Define a 1MOA rifle

[hw101]

Hi mungo
Interesting question - I’m obviously aware of your background as an academic and skilled statistician at a leading university.
My humble opinion in this as a lay person.
To prove or disprove the rifle shots 1moa obviously the variables should be removed .. environmental and mostly the shooter. So a tube range and using a bench rest sled?
Personally, under those conditions I’d say to define a rifle as ‘1 moa’ it should shoot 95% of shots into a 1 moa group.

 

[Mungo]

Hi mungo
Interesting question - I’m obviously aware of your background as an academic and skilled statistician at a leading university.
My humble opinion in this as a lay person.
To prove or disprove the rifle shots 1moa obviously the variables should be removed .. environmental and mostly the shooter. So a tube range and using a bench rest sled?
Personally, under those conditions I’d say to define a rifle as ‘1 moa’ it should shoot 95% of shots into a 1 moa group.

I think we’re getting to a consensus that most people would accept 95% of a ‘reasonable’ sample size, with reasonable being something like >25-30 shots.

So I reckon an adequate test for most purposes would be to put it in a pipe range, and shoot a box through it. If it can put 19 out of 20 inside an inch, you’re on solid enough ground to call it a 1moa gun.

 

[paul o']

The best MOA rifle can fail with the change of climate or the driver has got the sh&ts seen it been there pmsl.
Its what happens on target that matters not how big you wave your stick ! even a crap rifle can at some point prove a worthy Opponent to another's pride and joy ££££
££££££ most of the time its the nut on the butt that defines a shot or shots.

 

[hw101]

I think we’re getting to a consensus that most people would accept 95% of a ‘reasonable’ sample size, with reasonable being something like >25-30 shots.

So I reckon an adequate test for most purposes would be to put it in a pipe range, and shoot a box through it. If it can put 19 out of 20 inside an inch, you’re on solid enough ground to call it a 1moa gun.

Absolutely agree that outliers (flyers) can’t be excluded from the sample.
Would I be right to say we can’t do a power calculation to determine sample size as we don’t know the variance of group size presently. And therefore we don’t know what our 95% confidence intervals are?
To generate a robust ‘statistical’ answer, I’d fire 100 rounds in 20, 5 shot groups and measure the groups in the described controlled conditions.
I guess that would allow you to calculate a confidence interval and give an answer.
I also guess there isn’t an accepted definition to the ‘1 moa rifle’ term is because to prove it statistically requires alot of work.

 

[borbal]

This might help

Group Statistics

I do not have SSL encryption on the website, so Google will tell you it is 'unsafe'. But go ahead and push through...

 

[Mungo]

Absolutely agree that outliers (flyers) can’t be excluded from the sample.
Would I be right to say we can’t do a power calculation to determine sample size as we don’t know the variance of group size presently. And therefore we don’t know what our 95% confidence intervals are?
To generate a robust ‘statistical’ answer, I’d fire 100 rounds in 20, 5 shot groups and measure the groups in the described controlled conditions.
I guess that would allow you to calculate a confidence interval and give an answer.
I also guess there isn’t an accepted definition to the ‘1 moa rifle’ term is because to prove it statistically requires alot of work.

We can absolutely do a power analysis, and it will be the next thing I do.

One of the reasons I’m going into this in some detail is that I’m currently writing tutorials on power analysis, and this is actually a very useful case study to hang them on!

 

[Mungo]

This might help

Group Statistics

I do not have SSL encryption on the website, so Google will tell you it is 'unsafe'. But go ahead and push through...

That’s really useful. Thank you

 

[hw101]

We can absolutely do a power analysis, and it will be the next thing I do.

One of the reasons I’m going into this in some detail is that I’m currently writing tutorials on power analysis, and this is actually a very useful case study to hang them on!

Can you do a power calculation without preliminary data from the rifle ?
And I’m not questioning you - I know you know more about stats than me. Genuinely interested.

 

[Mungo]

Can you do a power calculation without preliminary data from the rifle ?
And I’m not questioning you - I know you know more about stats than me. Genuinely interested.

Oh!

No - you need some data.

But you can simulate different scenarios to give you an idea of the sample size you would need to detect what you want to detect.

So I can set up simulated groups assuming different levels of accuracy, and work out how many shots need to be fired to get a robust answer.

That’s actually where all this started: I needed a starting definition to use when setting up the simulations that would then allow me to work out how many shots were going to be enough.

 

[hw101]

Oh!

No - you need some data.

But you can simulate different scenarios to give you an idea of the sample size you would need to detect what you want to detect.

So I can set up simulated groups assuming different levels of accuracy, and work out how many shots need to be fired to get a robust answer.

That’s actually where all this started: I needed a starting definition to use when setting up the simulations that would then allow me to work out how many shots were going to be enough.

Thanks. Honestly I think you ask a series of interesting questions.
But then I spent 12 hours one New Year’s Day working out the mathematical foundations underlying the card game ‘dobble’.
My wife was less than impressed.

 

[billgatese30]

Absolutely agree that outliers (flyers) can’t be excluded from the sample.

There's arguments for removing or leaving them in. As sample size increases there is more arguments for leaving them in, but as we know there's significant variables we can't control or influence (in this case the shooter) so while the sample size is small (25-30 shots) I would argue some may be culled especially if the shooter remarks that they fluffed the shot for instance. After all we're looking for data to predict a larger population, not assume this sample as the entire population (in which case we should definitely leave them in).

 

[oldhamstocks]

Scared to wade in here as a relative newbie, but my .308 Sako 85 Carbonlight with the fluted 20 inch barrel pretty much cloverleafs 3 shots on the 100 metre pipe range at Braidwood every time from cold (and replicates-ish using sticks at field targets out to 250 metres). That's using my Roe sack up front to rest it and using Sako Gamehead 123g factory ammo. I'd be well chuffed with that using something heavier barreled and I'm lucky if I fire as many as 3 shots when I go out stalking so I have total faith in my rifle to deliver within a few centimetres at 100 metres every time. I would have faith in using any Sako to get 1 MOA at 100 yards with proven ammo based on that incredibly non-subjective basis.

 

[Mungo]

Can you do a power calculation without preliminary data from the rifle ?
And I’m not questioning you - I know you know more about stats than me. Genuinely interested.

Thinking about statical power very quickly leads you to realise that most people who are reloading have no statistical power at all, and the charge levels they’re choosing might as well be entirely random.

To detect the really small differences in group size generated by varying the charge, you need far, far bigger sample sizes than most people use. Firing a sequence with 3 shots at each charge is fantastically pointless.

 

[hw101]

There's arguments for removing or leaving them in. As sample size increases there is more arguments for leaving them in, but as we know there's significant variables we can't control or influence (in this case the shooter) so while the sample size is small (25-30 shots) I would argue some may be culled especially if the shooter remarks that they fluffed the shot for instance. After all we're looking for data to predict a larger population, not assume this sample as the entire population (in which case we should definitely leave them in).

I’d try and remove the shooter variable as described above.
As an aside, really enjoyed reading your posts. Very well thought out,analytical and accurate. Thanks!

 

[WalkedUp]

My summary: 7 is the magic number, but 5 is the practical one. 5x5 seems to be a natural sweet spot.

This might help

Group Statistics

I do not have SSL encryption on the website, so Google will tell you it is 'unsafe'. But go ahead and push through...

 

[hw101]

Thinking about statical power very quickly leads you to realise that most people who are reloading have no statistical power at all, and the charge levels they’re choosing might as well be entirely random.

To detect the really small differences in group size generated by varying the charge, you need far, far bigger sample sizes than most people use. Firing a sequence with 3 shots at each charge is fantastically pointless.

Most people, and I’d include myself in this, don’t really understand statistics.
I’m constantly amazed at my peers commenting on academic or scientific papers but when pressed it’s clear they don’t understand the statistical methods used to derive the papers conclusions.

 

[billgatese30]

I’d try and remove the shooter variable as described above.
As an aside, really enjoyed reading your posts. Very well thought out,analytical and accurate. Thanks!

Agreed we should remove as much as possible. Also agree with Mungo, most people's 2-3 shot strings for reloading velocity or accuracy is far too small. I tried to strike the balance between cost and data accuracy by doing 10 shot strings for velocity.




As everything with statistics, its important to remember we don't dissappear up our own bum and strike the balance between perfect stats and "good enough to be as practical as we need to be". I remember once arguing with one of our research PhD's about while his new formula was statistically significantly different (better) to the current formula, in the real world it made 2mV difference and we needed 200mV. Statistically significant it may be but who cares when in the context of the real world it wasn't worth the extra 3 hours of processing time which was a significant increase to the production cost.

 

[billgatese30]

Scared to wade in here as a relative newbie, but my .308 Sako 85 Carbonlight with the fluted 20 inch barrel pretty much cloverleafs 3 shots on the 100 metre pipe range at Braidwood every time from cold (and replicates-ish using sticks at field targets out to 250 metres). That's using my Roe sack up front to rest it and using Sako Gamehead 123g factory ammo. I'd be well chuffed with that using something heavier barreled and I'm lucky if I fire as many as 3 shots when I go out stalking so I have total faith in my rifle to deliver within a few centimetres at 100 metres every time. I would have faith in using any Sako to get 1 MOA at 100 yards with proven ammo based on that incredibly non-subjective basis.

And as we argue the finite minutiae of applied stats, this is the sort of real world performance that counts. Having the performance and confidence to reproduce these results in the field = dead target which is what matters!

 

[ejg]

Probably need at least ten.
ten barrels shot out to also figure out when is your 1 MOA rifle not a 1 MOA rifle anymore... change load and do it again.

I am happy with 3 shot groups, a few 3 shot groups and if they are all behaving I go hunting. Check group size /velocity every now and then as velocity often gets faster after a while. Did enough statistics in my life, told my old boss I'd rather be under a bridge with a bottle than be employed in any statistics job.
edi

 

[RCS Deer Management]

so the human factor was the error as I could not repeat the other 2.
Fact...

[/QUOTE]

I’m sorry, I disagree. 3 shots with two touching and one slightly further away is so invalid statistically that you cannot say that the only reason the 3rd wasn’t touching is down to human error. I wasn’t going to point this out until I saw you put ‘Fact’ behind something that isn’t a fact