Two different SD's. Which one is correct?

[LkeAF]

I shot a group the other day for a gun that I'm getting ready to sell and was trying to shoot each round with a cold barrel. I was tight on time and didn't get to finish the 5 round group. I shot a three round group and then went back a few days later and shot the final two rounds. There was @ 15 degree ambient temperature difference, so I realize my 5 shot group numbers won't be as good as they would have been had I been able to shoot all 5 the same day.
That said, what I'm trying to figure out is why my 3 shot group had one SD on my MagnetoSpeed, but has a different number if I plug the velocities into an online SD calculator.

The MagnetoSpeed info is shown in the photo. When I plug those velocities into the online SD calculator, I get an SD of 1.154

Which one is accurate? Why the difference?

 

[The Oregonian]

Standard deviation is a math formula and my math gets me to 1.154. Not knowing how MS calculates theirs I'd go with 1.154.

That being said, the difference between the two is meaningless.

 

[ShtrRdy]

The sample size is so small that it means nothing.

 

[Aloeus]

I suspect its using decimals that it isn't displaying on screen. With such a tiny sample size and such a tight grouping, rounding up can change the calculation.

 

[LkeAF]

The sample size is so small that it means nothing.

Naturally a larger group give you better info. My question was about why the difference in the numbers.
The next two rounds (fired 5 days later with temps @ 15 colder) were 2972 and 2976. According to the online calculator that gives an SD of 3.03 for a 5 round group. Maybe not good enough for some, but I'll shoot that all day long.

 

[LkeAF]

I suspect its using decimals that it isn't displaying on screen. With such a tiny sample size and such a tight grouping, rounding up can change the calculation.
View attachment 521164

That makes a lot of sense. I bet you're right.

 

[orkan]

Now be honest... you're only asking because you want to show off your SD.

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[DocUSMCRetired]

You need a 20 round string to have an accurate SD. 3 rounds is statistically and reliably meaningless.

 

[Hugnot]

Great start with the nice Magneto Speed! Save data, then shoot 10-15 more. I save my data on PC & use spread sheet to develop it. Having 3 or 4 times more data will provide a better assessment. I don't have a clue of what happens inside that tiny chip jammed inside a one function button box with a 9-volt battery.

Get a good spread sheet like:

Apache OpenOffice - Official Site - The Free and Open Productivity Suite

The official home page of the Apache OpenOffice open source project, home of OpenOffice Writer, Calc, Impress, Draw and Base.

www.openoffice.org

Transfer crony data to spreadsheet, run analysis without going on-line, use canned stat functions like VAR & SD, save files, backup using One Drive.




Note, the average displayed using the tiny Magneto speed display is truncated to a whole number - inadequate. The average should be displayed as a fractional number having more precision, like 2978.667. Displayed individual fractional velocity values are sort of witless.

The variance is calculated by adding succession of values of the square of each velocity minus the average of all velocities, then dividing that sum by the number of cases.

The SD or standard deviation is the square root of the variance.

At this point it can be seen why subtracting each velocity by 2878.667 then squaring it then adding a succession of results would be different than subtracting each velocity by 2879 then squaring it then adding the results.

3 cases, TVal. = 2.776, est. Var. = 1.333, 12 cases TVal. = 2.145. est. Var. = .970. Yes, more data is better.

Suppose upon shooting 3 more 3 shot stings having velocities of 2978, 2980 & 2978 the average would be 2978.66, unchanged but more cases. The spread & SD would be the same but having more cases (a lower 95% probability T val.) an improved projection of velocity averages of highs & low should a big batch of ammo be produced. Mean differences less.

Think of a nice pointy bell-shaped short tail curve No need to discard data - just add data.

 

[Doom2]

The answer is you are inputing numbers that are rounded into the on-line calculator while the MS is using higher precision numbers as @Aloeus showed.

 

[Hugnot]

The answer is you are inputing numbers that are rounded into the on-line calculator while the MS is using higher precision numbers as @Aloeus showed.

Magneto Speed calculated SD using some unknown values. What values did the Magneto Speed actually use to come up with a SD of 1.4? Magneto Speed shows a spread of 2 fps.


Values of, 2977.8, 2978.1 & 2980.4 were plugged in for SD = 1.161.



Values of 2978, 2980, & 2978 -- SD = .943
Equal SD values of .943 with my spreadsheet & the on-line calculator using whole numbers.

I was unable to come up with a SD = 1.4 using 2977.8, 2978.1, 2980.4. All 3 calculations show an equal mean value of 2978.8 but Aloeus' has SD = 1.4 -- might be a problem with that. The 1.4 might have been pasted in/over.

M-Speed comes up with a SD of 1.4. I don't have much confidence in the MS SD of 1.4.

Use more values. Save all data & keep running the On-Line calculator, bigger data sets will provide more useful stats. Difficult to say if sample distribution is a normal distribution with only 3 data points.

Many think SD means a behavior deficit.

 

[Aloeus]

Magneto Speed calculated SD using some unknown values. What values did the Magneto Speed actually use to come up with a SD of 1.4? Magneto Speed shows a spread of 2 fps.


Values of, 2977.8, 2978.1 & 2980.4 were plugged in for SD = 1.161.



Values of 2978, 2980, & 2978 -- SD = .943
Equal SD values of .943 with my spreadsheet & the on-line calculator using whole numbers.

I was unable to come up with a SD = 1.4 using 2977.8, 2978.1, 2980.4. All 3 calculations show an equal mean value of 2978.8 but Aloeus' has SD = 1.4 -- might be a problem with that. The 1.4 might have been pasted in/over.

M-Speed comes up with a SD of 1.4. I don't have much confidence in the MS SD of 1.4.

Use more values. Save all data & keep running the On-Line calculator, bigger data sets will provide more useful stats. Difficult to say if sample distribution is a normal distribution with only 3 data points.

Many think SD means a behavior deficit.

OK...I definitely am not going to fake an online calculator result for this thread lol.

You were using population stdev in that online calculator, I was using sample, and since I basically fiddled with the decimals to make a sample stdev come out to about 1.4, a population stdev would have a different result. I'm also pretty sure, but not certain, that the MS uses sample, and the garmin uses population, but I might have the reversed. Regardless, my point that the MS is using numbers with a decimal we can't see stands.

As for excel, I can't tell which formula you were using, but I came up with similar numbers to the online calculator.

 

[Justice1327]

Some smart folks here.

 

[LkeAF]

Now be honest... you're only asking because you want to show off your SD.

View attachment 521171

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Eating lunch and just about shot turkey soup out my nose on that one . Let's just say that if it holds together once I string it out to the required "20 shot string or it's as useless as an inflatable dart board", I'll be sure to come back here and show it off! I was just curious why the difference, but I think Aloeus nailed it right off. I hadn't even thought about the rounding.