Brent,
  Well, I see we're getting closer and closer to agreeing on the same points. Glad I'm geting you trained! 

  Seriously.... Will you be setting up that Excel program on your web site, and will it be set up so we can use it?

PETE

Brent,
  Well, didn't mean to upset you so much with my statement of coming around...... partially ..... to your way of thinking.    Hope you didn't hurt yourself!! Between your explanations here and that FAIRLY clear article in PS I can see where SD would be better than ES's. I'm not gonna commit on statistical analysis (SA) being useful in all phases of shooting tho, so don't get your hopes up to far.

  I realise that setting up a web page with all the things you need in order to show us the "true way" is not gonna be an easy task. I have no idea how you're gonna do it, and I've set up my own web site. But figure if it can be done you'll be able to do it. We ain't going anywhere so do what you can, when you can.

  On your .38/55. Your problem is the part where I think SA really falls down. As you say, your SD's are great, but the results on the target aren't. There is no way SA can help you there. It can only show you what you can expect from the loads you have prepared. Your problem is just gonna have to take a lot of grunt work to figure out. Hopefully we can find some of the answers this weekend.

PETE

Joe, 
If there is controversy in the stats world, it surely is not with respect to sample sizes for simple tests such as we do.  Baysian statistics vs standard parametrics might yet be considered a "great" controversy, but we ain't there.

Next, how do you know if your groups are not round?  If one group is a 1.5" by 2.5" group unround? Could SDs give you a hint about that?  You bet.  But to know that a group is unround is something that can be dealt with statistically and it's not even that hard.  - essentially, you would compare the mean displacement from the group's center in the horizontal dimension with the mean displacement in the verticle dimension.  A conventional two-sample t-test (comparison of means) would suffice nicely.   

Since you have taught statistics - you know that distributions have infinite tails, and you know that the probably of finding a datum in any sample of size whatever from the extreme of either tail is totally dependent on sample size.  Hence it is not a very useful measure.  Also, having obtained a range or ES, you then procede to do what?  You cannot use it in a t-test, or an Anova, or much of anything.  You could use a bunch of range estimates in a formal statistical test, but the distributions of such tests are not known to me, and I have never seen anyone do such a thing.  You will not find it in any stats text that I'm aware of.  Think of it this way, an SD uses all the information contained in each and every shot to characterize a variance (square of the SD).  Variance is a property that is very very well understood but statisticians.  SEs use information from only 2 shots regardless of how many you shot.  And, it tells you nothing about any distribution-defining parameter.   

Perhaps the best thing for you to do sometime, besides pulling out your old stats texts and looking at simple parametric comparsions of means (t-tests being the most obvious and simple, ANOVA being a possibility as well I suppose) would be to shoot 100 rounds or so, and plot SD for the first 2 shots, the first 3 shots, the first 4 shots, etc. up to 100 shots, and see what happens.  It is not "crazy".

FWIW, I have now written a program that will allow you to enter all the shots from a pair of targets and provides mean and SD estimates for the distances of each shot from the group center and also calculates a simple t-test comparison of means for a 1-tailed hypothesis testing (is my new load better than my old reference load?), estimating approximate confidence you can have that the two loads do indeed differ.

I will eventually post that software and a tutorial, example and description of what and why this is done on a website.  But right now, I'm going to go out and make a 100 shot comparison of Lapua Midas L and Wolf Match Extra ammo to decide once and for all, which is better.

Adios,
Brent

Dale, perhaps you are right.  I'm not so sure that lot to lot variation is quite as real as it often is credited for.  Again, because I'm not confident, or even aware of the data from whence these conclusions come.   

But I am pretty sure that different BRANDS of ammo are quite different.  For one thing, Lapual Midas L uses an oversize bullet relative to all the other ammo that I'm aware of.  Wolf Match Extra hits about 4" higher on the target at 100 yds so it is presumably considerably faster.  I'm willing to wager that whatever the batch to batch variation, the brand to brand variation is greater, and that is where I'm going to start.   

FWIW, I got in 45 rounds of each brand of bullet this morning before the rain arrived and with it wind.  Until then, it was darn fine shootin'.  Now to see what I actually go for results.   

Brent

Joe b.,

  I pretty well agree with your summation as I've argued that math isn't altogether useful for determining accuracy or reliability of any given load.  Personally I've never seen the best load SD-wise shoot the best. You have to have a good SD/ES but that doesn't mean it shoots the best.

  But you're losing me when you say if a group isn't round the process isn't in control. What do you mean by process or control..... The load isn't good, or I'm not in control for having shot a non round group?

  I'll freely admit what you guys are talking about is WAY beyond my 8th grade education, but if I get what you're talking about as far as "round groups" go, it means to me an actual group that's round. Doesn't happen that often in the real world just thru normal distribution of the shots, and the myriad other factors effecting a group. A case in point is target #1 that I put up on my web site. The measurement shown is 9/16" but if you measure across the next widest C to C it's also 9/16", yet that is far from being a round group.

  The SD of target #2 suggests that all other groups shot with this load/alloy have a pretty good confidence level that it will repeat. And in fact it does, most of the time, thru using that combo as a reference for all other testing. SD also bounces around quite a bit, as a group I shot with that combo had half the SD of the above, and the group shows it, being about half the above, altho it is strung out horizontally.

  So somewhere you're leaving me behind here, unless round to you means something it doesn't to me.

PETE

We say that the process (shooting the gun) is "in control" when the measurement of the output is kind of distributed normally, the bell curve. For groups, that would mean that the groups are round. Now round is sort of subjective, but we all know exactly what I'm talking about. You know a round group when you see it, and a non-round group too. Wednesday I shot a M54 Winchester 30/30 at 100 yds with 311299, and a contender 7TCU at 50 yds with 139 Hornaday. The 30/30 load is what I shoot in my SS bench gun/martini. The M54 averaged 1.192" for 8 "round" groups, the contender shot 1.975", 2.0" and 2.15" groups that were maybe twice as high as they were round. 
The 30/30 was "in control", the 7TCU was "out of control". Something other than random variation was affecting the pistol, my guess is that there isn't enough powder-the ignition is varying, and MV varies. The pistol doesn't have one process going on, it has a maybe 1400 fps process, a 1450 fps process, a 1500 fps process.....
There's no statistics applied to the pistol that makes sense.
The process is out of control.
The traditional CBA/ASSRA "oh shit" group has 4 in a single hole, and the fifth out toward Cleveland somewhere. The process is out of control-something happened, and if we can find out what that something is, we can fix it. Exotic measurement techniques won't help.

joe b.

Brent;

>>>But I am pretty sure that different BRANDS of ammo are quite different.  For one thing, Lapual Midas L uses an oversize bullet relative to all the other ammo that I'm aware of.  Wolf Match Extra hits about 4" higher on the target at 100 yds so it is presumably considerably faster.  I'm willing to wager that whatever the batch to batch variation, the brand to brand variation is greater, and that is where I'm going to start.   <<<

I am certainly in agreement here. My previous statement was predicated on the fact that I have considerable problems trying to fine tune my .22 ammo selection. I buy a small quantity of various brands and lots of ammo. By the time I get to the range on a "good" day, select which is best, no more of that particular lot is available. Sheesh!!

With a tuner on a bolt gun, at least you can "help" a "not so perfect" selection. However, with Single Shot rules , I cannot use a tuner so I am stuck with brand selection. I finally give up in disgust and just buy a case or two of what "looks good". Not really the best way around it, but there it is - the REAL world.

Dale53

Joe B,
I wrote another long dissertation concerning each of your points.  Of course, it was "too long" to post, according to the damn websoftware.  Told me to go back and modify it, and, of course, there was nothing there to go back to.  

But really, it was a waste of my time anyway, since you already know all about statistics and how they are so damn useless.  

But since you know all this stuff that I surely don't, perhaps you can tell me which of the targets on this webpage were made with a gun that was "in control", or out of control - horizontal, or out of control - verticle?  Cause w/o stats, I surely cannot tell...

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Brent