Calculating SD?
- Thread starter thefitter
- Start date
Keith Glasscock
Gold $$ Contributor
For the sake of argument, it should really be divided by the sample size minus one (n-1) because you are trying to determine a large population's variance (okay, the square root of the variance) based on a small sample.
In real-world terms, there is very little difference. In a situation where the SD is 12 based on dividing by the sample size of 10, the result would be 13 2/3 when dividing by the sample size less one. If we are looking at a more reasonable SD of 6, the change would be to 6 2/3. In other words, both are well within the error margin of the chronograph...
This is where I might as well stand up and say:
Hi,
My name is Keith and I took extra statistics in school because I thought it was fun.....
In real-world terms, there is very little difference. In a situation where the SD is 12 based on dividing by the sample size of 10, the result would be 13 2/3 when dividing by the sample size less one. If we are looking at a more reasonable SD of 6, the change would be to 6 2/3. In other words, both are well within the error margin of the chronograph...
This is where I might as well stand up and say:
Hi,
My name is Keith and I took extra statistics in school because I thought it was fun.....
Previous equation is close. Because we will not measure every shot, we are taking measurements on a sample of the population. Therefore we should use the sample standard deviation eqn...Sqrt of ((sum of the squared errors /( sample size - 1), where errors = observation - the mean of the observations.
http://en.m.wikipedia.org/wiki/Standard_deviation
The wording of the error squared can be confusing. Take observation 1 - the mean of the observations then square that value. Do the same for each observation then add them up, divide by sample size - 1, then take the square root.
http://en.m.wikipedia.org/wiki/Standard_deviation
The wording of the error squared can be confusing. Take observation 1 - the mean of the observations then square that value. Do the same for each observation then add them up, divide by sample size - 1, then take the square root.
Geronimo Jim
Gold $$ Contributor
Are you guys trying to give me a headache?
Keith Glasscock
Gold $$ Contributor
Thats why most college students call it sadistics.
Geronimo Jim said:
If you would truly enjoy a good headache, I am willing to explain why you need to divide by N-1 rather than just N. ???
Turbulent Turtle
F-TR competitor
I'm sure we are all aware there are built-in STDEV functions in Excel. They are based on the "n-1" method.
When I don't have the data already in my Chronograph I just Google "Standard Deviation Calculator" and use one of the free ones that show up.
Here's a simple one to use: http://invsee.asu.edu/srinivas/stdev.html
I prefer to use the "Mean Absolute Deviation" when evaluating my loads. In a large sample it gives a better idea of the variations in speed from the mid point which can often translate to how much higher or lower the shot will hit from the aim point. Here's another easy to use calculator for MAD: http://www.alcula.com/calculators/statistics/mean-absolute-deviation/
Here's a simple one to use: http://invsee.asu.edu/srinivas/stdev.html
I prefer to use the "Mean Absolute Deviation" when evaluating my loads. In a large sample it gives a better idea of the variations in speed from the mid point which can often translate to how much higher or lower the shot will hit from the aim point. Here's another easy to use calculator for MAD: http://www.alcula.com/calculators/statistics/mean-absolute-deviation/
A problem with using the SD function on the chrono' (or any calculator for that matter) is that SD only produces useful information if it has (a) a reasonable sample size and (b) the values being input fit, or at any rate approximate to, a 'bell-curve' if the number of readings for each value is plotted in a histogram or graph form.
Most of us only take a modest number of readings of MVs for a load combination, and all too often the spread of those readings bears little resemblance to a 'bell-curve'. It often makes more sense to keep an eye on individual values and the pattern. In my experience, most reasonably closely matched strings simply produce an SD that is half of the extreme spread when the sample size is small eg ES = 20; SD = 8-11, but more often than not exactly 10.
The bell curve or absence thereof problem comes with the a string that reads something like
3,000
2,995
2,998
3,045
3,004
2,997
3,010
3,001
2,998
3,000
Using Amlevin's calculator, our 10 readings give us an arithmetical mean of 3,005 to the nearest whole number and an SD of 14 likewise. Simple arithmetic says the ES is 50 (3,045-2,995 fps)
The problem is one value way out of the bell curve sitting on its own at 3,045 fps. Redo the calculation for the other 9 values and you get an arithmetic mean that hardly changes at 3,003, ES of 15 and SD of 4.2, a result that most people would be very happy with.
So, the issue is one shot out of 10 .... and why was it aberrant? Is it a chronograph / ambient light change on the range problem? Is is a bum case problem? Is it a scales consistency problem? Is it operator problem - eg distracted when weighing charges? ...... etc, etc. (If you're watching individual values as they appear, it can be useful to keep the case for an aberrant shot on one side and see if it does the same thing when reloaded, and if so scrapping it.)
More to the point:
(a) did the 10 shots group well?
(b) if the exercise is repeated, do you get similar results?
A problem I've run into repeatedly in this sort of exercise, is that results are often not repeatable. A string that gives small ES and SD values one week can be very different and poorer the following week using the same components etc. The problems are small sample sizes and the number of variables in smallarms ammunition and handloading practices.
What to do about it? Don't get over hung up on ES and SD; look at the patterns not just the calculated summary results; if the load groups well at the desired range or in a ladder test, that's more important than wearing the barrel out trying to screw the SD down to tiny values. A friend who holds the UK BR Assoc 1,000 yard group record always tells me to look at group and don't worry about spreads and SDs - his record winning load never produced particularly good figures in either.
What might be interesting in all this would be for a forum member who is a statistician or an engineer who uses this sort of data professionally to say what would be regarded as a good sample size in this sort of exercise. I suspect strongly that we'd be wearing barrels out prematurely trying to get reasonably meaningful results here.
Most of us only take a modest number of readings of MVs for a load combination, and all too often the spread of those readings bears little resemblance to a 'bell-curve'. It often makes more sense to keep an eye on individual values and the pattern. In my experience, most reasonably closely matched strings simply produce an SD that is half of the extreme spread when the sample size is small eg ES = 20; SD = 8-11, but more often than not exactly 10.
The bell curve or absence thereof problem comes with the a string that reads something like
3,000
2,995
2,998
3,045
3,004
2,997
3,010
3,001
2,998
3,000
Using Amlevin's calculator, our 10 readings give us an arithmetical mean of 3,005 to the nearest whole number and an SD of 14 likewise. Simple arithmetic says the ES is 50 (3,045-2,995 fps)
The problem is one value way out of the bell curve sitting on its own at 3,045 fps. Redo the calculation for the other 9 values and you get an arithmetic mean that hardly changes at 3,003, ES of 15 and SD of 4.2, a result that most people would be very happy with.
So, the issue is one shot out of 10 .... and why was it aberrant? Is it a chronograph / ambient light change on the range problem? Is is a bum case problem? Is it a scales consistency problem? Is it operator problem - eg distracted when weighing charges? ...... etc, etc. (If you're watching individual values as they appear, it can be useful to keep the case for an aberrant shot on one side and see if it does the same thing when reloaded, and if so scrapping it.)
More to the point:
(a) did the 10 shots group well?
(b) if the exercise is repeated, do you get similar results?
A problem I've run into repeatedly in this sort of exercise, is that results are often not repeatable. A string that gives small ES and SD values one week can be very different and poorer the following week using the same components etc. The problems are small sample sizes and the number of variables in smallarms ammunition and handloading practices.
What to do about it? Don't get over hung up on ES and SD; look at the patterns not just the calculated summary results; if the load groups well at the desired range or in a ladder test, that's more important than wearing the barrel out trying to screw the SD down to tiny values. A friend who holds the UK BR Assoc 1,000 yard group record always tells me to look at group and don't worry about spreads and SDs - his record winning load never produced particularly good figures in either.
What might be interesting in all this would be for a forum member who is a statistician or an engineer who uses this sort of data professionally to say what would be regarded as a good sample size in this sort of exercise. I suspect strongly that we'd be wearing barrels out prematurely trying to get reasonably meaningful results here.
I couldn't agree more with Laurie's analysis.
I try to shoot more than 10 shots when seriously evaluating the statistical performance, usually no less than 25. One of the several reasons I retired my old Chronograph as it only kept the last 10 shots in memory, replacing the oldest with the latest when this number was exceeded. I now have a chronograph that keeps up to 100 shots in memory. In the end though, it's group size that matters. It is nice however to have some meaningful data concerning the consistency of speed so one can have an accurate basis when calculating changes needed for first shot accuracy at longer ranges.
I try to shoot more than 10 shots when seriously evaluating the statistical performance, usually no less than 25. One of the several reasons I retired my old Chronograph as it only kept the last 10 shots in memory, replacing the oldest with the latest when this number was exceeded. I now have a chronograph that keeps up to 100 shots in memory. In the end though, it's group size that matters. It is nice however to have some meaningful data concerning the consistency of speed so one can have an accurate basis when calculating changes needed for first shot accuracy at longer ranges.
Based upon Lauries great post. I would say that there in lies a consperiacy among the barrel makers to subject us to these torments, in order to drive us shooters into wearing those barrels out to prove some empirical point or theory. As if the barrel makers needed a boom in their buisness.. Pun intended.
I don't know Laurie, but I would like to meet her or him. Whenever these discussions arise, it often leads to polarizing debates. Traditionalists who have followed a routine for testing vs a few others that have had some background in school stats or experimental design that question those procedures. I think the reality is that most people don't really want to know the realities of testing because it may put their methods in question, create anxiety and/or raise issues that are just not practical (read affordable) to solve effectively for most shooters. With regard to load development, the question really just boils down to "Is this load (L1) better than this load (L2)". The standard deviation or extreme spread are nice descriptive measures, but are not sufficient to answer the prime question as Laurie pointed out so nicely. The difference between groups is what will determine if there is an effect of any significance, not how a single group looks. To have any confidence that the conclusion drawn is a meaningful one, eg this load is better for my rifle than this one, error must be reduced (there is always error). To decrease error, sample size must be increased. Not my opinion, it is just a law of nature. Also, the smaller the effects measured, the sample size must be increased. Measuring group size differences of a 1/10th of an inch or a few feet per second of velocity with a mean of almost 3000 fps are definitely small effects. Sample sizes of 3, 5, 10, 25 are just way too small to be statistically meaningful. It is really just a psychological exercise to allow one to feel good, make a choice and go on to something else. Start thinking of sample sizes of 40 - 100 for each load. Now there are some interesting numbers.
Nobody will do this for all sorts of valid reasons, including me. There are all sorts of analyses available to determine actual sample sizes required to study group differences at varying confidence levels. They're not too much fun to look at.
Dennis L
Nobody will do this for all sorts of valid reasons, including me. There are all sorts of analyses available to determine actual sample sizes required to study group differences at varying confidence levels. They're not too much fun to look at.
Dennis L
dblinden said:
HeeHeeHee..
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