Statistics guys ?

[williamwaco]

I don't see a good forum for this question so I am posting it here .

Move it if you think it is inappropriate.

Is it possible for a list of .38 special case lengths to have a Standard Deviation of ZERO?

I am doing a study of case uniformity vs 25 yard accuracy of various factory ammo compared to my reloads.

Excel is telling me this this list of empty once fired cartridge lengths for Winchester 130gr FMJ Target/Range ammo is ZERO. ( To 10 decimal places.)
Granted they are VERY uniform in length but ZERO std deviation?

I don't believe it.





1.145


1.143


1.144


1.144


1.144


1.145


1.142


1.143


1.143


1.145


1.144


1.145


1.145


1.143


1.144


1.145


1.144


1.145


1.145


1.144


1.143


1.144


1.143


1.145


1.145

[Cherokee]

I guess I'm not surprised, factory ammo is good stuff - just expensive for a reloader.

[fatnhappy]

the quick answer is no. The long answer is yes. Your data has variation so therefore it has confidence intervals, standard deviation, mean, mode and median. It's statistically valid given N=25, however......
Your only working with four significant digits so with an extreme spread of two thousandth of an inch. That's a pretty tight standard normal distribution. Just to ball park your distribution apply the 99.7% rule and divide .002" by 6 and I'd say your SD is pretty close to 0.0003333


That of course is based entirely on the premise that the instruments you used were extremely accurate to .001" Assuming you used dial calipers I haven't enough faith in the accuracy of your fourth significant digit to say my previously posited hypothesis is valid. So my long answer is yes. I don't trust the data.

So... that begs the question: why the exercise?

[MtGun44]

Technically, unless all the values in the calculation are the same, then the
standard deviation is NOT zero. But it can be quite small, and therefore might
be rounded off to zero.

Are you familiar with the meaning of standard deviation? Perhaps the first thing to
mention is that it is pretty useless without at least 25 sample data points, and really
comes into it's own out past 100 data points. Also - it assumes a normal distribution,
and there are some really good reasons why some of our kind of measurements are
NOT uniformly distributed around the mean, but are strongly "sided" in their
distribution, so std dev is worthless drivel.

Bil

[williamwaco]

Well, I leaped before I looked.

I reviewed the formula for Standard Deviation and sure enough - it is NOT possible for it to return a zero result unless each and every number in the sample is identical.

( I have a degree in mathematics and computer science. All of my two statistics classes came from business school.) So, no, I am not familiar with measuring it or using it. For my preferences, maximum deviation and average deviation as a percent of the mean, makes more sense. I just throw it in because it seems to be the "thing to do".

So, Why was it zero to 10 decimal places? Some idiot, formatted that column as text. It was calculating the Standard deviation of 25 zeros!

The purpose of the exercise is to look for a correlation between case uniformity and accuracy in the .38 Special.


Thanks for your replies.

[I'll Make Mine]

The purpose of the exercise is to look for a correlation between case uniformity and accuracy in the .38 Special.

There are all sorts of causal arguments as to why more uniform cases will give more accurate rounds, but the question (from a causal point of view) is what variations cause the most loss of accuracy -- case length, case capacity, and flash hole diameter are three that I can see having significant effect (exclusive of non-case variations like powder charge, primer brand/type, ignition efficiency, revolver chamber dimensions, and bullet variances) -- one of which is fairly hard to measure with high precision (though one can use case weight normed against length as an inverse analog of case capacity).

What would be useful information is which case variables, at what values, are significant predictors of loss of accuracy -- that is, with cases at the same trim length, at what level do variations in weight (indicative of variations in capacity) have a significant effect on accuracy (presumably via velocity variation)? Does 0.1 grain case weight make a difference, or 1 grain, or some larger figure?

[runfiverun]

case tension.. is the answer.
your number sample looked to + -.001, with only one variable outside that.
if the +s and -s equaled out, the mean would be zero.
i think your program was giving you an average.

[MtGun44]

IMO, the problem with using std deviation in our field is that some of our
processes are inherently unsymmetric. For example, powder measurement. If you
are using a volumetric powder measure there are all sorts of ways that it might
get filled LESS than full, but not too many ways for it to get filled MORE than
full, so I would expect to see a distribution with the low side having something
that MIGHT look like half of a normal distribution, but a high side that has a
pretty hard cutoff at some point when you have jammed all the powder
that is going to go into that volume, and no more will go.

So working with mathematics that describes processes where the variance
is distributed uniformly on either side of the mean is fundamentally
wrong and cannot provide useful insight into the process.

Mathematics is a tool kit and grabbing a tool that is inappropriate and
applying it to a problem can cause loss of insight or incorrect
"insight" rather than shedding light. Careful understanding of the
underlying assumptions made when mathematics is used to describe
the real world is critically necessary, and sometimes gets overlooked
in the shuffle.

Bill

[fecmech]

As a previous poster stated it's bullet pull or case tension. When I had my Ransom Rest I did a lot of work with the .38 spl and mixed cases are anathema! Even the same headstamp but different lots can be problematic if you are going for ultimate accuracy.

[cbrick]

Are you familiar with the meaning of standard deviation? Perhaps the first thing to
mention is that it is pretty useless without at least 25 sample data points, and really
comes into it's own out past 100 data points.

so std dev is worthless drivel. Bil

Yea, what Bill said.

Standard deviation is a number (a tool) that we can look at to see how uniform (consistent) our ammo is. But as Bill said the smaller the sample size the less confident we can be that our chrono test for either velocity or standard deviation has validity. If we load a box of 100 rounds and head to the range for a chrono test and put 5 rounds over the chrono and get an average of 2,000 fps and a SD of 10 we should have very little confidence that the remaining 95 rounds will fall within that criteria. If we shoot 25 rounds over the chrono and the average velocity is still 2,000 fps and the SD is still 10 we can have some confidence that the remaing 75 rounds will fall at least close to the test results. If we fire all 100 over the chrono and the AV is still 2,000 fps and the SD is still 10 we can have 100% confidence that all of the ammo in that lot is within that test criteria. But it wouldn't matter because the entire lot of ammo is now gone.

I wouldn't say SD is worthless drivel but it is important to understand how it works and what it is. A few or even a handful of shots over the chrono should give you nothing more than a vague idea of the consistency of your ammo or even what the average velocity is.

Rick

[fredj338]

I am not even sure what the question is? Manuf all the cases to one length & sure, they will all be the same length within a fraction. A 0.001" diff is not even a sheet of paper.

[44man]

case tension.. is the answer.
your number sample looked to + -.001, with only one variable outside that.
if the +s and -s equaled out, the mean would be zero.
i think your program was giving you an average.
This is the answer. No way to control brass structure. SD of zero, not hardly.
My best loads are made by measuring boolit seating pressure. That is the closest you can get to controlling burn and boolit release.
It is why BR shooters use the same brass for a match, because they are even and shoot to the same place.

[williamwaco]

For example, powder measurement. If you
are using a volumetric powder measure there are all sorts of ways that it might
get filled LESS than full, but not too many ways for it to get filled MORE than
full, so I would expect to see a distribution with the low side having something
that MIGHT look like half of a normal distribution, but a high side that has a
pretty hard cutoff at some point when you have jammed all the powder
that is going to go into that volume, and no more will go.


Bill

EXCELLENT observation. Thanks