In rifle cartridges designed for large rifle primers, changing primers usually results in only small if any changes in pressure and velocity, but they can produce significant differences in velocity SD. In rifle cartridges using small rifle primers and in some pistol cartridges for either size primer, there can be more significant differences.
In the 223/5.56 specifically, in a 2006 Handloader article series, Charles Petty produced a velocity change with 55-grain V-max bullets over a fixed charge of Reloader 10X of 3150 to 3300 fps just by changing primers. That's equivalent to about 5% change in the powder charge, according to QuickLOAD. In the 22 Hornet, velocities can not only change significantly, but they can also become quite erratic when the primer has too much power. This appears to be caused by a primer that is too powerful, starting to unseat and move the bullet before the powder charge is burning fast enough to do the job. This means the bullet is in differing proximities to the throat when the powder does take command of the pressure, causing an associated peak pressure variation. The same can happen with pistol cartridges when the powder space is small.
The way I test for this is to try different primers and see which one produces the smallest velocity standard deviation for a 30-shot sample. That's a lot of shooting but it gives you a pretty reliable result. For smaller samples, you really want to perform a separate test to see if the difference is real or random. Usually for 95% (0.95 probability) confidence. Student's T-test is the standard method and it is built into Excel's solvers, but you will have to watch a YouTube video or two to know how to interpret its output numbers.
The reality is that the bigger the difference in SD, the smaller the number of shots you can get away with in your sample, but we have to dig into the complexities of statistics to know how to determine that number. Also, be aware that the standard method of calculating sample standard deviation that is built into your chronograph gets less reliable than some other methods for samples smaller than eight.
https://www.shootingsoftware.com/ftp/Perverse%20Nature%20of%20SD.pdf for samples smaller than eight, you divide the extreme spread by a fixed coefficient to get a better estimate.
If you are in a situation where you have to use a smaller sample than eight, you can compare the machine calculation to the result from Bramwell's method, and if they aren't close, refire the test. Assuming that refire gives you a combined number of samples that exceed eight, add the squares of the two machine SDs from the two samples and take the square root of that sum. That will give you the machine SD for the combined shots. If you do the same with the SD's arrived at by Denton's method, at that stage the results should be much less different.
To get sigma (population SD) estimate:
Code:
Sample Size Divide ES by
2 1.128
3 1.693
4 2.059
5 2.326
6 2.534
7 2.704