Joined

·
14,406 Posts

Fortunately, all the number crunching can reveal things that would be hard to see otherwise. So, here's kind of a summary of the results of the three statistical tests I did.

First, it really bothered that I was getting great 3-shot groups but the composites were not impressive as can be seen here...

3/10/2023 10 groups: 1.320 MOA / average size of the 10 groups: 0.587 MOA

3/15/2023 15 groups: 1.553 MOA / average size of the 15 groups: 0.562 MOA

3/16/2023 16 groups: 1.602 MOA / average size of the 15 groups: 0.536 MOA

Hmmm, near 0.5 MOA average group sizes and yet composites about 3 times that - is something going on I haven't caught? Let's look at plots of the groups versus vertical displacement. That is, how far is the group from the POA.

See anything common to all three? Yep, you got it - the vertical position of each set is trending downward. That would certainly strongly contribute to large composite groups!

This may be due to barrel heat from so much shooting. I thought I was shooting slowly enough that heat wouldn't be a problem. I could comfortably lay my hand on the barrel (near the muzzle) and it was warm, but not hot. I was shooting at a pace of about 1 round per 30 seconds. That may be too fast to prevent heat build up near the chamber.

How I see this is that the gun/load is shooting much better than the composites suggest. Let's look at some tables...

The tables have a lot of data in them but we only need to look at part of the data. I'll start with the +2 SD data. Why is the +2 SD important? In statistical analysis, the

**+/-2 SD points are where 95% of the data should fall**. We really don't care about the -2 SD that would just indicate really small group sizes and what we're concerned with is BIG group sizes. Without getting into the math, I'll just say that there is only a 2.5% probability that a group will be large enough to fall outside the +2 SD point. Know why it's only 2.5% and not 5%? The other 2.5% is below the -2.5 SD point.

OK, there are three ways we can analyze group sizes, composite, average, and +2 SD. I was really big on the composite until I started to see problems with it. One problem is it addresses both group size and positional relationships of the groups.

I picked these groups because they are well under 0.5 MOA, but when you look at the composite of these three excellent groups, it suggest a different story. The composite shows a 1.052 group. The size isn't larger because the groups got larger, it's because the position of the groups varied.

While the composite is interesting, it is worst case and it does not give us any indication how likely (probability) it is that size group would occur. What if the reality was that composite only had a 1% probability of happening. Would you care? I wouldn't; I'd want to know more closely what I could expect consistently.

**So I don't much like the composite analysis anymore.**

So what about the average? Statistically, the average is where data will appear about 50% of the time. Some groups will be larger and some smaller and we still don't know how probable we are to get a larger group than average.

Which brings us to the +2 SD method. Where the composite deals with both the groups' size and position, and gives us a worst case, and no probability, the +2 SD method deals ONLY with group size and does give us probability of occurrence. Let's look at the tables above at the +2 SD column. As you can see, the +2 SDs are 0.944, 1.063, and 0.901 MOA. That means that there is a 97.5% probability that our groups will be equal to or less than those values.

**So in essence, the +2 SD gives us precision, but not accuracy.**

OK, let's nail this down. In the third table, we have a +2 SD of 0.901 MOA. Since this was a 45 shot group, we can expect 44 (97.5%) out of 45 shots to be less than or equal to 0.901 MOA. Here's the distribution chart -

**notice one group lies beyond the +2 SD line.**

We do have to be careful here because that dot beyond the +2 SD line is a group, not a single shot. So, I looked at the group that generated that point and it has one shot that was low. The other two hits measured 0.443 MOA. So it was indeed one shot that caused the group to be larger than 0.901 MOA.

Whew! I'm tired - this was supposed to be a quick post - didn't work out to be so quick - or short. Gotta go eat now.