This may be getting in the weeds, but my background is in statistics for research.
Assume that each shot is from a population of shots with a bell-shaped distribution peaking at the mean.
Say you shoot a 10-shot group today, with an average muzzle velocity of 2900 fps, standard deviation of 10 fps.
You try a different load the next day, 10-shots with an average muzzle velocity of 2850 fps, standard deviation of 10 fps.
Is the first day's load significantly faster than the second day's load? Yes
The 90 percent confidence interval is 40 to 60 fps based on these 2 sample days with the sample difference of 50 fps.
Say you shoot a 10-shot group today, with an average error of 0.50 inches, standard deviation of 0.10 inch.
You try a different load the next day, 10-shots with an with an average error of 0.70 inches, standard deviation of 0.10 inch.
Is the first day's group significantly tighter than the second day's group? Yes
The 90 percent confidence interval is .10 to .30 inches with the sample difference in means of 0.20 inch.
Say you shoot a 10-shot group today, with an average error of 0.70 inches, standard deviation of 0.50 inch.
You try a different load the next day, 10-shots with an with an average error of 0.90 inches, standard deviation of 0.50 inch.
Is the first day's group significantly tighter than the second day's group? No, there is too much variation.
The 90 percent confidence interval is -27 to +.67 inches