Calculating standard of deviation

[Whiterabbit]

One question on the chronograph and SD calcs. Whats the expected precision of the chrono? + or- a certain percentage?, number?....lets say 1%, so 2,700fps at 1% would add or subtract 27fps....a total of 54fps from your group. Hmmmm, subract 27 from your slowest and then add 27 to your fastest velocity is entirely possible. Even if it is a half %, thats still swinging the SD around. Just curious if this is a factor to be concerned?

You BET it is a concern to keep in mind.

[rdtompki]

ES divided by 2 is a number I see used more often than 3. Actually I have never seen divide by 3. I have seen SD pretty close to divide by 3 though.

I'd still consider using the full ES though.

If you have a large sample size (which we generally don't collect), then ES/2 would probably be closer to 3 standard deviations for what is known as a normal distribution, so ES/6 might be reasonable approximation. Get ES down to something reasonable and it won't matter what the SD is.

[Whiterabbit]

Get ES down to something reasonable and it won't matter what the SD is.

I agree 100%.

And if I don't need a reasonable ES (like for a 100 yard rifle or revolver), then it still doesn't matter what SD is.

My opinion.

[mjmagee67]

If you have a large sample size (which we generally don't collect), then ES/2 would probably be closer to 3 standard deviations for what is known as a normal distribution, so ES/6 might be reasonable approximation. Get ES down to something reasonable and it won't matter what the SD is.

ES/3 as an approximation of SD was told to me by someone who spent 33 years teaching math and statistics. I went back and played with ES and SD on past Chrono data the ES/3 normally got me with 1 of my calculated SD.

SD is really a validation of your process, it is not an inherent measure of accuracy. If you have your reloading prosess down and things like case volume, bullet weight, powder weight, neck tension, and so on are consistent you should have a low SD. But if you or your rifle suck and your SD is great your shots are still going to suck.

There is a great calculation for using SD to reload for USPSA and never fail to make Power Factor. You shoot a 10 round string, calc out the SD. Then multiply the SD times 2.5 add that number to the minimum required velocity and that will give you a velocity to shoot for. That velocity statistically will make PF 99.9% of the time.

[Whiterabbit]

IMO, and I'm about to say something rude, but if your ES is 3x your SD I suspect you have process INvalidation that is causing 1-sey 2-sey rounds to go out of the population set.

In short, if I saw half-range way higher than SD, I would suspect exactly what you suggest: there's a problem with the process; case volume, neck tension, etc.

[5gnut]

Thanks. Almost everyone was helpful. Fastattack - pardon me for trying to learn more from this site. I guess your name could not be more appropriate.

Try not to worry about the people that respond like that. The vast majority of people here are helpful. I've had to deal with the same thing. And you're right, we're just trying to learn

[jimmykan]

OP, here is the rigorous definition of standard deviation:



It is the square root of the variance of the data set.

The variance is a quantity that measures the "spread-out-ness" of the data points with respect to the average (mean) of the data set.

Here is a better explanation than I can provide:

Quick MBA - Standard Deviation and Variance

[smoothy8500]

So I just wanted to see how much a ES of 60fps would affect my M14 load when shooting 600yd portion of NRA XTC. Looked up Hornady's ballistic calculator to run some numbers and see how much elevation is affected. Nosler 168 Custom Comp has a BC of .462 and I rounded off the velocity at 2600 "average" to keep it simple. So out of my 20 rounds fired we'll say a slow one was 2570, and a fast one was 2630.

Elevation change was + or- 2.75" a hair under 1 MOA total. I don't shoot F-class, but this would definitely throw rounds out of the X-ring and maybe past the 10 ring. For service rifle XTC the target is more forgiving, X ring is 1MOA, 10 ring is 2 MOA. Still, thats points that "leak" into the next ring.

I can see now why the benchrest shooters are trying to get their ES into single digits.

[Whiterabbit]

Agree. which mean your fliers are much more OOS than those in the group. That's exactly my point.

[AAShooter]

Make sure you understand SD, what it means and how it applies to differing distributions. Further, can you control enough other factors to be able to use SD to quantify the parameter you are interested in.

[JMP]

IMO, don't worry about SD and pay attention to ES (extreme spread [highest velocity - lowest velocity]).

Try to get the ES as close to single digit numbers or in the teens. SD is usually about half of your ES number.

Do this. But, variance is easy to calculate, the expectations of the square of the random variable, minus the square of the expectation. Then, SD is simply the square root of the variance. Standard deviation is commonly used in statistics with normal distributions and large samplings. It's not valuable without a very large sampling so it generally does not mean beans for several shots through a chrono. Use the range, or "ES", and don't worry about standard deviation.

[mjmagee67]

You people keep saying SD is normally half your ES, I would love to see the data sets where this is happening. rsrocket1 provided 5 data sets and in 4 of them SD was 1/3 the ES and the other it was almost 1/4. In my data analysis this is what I've seen from all my data and others.

This is all based on a minimum 10 shot population, less than 10 shots are not a big enough population to make the statistics useful. As your population gets smaller your SD becomes closer to your ES. In some sense rsrocket1's data verify this. 5 shot population are useless. I use 10 but people smarter than me say 20 is best. Shoot a 20 shot population and calc it, then pull out 10 random shots and calc those, then do the same for 5 and look at the difference in the data you get. Do that several times and you will learn a lot about how valuable the info is.

As far as popular set size, larger is always better, when is that never true? Statistics and SD is predicting what you will see in the next shot. ES is what you saw and has nothing to do with the future. One bad load can skew ES horribly, but SD will average it out with the rest of the data. They are both important but if both are small tiny numbers it still doesn't mean your going to be accurate. But if your SD is huge I garrentee you are not going to be accurate.

[JMP]

That is why the labradar chronograph is useful as you can shoot and measure simultaneously, and you will likely be getting more data in practice.

[LynnJr]

You people keep saying SD is normally half your ES, I would love to see the data sets where this is happening. rsrocket1 provided 5 data sets and in 4 of them SD was 1/3 the ES and the other it was almost 1/4. In my data analysis this is what I've seen from all my data and others.

This is all based on a minimum 10 shot population, less than 10 shots are not a big enough population to make the statistics useful. As your population gets smaller your SD becomes closer to your ES. In some sense rsrocket1's data verify this. 5 shot population are useless. I use 10 but people smarter than me say 20 is best. Shoot a 20 shot population and calc it, then pull out 10 random shots and calc those, then do the same for 5 and look at the difference in the data you get. Do that several times and you will learn a lot about how valuable the info is.

As far as popular set size, larger is always better, when is that never true? Statistics and SD is predicting what you will see in the next shot. ES is what you saw and has nothing to do with the future. One bad load can skew ES horribly, but SD will average it out with the rest of the data. They are both important but if both are small tiny numbers it still doesn't mean your going to be accurate. But if your SD is huge I garrentee you are not going to be accurate.

This is exactly why SD is not as useful as ES.
That one bad load is what wins and loses matches.
If we could shoot 5 10 or 20 shots and pick the best 3 8 or 15 out of those SD would matter.
But as all of your shots count rounding the fliers down in a calculation doesn't fix the error seen on the target.
ES shows you the group you will get.
SD shows you what is possible if you throw away your bad loads.
Problem is nobody can tell which loads are bad until after they have ruined your target.

[smoothy8500]

This is exactly why SD is not as useful as ES.

ES shows you the group you will get.
SD shows you what is possible if you throw away your bad loads.
Problem is nobody can tell which loads are bad until after they have ruined your target.

After the little anectdotal test I did, I'm starting to see this makes more sense.