, since it's related to velocity, affects mostly bullet drop which is why the 1000 yard competitors try for single digit SD's. For hunting loads, and ranges to about 300 yards, try for SD's in the teens. Even low 20's are good. Only proof is on paper. I've had SD's in the single digits with group size I'd be ashamed to admit. Conversely, I've seen nice tight groups with high SD's in the 30's. The low SD's, along with tight groups are apt to be on the better and more consistent loads in the long run.

29 April 2002, 04:56

<JimmyDee>

MM,
You're on the right track. All the squares and square roots are in the formula to remove negative numbers.

You will get a more meaningful number (i.e., one which matches "sample standard deviation" as it's usually calculated) if you divide your sum of the differences by one less than the number of observations (rounds fired). So, if your average of ten rounds is 2650, and the sum of the differences from the mean (average) is, let's say, 126, your rounded, calculated SD would be 13. If, instead of dividing by the sample size (10), you divide by sample size minus one (10 - 1), the sample SD would be 14. In this example we're talking about an SD which is about one-half percent of the mean - an excellent performance.

For our purposes the difference is trivial and can be ignored; your technique will work fine.

29 April 2002, 05:02

<.>

quote:
Originally posted by MontanaMarine:
Am I wrong?
I usually:
1. Chrono 10 rounds.
2. Determine average velocity.
3. Determine the deviation of each round from the average velocity.
4. Total the 10 deviations and divide that number by 10.
5. The result is the standard deviation.
If I am off the mark, please school me.
Thanks, MM

Close, but my math gets fuzzy. Here's a link that explains SD:

http://davidmlane.com/hyperstat/A16252.html

The variance is a measure of how spread out a distribution is. It is computed as the average squared deviation of each number from its mean. For example, for the numbers 1, 2, and 3, the mean is 2 and the variance is .667

Standard Deviation
The formula for the standard deviation is the
square root of the variance. It is the most commonly used measure of spread.

If the variance is .667, the square root of the variance would be .8167

Standard deviation of 1, 2, 3 would be .8167. That would mean (should mean) that 2/3 of the numbers deviate from 2 (the mean) by .8167.

SD for 2,4,6 . . .

Mean = 4

Variance = 2.666

SD = 1.632 -- 2/3 of the numbers 2,4,6 will fall within 1.632 of 4 -- the mean.

But I teach English . . . Somebody tell me if I did it right. Seems to make sense.

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29 April 2002, 11:26

<JimmyDee>

Genghis, you're computing the standard deviation for what is commonly refered to as a population, i.e., when you measure every element of a set. This is "capital S" on the page for which you gave the link. The "sample standard deviation" is "little s" on the same page and is what's used when a fraction of the population is measured.

For the two sets you cited, {1,2,3} and {2,4,6}, the sample standard deviations are a bit larger: 1 and 2, respectively. Your statistics are a bit smaller and are identical to what MM would have calculated.

29 April 2002, 14:13

<El Viejo>

Genghis,
If you need to calculate the standard deviation, do what I do. Buy a $20 scientific or financial calculator, the function will be programed in.

------------------
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It wastes your time and annoys the pig

30 April 2002, 02:05

Zero Drift

Genghis - Keeping your SD below double digit is generally sufficient for any hunting rifle. For LR target/varmint keeping your SD at or below 7 is great. You will find as you use your chrono, keeping your SDs in the single digit area can be a challenge.

Obliviously keeping your charge weights consistent is very important. However, maintaining the volume of the pressure vessel (brass) is as important. The best way to accomplish this is to trim all your once fired brass to the same length and then sort by weight. You will find the quality brass also is important in maintaining low SDs. Laupa brass is the best that I have found based upon this measure. (Remington is the worst.)

30 April 2002, 03:46

<.>

quote:
Originally posted by El Viejo:
Genghis,
If you need to calculate the standard deviation, do what I do. Buy a $20 scientific or financial calculator, the function will be programed in.

My chronography (Oehler 35P / printer) computes standard deviation for me. I want to understand what the math is about. Otherwise I'm using a statistic and have no clue as to what it is or why it's important.

Thanks

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30 April 2002, 05:01

Recono

quote:
Originally posted by Genghis:
My chronography (Oehler 35P / printer) computes standard deviation for me. I want to understand what the math is about. Otherwise I'm using a statistic and have no clue as to what it is or why it's important.
Thanks

It's NOT important. It's there because it's easy to program the chrono to calculate it, and it is a common mathematical expression. It doesn't have any special value for people who aren't statisticians. Extreme spread is much more useful, and even that is lot more useful to long-range shooters than it is to bench-resters.

It is the square root of [the sum of the squares of the deviations from the mean divided by one less than the sample size].

30 April 2002, 09:45

rogerinneb

It is a measure of dispersion. We don't want our shots dispersed, now do we?

OK, let's move on to sampling methodology and how much one can infer from comparing two different five shot groups! OR said another way, how many five shot groups of two different loads does one have to shoot to know that one load is truly more accurate than the other. Let's say at .01 level...

30 April 2002, 09:56

Recono

quote:
Originally posted by rogerinneb:
It is a measure of dispersion. We don't want our shots dispersed, now do we?

No, in this case it's a measure of deviation from mean velocity, and not a particularly good one, at that. Some shooters don't care much about whether their shots have deviant velocities, as long as the bullets all go to the same place. Others, hereinafter referred to as deviants, are highly concerned about such things. Usually both are right, particularly if the deviants are long-range shooters and the others aren't.

Addition by editing:

Sorry if I misunderstood your post. Maybe you were making the same point I was. SD is an abstruse calculation used for much more abstruse applications of statistics to learn things that no shooter gives a shit about.

Sometimes you do care whether your velocity varies a little, or a little more. In those cases, usually involving shooting at at least 300 yards, just look at the lowest and highest velocities, and plug them into the ballistics program you're using (I like Pejsa's, but I think there are other good ones), and see if those extremes of velocity give you different enough results downrange to notice.

[This message has been edited by Recono (edited 04-30-2002).]

30 April 2002, 10:49

rogerinneb

Recono,

Interesteing.

"No, in this case it's a measure of deviation from mean velocity." Isn't that another way of saying it's a measure of dispersion?

If not, when is it appropriate to call the SD a measure of dispersion? I've always described it that way to non stats folks and have never had even hard core measurement folks challeng it. I guess I'm still Learning!

30 April 2002, 11:03

denton

Estimates of standard deviation based on small samples tend to be quite inaccurate. A true 1 MOA rifle will routinely shoot .5" to 1.5" 5 shot groups, just from random variation in your sample.

For 3 shot groups, divide your "extreme spread" by 1.69 to get an estimate of standard deviation. For 5 shot groups, divide by 2.33. For reasons nobody wants to go into (trust me on this!), this is actually a little better estimate of standard deviation than the sum of squares calculation when the sample is so small.

01 May 2002, 03:55

Recono

quote:
Originally posted by rogerinneb:
Recono,
Interesteing.
"No, in this case it's a measure of deviation from mean velocity." Isn't that another way of saying it's a measure of dispersion?
Depends on what you mean by "dispersion." Here is what you posted:
It is a measure of dispersion. We don't want our shots dispersed, now do we?
OK, let's move on to sampling methodology and how much one can infer from comparing two different five shot groups! OR said another way, how many five shot groups of two different loads does one have to shoot to know that one load is truly more accurate than the other. Let's say at .01 level...
R
That makes me think that you are talking about shot dispersion, not velocity dispersion. SD of velocity is not a measure of shot dispersion, nor a measurement of groups, although there will be some relationship between [particularly vertical] dispersion and velocity dispersion at long range. As for short range (100 -200yd), I suggest you consult the benchresters.
If not, when is it appropriate to call the SD a measure of dispersion? Whenever you say what dispersion you're talking about. I've always described it that way to non stats folks and have never had even hard core measurement folks challeng it. I guess I'm still Learning!
R

01 May 2002, 07:42

denton

Standard deviation is always a measure of dispersion. It measures how "spread out" your data are from the mean (average). It measures nothing else.

01 May 2002, 07:54

Recono

quote:
Originally posted by denton:
Standard deviation is always a measure of dispersion. It measures how "spread out" your data are from the mean (average). It measures nothing else.

Denton,

Roger says, "It is a measure of dispersion. We don't want our shots dispersed, now do we?"

What are you telling us about Roger's statement?

01 May 2002, 11:40

<.>

We're discussing variations in velocity NOT the size of a grouping at the target.

The chronograph measures velocity and variations in velocity. It provides a standard deviation in the variance of velocity in a group of shots.

In only the most indirect and obscure way does the chronograph provide data relating to size of shot grouping at the target.

This seems like an obvious statement, but it also looks like it's being missed.

What's the story with the repeated posts?
What's the story with the repeated posts?
What's the story with the repeated posts?

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01 May 2002, 11:46

Recono

Genghis,

I agree.

Recono

01 May 2002, 12:02

denton

I was not referring to Roger's statement in particular.

Standard deviation measures dispersion. If you are measuring muzzle velocity, it measures the dispersion of the muzzle velocity. If you are measuring distance from the center of a 5 shot group, it measures the dispersion of your group. If you are measuring miles per gallon, percent body fat, or income, it measures the dispersion of miles per gallon, body fat, or income. If you wish, you can also use range ("extreme spread") as another measure of the same thing.

01 May 2002, 12:48

<MontanaMarine>

Ghengis,

At 1000 yards, a 190gr Sierra MK started at 2850 fps will impact approx 12 inches lower than one started at 2900 fps, both with a 100 yard zero. A chronograph reading can predict this with certainty.

My point is that the chronograph is useful for assessing long range grouping potential of a given load.

01 May 2002, 13:24

Ben_Wazzu

From my Quantitative Chemical Analysis book (by Daniel Harris, 5th edition):

ï¿½The smaller the standard deviation, the more closely the data are clustered about the meanï¿½

For a large sample size data will form a ï¿½Gaussianï¿½ or ï¿½bellï¿½ curve when graphed (x-axis is the data points of interest, say certain velocities; y-axis the number or each data point, say the number of rounds at that certain velocity). The standard deviation tells us on any Gaussian curve, 68.3% of the area under the curve is plus or minus one standard deviation.

So, if your average velocity is 3000 fps and your standard deviation is 50 fps then 68 out of 100 shots will statistically have a velocity of 2950 to 3050 fps. The rest of the shots will have a velocity greater than 3050 fps, or less than 2950 fps.

I hope that that made some sense. Now, if someone can tell me how to use a semicolonï¿½ (Genghis?)

BTW, Harris has a few decent pages on statistics and if quite popular (as far as chemistry text go). I would think you could find a copy in a university library if you really wanted. My guess is that you could also find the stuff on the net.

01 May 2002, 13:29

Red Label

my head hurts.

01 May 2002, 14:51

Bob338

Denton~
How does "extreme spread" and body fat relate to standard deviation?

01 May 2002, 15:17

rogerinneb

My comment "we don't want our shots "dispersed" was a tongue in cheek way of saying, dispersion is not good. Less is better. The opposite of "clustered around the mean" as Ben noted would be for the velocities to be dispersed widely around the mean. SO, we don't want our velocities dispersed, and while, as some have noted, dispersed velocities are not always correlated to tight (low dispersion) groups, they often are.

I had the pleasure of shooting at an indoor 100 yd. range this past Sunday. My partner was shooting a high end Les Baer AR-15 target rifle, and he shot many five shot groups of .5 MOA or better. His indoor range has an Oehler chronograph on 8 foot centers, with a proof channel and overhead halogen lighting all in a custom made steel frame (looks like a big box kite). On one particular group, he had 3 shots in a nice one hole cloverleaf, and very close velocities. The fourth shot was about .8" below that group, and was 101fps slower than the mean velocity of the first three. The fifth shot, split the difference velocity wise and, low and behold, split the difference between shot 4 and the first three.

Shooting inside with even, constant lighting and no wind is very cool, and really teaches you a lot about how your guns function. Saeed and the team are very lucky.

I will tell you that if someone had told me they had an AR-15 style gun that would shoot Black Hills reloads as well as my friend's Les Baer number, I would have howled. I had an Olympic Arms Ultramatch AR-15 that was accurate, but nothing like the Baer.

Oh, and by the way, I hardly pay attention to my SD's when using my chronograph. And, I really like my CED chronograph.

02 May 2002, 04:49

denton

Bob338...

Fat people's body cells are more widely dispersed than skinny people's, so they have a higher personal standard deviation. This can be caused by consuming too much "extreme spread" on toast or bagels. Extreme spread is very high in calories.

Non-standard deviations are socially unacceptable activities. We won't go there.

Try to not be under the bell curve when it rings, unless you are wearing 28 dB hearing protection.

I hope this clarifies the issue.

02 May 2002, 17:24

<JimmyDee>

Ben_Wazzu hit upon the useful use of standard deviation: predicting performance for a collection of normally distributed "things" - in our case, batches of cartridges. It won't tell us how any one cartridge will perform and it makes huge assumptions about what is normal, but it gives us a pretty good measure of how consistently a given batch has been assembled and gives us a criterion for comparing batches. As to whether they shoot well or not: you've got to do your paperwork!