### Mean Radius vs. Group Size

Posted:

**Tue Feb 24, 2015 9:47 pm**I'm in the process of converting my load testing over to mean radius rather than group size.

The mean radius method is nothing new, it's been the standard procedure for military ammo for ages. But it is rarely used by civilians because it's a pain in the butt.

So why use mean radius, if it is a pain in the butt? Because I try to PROVE things, and it's tough to prove a statistically significant difference using conventional group shooting. Three groups won't do it. Six groups are marginal. You really need at least 10 groups to prove statistical significance. That's a lot of shooting.

Group shooting gives you only one data point for every group, but mean radius gives you one data point for every shot.

For example, if I shoot four 5 shot groups, that gives me 4 data points, not enough to prove anything. But if I take the same 20 cartridges and shoot two 10 shot groups and calculate mean radius, I get 20 data points, which is often enough to prove statistical significance.

Here's a link to a good explanation of mean radius. It's also discussed in Hatcher's notebook.

There is no exact formula to convert between mean radius and group size, but in practice, a 10 shot group tends to be 3 to 4 times the mean radius. For example, a recent session with a TC 357 rifle produced a 0.55" mean radius and 10-shot groups averaged 2.03", or 3.68 times the mean radius. If that ratio held constant, I'd need a 0.27" mean radius to shoot an MOA 10-shot group.

FYI I measure the coordinates of each bullet hole the old fashioned way (it helps if your target has a grid background) and then use a spreadsheet to crunch the numbers. I'm still tweaking the spreadsheet but if I ever get it perfected I'll share it, or perhaps convert it to a web page so everyone can use it. You can also buy software to help you measure mean radius.

The mean radius method is nothing new, it's been the standard procedure for military ammo for ages. But it is rarely used by civilians because it's a pain in the butt.

So why use mean radius, if it is a pain in the butt? Because I try to PROVE things, and it's tough to prove a statistically significant difference using conventional group shooting. Three groups won't do it. Six groups are marginal. You really need at least 10 groups to prove statistical significance. That's a lot of shooting.

Group shooting gives you only one data point for every group, but mean radius gives you one data point for every shot.

For example, if I shoot four 5 shot groups, that gives me 4 data points, not enough to prove anything. But if I take the same 20 cartridges and shoot two 10 shot groups and calculate mean radius, I get 20 data points, which is often enough to prove statistical significance.

Here's a link to a good explanation of mean radius. It's also discussed in Hatcher's notebook.

There is no exact formula to convert between mean radius and group size, but in practice, a 10 shot group tends to be 3 to 4 times the mean radius. For example, a recent session with a TC 357 rifle produced a 0.55" mean radius and 10-shot groups averaged 2.03", or 3.68 times the mean radius. If that ratio held constant, I'd need a 0.27" mean radius to shoot an MOA 10-shot group.

FYI I measure the coordinates of each bullet hole the old fashioned way (it helps if your target has a grid background) and then use a spreadsheet to crunch the numbers. I'm still tweaking the spreadsheet but if I ever get it perfected I'll share it, or perhaps convert it to a web page so everyone can use it. You can also buy software to help you measure mean radius.