Chronograph numbers

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hounddawg

New member
Just my opinion here but I am at the point where I believe that barrel harmonics smooth out vertical dispersion in small differences (100 FPS or less) and that a consistent hold yields smaller ES's. My evidence for those statements comes from the prepped vs non prepped experiment.

Two things to note is the POI did not correlate with the FPS in that experiment and the best chrono numbers came with my jacket removed, 20 rounds fired from ammo loaded at the same time and just randomly pulled from the box. 10 were fired with jean jacket on and 10 with jacket off and a just a long sleeve T shirt. Radically different ES and SD

Now I will say this, the lowest ES/SD had the smallest vertical spread but a 47 FPS ES still had less than .5 MOA vertical at 300 yards

My Shot Marker target system was delivered yesterday so combined with my chrono I will be able to get a better idea of whether that theory is correct
 
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jmr40

New member
Depends on your goals.

I can find out what I need to know with 3-5 shots. When I'm working on a new load the main thing I'm concerned with is making sure I'm not overloading the cartridge. I've seen loads faster than they should be while still 1-2 gr below book max.

I don't worry about SD. If the bullet holes are all close enough on the target then I'm happy. And if the actual velocity is within 50 fps of what the chronograph says that is close enough when calculating trajectory. At the ranges I shoot, (usually 300 or less), 50 fps at the muzzle just doesn't make that much difference down range.
 
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WESHOOT2

New member
depends on your goals

For my 'standard' commercial stuff it would get tested hundreds of times over multiple-year periods after being subjected to various environmental stressors.

If its life is hole-punching, then only close holes matter.
If its life is meat-punching, perhaps more rigorous standards need apply.

If its life is life-saving, then oh my......
 
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Aguila Blanca

Staff
jmr40 said:
I can find out what I need to know with 3-5 shots. When I'm working on a new load the main thing I'm concerned with is making sure I'm not overloading the cartridge. I've seen loads faster than they should be while still 1-2 gr below book max.
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WESHOOT2 said:
If its life is hole-punching, then only close holes matter.
If its life is meat-punching, perhaps more rigorous standards need apply.

If its life is life-saving, then oh my......
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I know this is an Internet forum and the unwritten rules say that staying on topic is not allowed, BUT ... in this case, could we please make an exception, and just answer the question?

This has nothing to do with deciding which load shoots best, which load generates the fastest muzzle velocity, using ladders to arrive at an optimum load. The question specifically asked about Standard Deviation, and nothing else. In an e-mail exchange with a fellow shooter, the question came up as to how many shots are required in a series to have the SD number be meaningful.

He uses three, which I said is not a large enough sample. In the past, I have shot 5-shot groups and reported the SD (along with max, min, avg, and ES), and been told that five shots is not enough for the SD to be statistically meaningful. I have long thought that a sample of ten is probably the minimum but I'm sure there are people here who have forgotten more about statistics than I ever knew, so I decided to ask.
 
7

74A95

New member
What is the issue with statistically significant SD?

https://en.wikipedia.org/wiki/Standard_deviation

In science, it is common to report both the standard deviation of the data (as a summary statistic) and the standard error of the estimate (as a measure of potential error in the findings). By convention, only effects more than two standard errors away from a null expectation are considered "statistically significant", a safeguard against spurious conclusion that are really due to random sampling error.

Could you clarify what/why a statistically significant SD means, and why it matters? Thanks.
 
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Aguila Blanca

Staff
74A95 said:
Could you clarify what/why a statistically significant SD means, and why it matters? Thanks.
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Nope, I can't.

I took one class in statistics, well over 50 years ago, and never encountered the term again until I bought a chronograph and found that Standard Deviation is one of the numbers that chronographs spit out. I don't know just what it means or what value it has to most shooters, but I reckon the chronograph makers wouldn't put SD in there if some people didn't find that data point to be useful.

My concern is that we have devices that report a number for SD. For those who care about that number, it would then make sense to want to use a large enough sample for the number to be statistically significant. I don't know what that sample size is, so I hoped someone who knows more about statistics than I could tell me.

Let me offer an example:

Take a 5-shot string. Values are 100, 98, 99, 97, and 80.

Average is 94.8. Extreme spread is 20. SD is 8.35.


Now take a 10-shot string. Values are 100, 97, 98, 97, 99, 98, 99, 97, 99, and 80.

No value in either string is below 97, except for the last, which would be the outlier.

In the second string, the average is higher: 96.4. This is to be expected, since the sample size has added five additional values that are all higher than the average for the first group. In both groups, the extreme spread is the same: 20.

But for the second group, the SD is 5.85. That's a big difference from 8.35. So, it's clear that the sample size affects the result, but at what point does enough become enough? If a sample of 10 is better than a sample of 5, then a sample of 100 is probably better than a sample of 10. But where does one draw the line and say, "This sample is large enough for the SD value to mean something"?
 
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WESHOOT2

New member
Fair.


During development I used at least twenty rds fired to determine if the load was worth pursuing.
Before offering the load I would normally use a MINIMUM of 100 rds fired to increase the data.
I often used multiple launch platforms during the testing.

But, as always, I used the stated criteria for SD relevance.
 
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74A95

New member
Aguila Blanca said:
But for the second group, the SD is 5.85. That's a big difference from 8.35. So, it's clear that the sample size affects the result, but at what point does enough become enough? If a sample of 10 is better than a sample of 5, then a sample of 100 is probably better than a sample of 10. But where does one draw the line and say, "This sample is large enough for the SD value to mean something"?
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I think you're trying to apply a meaning to the SD which does not exist.

from the previous link;

" . . . the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range."

You don't pick a sample size to best reflect or to reach a certain SD because a certain SD is not the goal. The SD simply is a calculated value that tells you something about your data - " . . . the amount of variation or dispersion of a set of values". That's it. Nothing more.
 
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scatterbrain

New member
For what ever reason, the lower SD my offered loads have, the tighter the group size and the fewer "flyers" I have. The SD may have had nothing to do with it.
 
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Aguila Blanca

Staff
74A95 said:
I think you're trying to apply a meaning to the SD which does not exist.
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No, I'm not.

74A95 said:
You don't pick a sample size to best reflect or to reach a certain SD because a certain SD is not the goal. The SD simply is a calculated value that tells you something about your data - " . . . the amount of variation or dispersion of a set of values". That's it. Nothing more.
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I never even hinted at trying to pick a sample size to attain a certain SD. I asked what minimum sample size is necessary for the SD to be statistically significant (or "valid," or "useful").

To attempt stating the utility of the SD to shooters in everyday language (which is the only language I know when we get into probability and statistics), consider the data we can collect from a report on a batch of commercial ammo. Someone test fires a certain number number of rounds, and they throw some numbers at us. What do those numbers tell us?

Maximum and minimum velocity are self-explanatory, but if they are moderately far apart we want to know more about what happens in between.

Average: I hope we all know how the average is calculated, but unless we have the velocity for every shot in the sample set, the average doesn't tell us much. Using my numbers from above, say the max is 100 and the min is 80. Now let's say we have an average of 90. There are many ways that could happen: in a 10-shot sample we could have five at 100 and five at 80; we could have one at 100, four at 95, four at 85, and one at 80; we could have three at 100, two at 95, two at 85, and three at 80; and there are many other distributions of the ten velocity readings that would average out to 90. So we want something else.

What are we looking for in ammunition? Consistency. Absent other factors, the more consistent the muzzle velocity, the better the odds are of getting small (consistent) groups. A lower SD is the best indicator that the next round will probably be pretty close in velocity to the previous round. And -- at least to a point -- as the sample size increases in number, the SD becomes a better indicator of consistency.

But, while shooting 100 rounds would give a SD that's probably very representative of the entire population (i.e. the total run of that batch of ammunition), in today's market of components (especially primers) being unobtainable it's not realistic for a home reloader to shoot 100-round strings to develop the SD for his/her ammo. We want to use up as little ammo as possible, but enough for the results to be meaningful.

The question then becomes: How many are enough?
 
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WESHOOT2

New member
component costs are higher than me

20 rds is 'enough', if one cannot afford more.



I was able to buy 2,000 Federal Small Pistol Match primers recently, at a local gunshop, for just over $203.
The last 1,000 I'd bought last year were $55.
I became complacent.




I still have a fair supply of powder......
 
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74A95

New member
I'm not saying that SD is not useful, but it has rather limited usefulness. Consistency matters if your loading for power factor, which means you're trying to find a load or velocity that will prevent you from going lower than the minimum speed for power factor and you're loading to be barely above that.

But SD does not predict group size in a typical handgun at typical handgun shooting distance (see the link in post #2), and it's even mentioned in that article that, "Even the Army Marksmanship Unit recognizes that, “Extremely uniform velocities alone are ‘not’ a reliable predictor of accuracy!"" They should know. It might, and can be useful for very long distance shooting.

But since consistency is not correlated with accuracy, one should not bet on that to predict group size. From that article, which is supported by data and statistical analysis, "The real proof of accuracy is how well they group, and not the consistency of their speed. Chronographs measure velocity, and targets measure accuracy. Trust the target, not the chronograph."

You don't need a chronograph when testing accuracy. Only targets.
 
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Aguila Blanca

Staff
74A05 said:
Then the answer to your question is - there is no sample size in which the SD becomes statistically significant.
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If that were true, standard deviation would not exist.

Please stop derailing MY thread. It's a simple question. If you don't know the answer, don't post. If you have no interest in standard deviation for your shooting, skip this thread and move on to some other topic.
 
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74A95

New member
Aguila Blanca said:
If that were true, standard deviation would not exist.

Please stop derailing MY thread. It's a simple question. If you don't know the answer, don't post. If you have no interest in standard deviation for your shooting, skip this thread and move on to some other topic.
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By your own admission, you don't know what it means. Your question of when SD reaches statistical significance proves you don't know what SD is for.

I've had more than one statistics class, in college and graduate school and applied that in a science career. Take the hint: I probably know more about what SD is and what it's used for than you do.

As noted at the Wiki page, " the standard deviation is a measure of the amount of variation or dispersion of a set of values." That's it. It's simply a "descriptive" statistic. It's just a measure of variation. So is standard error. So is extreme spread. And a bunch of others. You're trying to make SD more than it is, which you don't understand.

SD, as a measurement of error, is used for hypothesis testing to make statistical comparisons, such as in t-tests, ANOVAs and so on.

As for the question of how many shots are required for the SD to be meaningful? There is no answer to that because the question is nonsensical. SD has squat to do with determining sample size.

Standard deviation is not what you use to determine how many shots in your sample. Period. That's what you should tell the person who emailed you.

What you can do is look at the conventions used in shooting. 10 shots is generally a good enough value to have reasonable confidence that the average (mean) calculated from those velocities will be a reasonable representative of the 'population' average.

If you want to get a better feel for selecting sample size and what that means, see the Wiki page. https://en.wikipedia.org/wiki/Sample_size_determination. Here is the important message about sample size, "The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample."

Selecting sample size is NOT about how many data points are required to make the SD magical. Sample size is about being a reasonable representation of the population you're measuring. See the underlined part.

Clear as mud?
 
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