Does ballistic software use sample or population standard deviation?

[Arizona_Mike]

As someone who does quality control for a living, I know they should use sample standard deviation (S) not population standard deviation (sigma), but which do they actually use?

Mike

 

[CarJunkieLS1]

Ballistic Apps that I use on my phone has you put Standard Deviation into the calculation yourself.

 

[denton]

Mike, as you point out, they should be using s, the estimate of a population SD based on a sample. What they actually use is anybody's guess.

There was a time that Excel used a computational shortcut instead of the square root of the sum of the squared deviations. The answer was close, but not quite perfect. Even respectable software fairly often gets it wrong.

The other thing to keep in mind is that it takes a lot more samples to get a precise estimate of SD than it takes to estimate a mean. Standard deviations are slippery devils that do not like to be cornered and made to tell the truth.

 

[wally]

I always thought sigma was the abstraction of population variance -- a property of the population as a whole, and that S is its empirical estimate obtained by sampling the population.

Other than "toy problems" where you can actually sample the entire population, any one got a real world example where sigma is actually "known" instead of estimated?

I'd argue you want the estimated S for a given lot of ammo and not the population sigma from all lots, unless you are shooting mixed or random lots, something I doubt anyone really concerned with this would be doing.

Ballistic Apps that I use on my phone has you put Standard Deviation into the calculation yourself.

I've only played with a few that input this and thus you could put in whichever you think appropriate.

 

[denton]

any one got a real world example where sigma is actually "known" instead of estimated?

Sure. Someone makes 10 pistol barrels, and then discontinues production forever. The 10 barrels are the population, and the standard deviation is not an estimate from a sample.

I'm not sure it makes much real difference, though. Prior to Fisher's invention of ANOVA, people pretty much used what we now call the population standard deviation and called it the RMS deviation. But ANOVA does such a neat job of accounting for degrees of freedom that after his book came out, people pretty much switched to SD as we know it today. The information content of RMS deviation and SD is the same. That is, they both account for all the variation in all the data.

SD tends to systematically underestimate variation (biased estimator). Using N-1 in the denominator reduces the error just a bit.

As I said earlier, unless you have very large samples, estimates of SD have a lot of uncertainty in them. That's usually large enough to swamp such details as N-1 vs N in the denominator.

 

[JohnKSa]

Sure. Someone makes 10 pistol barrels, and then discontinues production forever. The 10 barrels are the population, and the standard deviation is not an estimate from a sample.

While that is a real-world example; it's worth pointing out that it's not the kind of situation that would apply to the vast majority of real-world situations. It is rare to actually test an entire production run of anything and it's clearly nonsensical to talk about testing every round from a production run of ammunition as that wouldn't leave any ammunition for which the results would be meaningful.

 

[denton]

that wouldn't leave any ammunition for which the results would be meaningful

And that is the central truth of most testing. You have two choices:

1. Settle for an estimate based on a sample, and for never know the true value, or

2. Measure everything until the material is used up or worn out. In that case, you have perfect information but it is no longer of any interest.

Of course, you are right that having the population mean is less common that having an estimate based on a sample. But it's not hard to quickly think of population examples: inside diameter of every 16 inch gun built for the US Navy, gross weight of every 747 that ever flew, the weight of my grandchildren, the hours spent in space by all US astronauts.

 

[wally]

any one got a real world example where sigma is actually "known" instead of estimated?

Sure. Someone makes 10 pistol barrels, and then discontinues production forever. The 10 barrels are the population, and the standard deviation is not an estimate from a sample.

This is basically the definition of a "toy problem" where you can actually sample the entire population.