Garmin ES/SD calculations vs Excel

[RegionRat]

Not sure how we got from trying to help folks understand the difference between sample-based values versus population-based values for SD, and now we are veering off the tracks with the statements about ES not being useful.

Folks the ES is just as important as the other stats and taking your eyes off of it in favor of the SD is just as wrong as not understanding the value of the SD or average.

The advice I am giving you is to watch both the SD and ES together and relate them to the average for balance and proportion.

To put it very simply, without doing complex stats to determine if you are in trouble isn't very hard.

To know if you are seeing warning signs in your AVG, SD, and ES, trust your eyes, these things should be balanced and proportioned.

Mother Nature is cruel most of the time, but sometimes she helps us too.
When she gives us a balance and symmetry, then we can see quickly if samples are out of balance or off center, just by eyeball.

If your ES doesn't sit balanced on your average, you might be in trouble.

If your SD and ES are not proportioned in terms of the ES being 4X to 6X times the SD, then you might be in trouble.

That is a very simple multiplication, and you only need to give it a rough look to know when something is wrong. A skinny test can mean the SDx4 = ES, and well populated test and the value approaches SDx6=ES.

It really isn't a guarantee you are locked in golden when your SD is 4X to 6X your ES, but the other way around is known to be trouble in that the ES is telling you something is wrong or you are under-sampled, or both.

A tight gun/load may take less than 15 samples to show you a decent stable SD, and a loose one takes 30 or more.

Here is an example. Suppose your average is 3000 and your ES is 60 and your SD is 10. The idea is your high and low values should sit roughly at 2970 and 3030. Your SDx6 = 60 Things are in balance and proportion so far.

But if your average is 3000 and your SD is 10 but your ES is only 20, something is wrong and you are probably under-sampled. The next time you shoot, you will see something change almost guaranteed.

The ES tells you plenty. If your average isn't centered, or if your SD isn't proportional, something is wrong.

Don't ignore the ES, it is just as important as the average and the SD. Carry On.
Merry Christmas and Happy New Year!!!

 

[Doom]

Not sure how we got from trying to help folks understand the difference between sample-based values versus population-based values for SD, and now we are veering off the tracks with the statements about ES not being useful.

Folks the ES is just as important as the other stats and taking your eyes off of it in favor of the SD is just as wrong as not understanding the value of the SD or average.

The advice I am giving you is to watch both the SD and ES together and relate them to the average for balance and proportion.

To put it very simply, without doing complex stats to determine if you are in trouble isn't very hard.

To know if you are seeing warning signs in your AVG, SD, and ES, trust your eyes, these things should be balanced and proportioned.

Mother Nature is cruel most of the time, but sometimes she helps us too.
When she gives us a balance and symmetry, then we can see quickly if samples are out of balance or off center, just by eyeball.

If your ES doesn't sit balanced on your average, you might be in trouble.

If your SD and ES are not proportioned in terms of the ES being 4X to 6X times the SD, then you might be in trouble.

That is a very simple multiplication, and you only need to give it a rough look to know when something is wrong. A skinny test can mean the SDx4 = ES, and well populated test and the value approaches SDx6=ES.

It really isn't a guarantee you are locked in golden when your SD is 4X to 6X your ES, but the other way around is known to be trouble in that the ES is telling you something is wrong or you are under-sampled, or both.

A tight gun/load may take less than 15 samples to show you a decent stable SD, and a loose one takes 30 or more.

Here is an example. Suppose your average is 3000 and your ES is 60 and your SD is 10. The idea is your high and low values should sit roughly at 2970 and 3030. Your SDx6 = 60 Things are in balance and proportion so far.

But if your average is 3000 and your SD is 10 but your ES is only 20, something is wrong and you are probably under-sampled. The next time you shoot, you will see something change almost guaranteed.

The ES tells you plenty. If your average isn't centered, or if your SD isn't proportional, something is wrong.

Don't ignore the ES, it is just as important as the average and the SD. Carry On.
Merry Christmas and Happy New Year!!!

I knew that somewhere along the line I knew we would disagree! Well, maybe not disagree but I think that maybe some additional info might be useful.

The ES relationship is still a very strong function of the sample size. Looking at ES for 3 shot or a 5 shot group and trying to assign a 4x or 6x can be hit or miss depending on a number of factors. The sampling odds are that the number is going to be very biased to the low side because the majority of the potential samples (68%) is biased to the 1 SD. This is true for both SD and ES. This is why it can make sense to stop sampling when the first two shots show a high ES. Also, in the case of the 3 or 5 shot samples the ES makes up 67% of the SD for a 3 shot sample. and 40% of the 5 shot sample hence the SD is heavily biased towards the ES. At least that is what usually happens. Actually looking at ES and ignoring the SD probably makes more sense with a 3 shot and maybe even a 5 shot sample. But with 5 samples a little less than 2x to around 2.7x seems to generally start coming into play, 10 shots will likely range from 2.5 to about 4, and it isn't until about 15 samples that generally 3x to about 4.5 x is approached most of the time. It also seems to start showing the "balance and proportion" you refer to. That "balance" and precision meaning that the two extremes fall approximately the same distance from the average (mean). These ranges are not absolute and will vary as you have noted.

To see a ES approaching 6x is likely to not show up very often as to see it requires pulling 2 samples that represent only 0.3% of a large population at in the same sample set.

Back in the 1960s Frank Grubbs wrote a paper called "STATISTICAL MEASURES OF ACCURACY FOR RIFLEMEN AND MISSILE ENGINEERS." In it he looked at several measures of precision such as mean radius and circular error probable and determined a relationship for each measure that actually relied on the ES to provide a estimate of the population (true) standard deviation based on the ES. While the subject was related to group size a similar analysis would. likely apply to velocity. This paper is highly technical but his conclusions are interesting.

 

[RegionRat]

I knew that somewhere along the line I knew we would disagree! Well, maybe not disagree but I think that maybe some additional info might be useful.

Not a disagreement, you gave more reasons to watch all three values, the AVG, the SD, and the ES.

In the working world we don't stop with those three, there are several other things we watch for signs of trouble with the guns and ammo too.

Don't worry, if you are really looking forward to a disagreement, we can argue about single barrel Scotch versus multi-cask Scotch.... or maybe Macanudo versus Cohiba?

 

[Doom]

Not a disagreement, you gave more reasons to watch all three values, the AVG, the SD, and the ES.

In the working world we don't stop with those three, there are several other things we watch for signs of trouble with the guns and ammo too.

Don't worry, if you are really looking forward to a disagreement, we can argue about single barrel Scotch versus multi-cask Scotch.... or maybe Macanudo versus Cohiba?

Well, there you go. You can talk scotch all you want but my taste buds favor a flavor from Tennessee with a Cohiba!

 

[CharlieNC]

Fewer shots are required to find a stable poi node based on a target than chasing velocity stats to achieve the same result.