Standard Deviation

[atlscrog]

Why does my chronograph calculate standard deviation as a sample and not as a population?

I get that the recorded shots are a sample of all the rounds of that lot that could be fired, but I'm really only interested in the shots that were fired.

Looking forward to some knowledge

[Steve L]

Standard Deviation basically is that 2/3 of all your shots will be within the SD number of the Mean. The mathematical equation goes way beyond the 3 or 5 or 15 rounds fired through the chronograph.

I hope this helps, otherwise I did not really understand your question.

[warpspeed]

Why does my chronograph calculate standard deviation as a sample and not as a population?

I get that the recorded shots are a sample of all the rounds of that lot that could be fired, but I'm really only interested in the shots that were fired.

Looking forward to some knowledge

< I'm making a lot of assumptions here >

Because all it has to choose from are those that are in the current string.

[bbbean]

Why does my chronograph calculate standard deviation as a sample and not as a population?

Because you only tested a sample!

I get that the recorded shots are a sample of all the rounds of that lot that could be fired, but I'm really only interested in the shots that were fired.

Isn't the point of testing the rounds you shot to predict how the remaining rounds will behave?

[atlscrog]

All,

Thanks for the replies!

I still think I would measure standard deviation as a population instead of a sample, but I like dialog... thanks again!

Scott

[dauntedfuture]

Dont forget to look at ES as well. If your shooting long range rifle its often more important than the SD and for LR rifle all i look at is ES.

[warpspeed]

All,

Thanks for the replies!

I still think I would measure standard deviation as a population instead of a sample, but I like dialog... thanks again!

Scott

For the situation you describe, the sample is the population.

[ErieRich]

I get that the recorded shots are a sample of all the rounds of that lot that could be fired, but I'm really only interested in the shots that were fired.

Why would you only want to know standard deviation of the shots fired? The point of firing a sample is to get an estimate on how the rest of your rounds will perform. Can you provide us more detail on why you only care about the deviation in the 10 or so rounds you fired over the chrono?

[Chills1994]

standard deviation for sample has everything divided by N-1 , then find the square root of that.

SD for population has everything divided by just the N. so in a 10 shot string, for population you would divide by 10, then find the square root.

for the same 10 shot string, you would divide by 9, then find the square root, to find the SD for sample.

I guess if I get really bored here in a little while I can break out my reloading 3 ring binder and look through my old chrono results and see how my CED chrono calculated its SD, most likely the sample SD method, and then do a calculation by hand using the population formula instead to see if it really makes all that much difference.

probably at one point, most likely during my undergrad days, I knew why or what the logic was behind dividing by (N-1) versus just the N.

right now, my initial gut reaction is that dividing by (N-1) yields a larger SD, and when comparing means to see if there is a statistically significant difference, it is a way of erring on the side of caution....I think.... it's been a while since I have had to do ANOVA's and t-tests.

[Chills1994]

not to totally pick nits here, but the 2/3rds assumption as far as shots falling between plus or minus one standard deviation from the mean is based on the ASSumption that the data follows a normal distribution.

I have never gone so far as to actually calculate the median for any of my chrono results.

Maybe next time...eh?

[Skydiver]

Yup, there is the assumption that velocities are in a normal distribution. I've seen proofs that bullets hitting a target impact in a normal distribution, but I've never seen anything proving that velocities will be in a normal distribution. I guess it just has to be checked against empirical data.

[bbbean]

right now, my initial gut reaction is that dividing by (N-1) yields a larger SD, and when comparing means to see if there is a statistically significant difference, it is a way of erring on the side of caution....I think.... it's been a while since I have had to do ANOVA's and t-tests.

ding ding ding! We have a winner!

[Steve L]

not to totally pick nits here, but the 2/3rds assumption as far as shots falling between plus or minus one standard deviation from the mean is based on the ASSumption that the data follows a normal distribution.

I have never gone so far as to actually calculate the median for any of my chrono results.

Maybe next time...eh?

Standard Deviation is based off an assumption. It is also used by stock brokers to get a projection of how a stock will perform. We won't go into how the stock markets fares using standard deviation, but if everything being constant, ie the temperature, overcast, powder charge, etc. all the numbers should be bases off of normal distribution. We don't live in a perfect world so the numbers can't be normal distribution but the lower the variance the closer to perfect it could be. So in that case the average(mean) should be about 68%(2/3) the standard deviation(variance). I got this information from an old article by Oehler.

It is also explained here to an extent.

[Graham Smith]

The sample and population are the same, in this case, because the only thing you can include in the calculations are shots you just fired. Now, if you periodically chrono your loads and keep track of all the different velocities, then you can calculate an SD on the entire population which will give you a better indication of how your load is going over time.

FWIW, SD is pretty useless you are shooting a large enough sample, just shooting 5 rounds is not enough. If you want a good feeling for what your load is doing, shoot at least 10 rounds (20 is better) and then look at the numbers. If you have a fairly good load, you should see all the values concentrated around a central value. Throw out the flyers and calculate the mean and the spread (and the SD if you are interested). This should give you a fairly good idea of what your "average" velocity is. Be aware that, if you have a lot of flyers or a large spread, then there is a problem with your load.

Also, for USPSA it is very helpful to convert all your velocities into PF and run the numbers that way. In the long run, that's a more practical number.

Edited November 2, 2011 by Graham Smith

[bbbean]

The sample and population are the same, in this case, because the only thing you can include in the calculations are shots you just fired.

No. The only time you use a population measure is when you actually measure the entire population. The entire population would be all rounds made using a given load/gun combination. Certainly if you intend to use your chrono results to determine whether your load makes PF, is accurate, or runs reliably, then you intend to apply the findings to more rounds than you measures. That makes the rounds you measured a sample.

Now, if you periodically chrono your loads and keep track of all the different velocities, then you can calculate an SD on the entire population which will give you a better indication of how your load is going over time.

No, this is just increasing the sample.

FWIW, SD is pretty useless you are shooting a large enough sample, just shooting 5 rounds is not enough. If you want a good feeling for what your load is doing, shoot at least 10 rounds (20 is better) and then look at the numbers. If you have a fairly good load, you should see all the values concentrated around a central value. Throw out the flyers and calculate the mean and the spread (and the SD if you are interested). This should give you a fairly good idea of what your "average" velocity is. Be aware that, if you have a lot of flyers or a large spread, then there is a problem with your load.

Note that SD takes sample size into account. It will always be higher for a 5 round sample than for a 20+ round sample (assuming all other factors held equal) by virtue of the formula. This is because the chances of error are much higher in a small sample.

Also note that if you start pulling out fliers, your stats aren't accurately representing what your load is doing. If fliers are randomly distributed, they're just as likely to show up at the chrono station at a major match as they are at practice. I recommend running multiple 20 round strings and including all rounds.

Also, for USPSA it is very helpful to convert all your velocities into PF and run the numbers that way. In the long run, that's a more practical number.

I agree. It also makes it easier to compare results with different bullet weights. In the end, what we're concerned with is making sure the number is 165+ (or 125+) at the match!

BB

[rsrocket1]

This is why I enter all my data into a spreadsheet when I get home. I also enter the bullet weight, powder name, charge, OAL, temperature and gun. For rifle rounds, I also note how far off bullseye each round landed. I have a running record of every shot the chrony captured. With the spreadsheet you can simply add a column to the string of shots and see if all of them made PF or what the muzzle energy was or even if temperature affected the load compared to another session on another day. With a spreadsheet you can also combine data from many hundreds of shots with similar loads under conditions throughout the year to see how a particular load will behave.

It only takes about 5-10 minutes to enter the data from a session and it comes in real handy when making decisions on what a "favorite" load is.