I am an amateur trying to recall high school/college statistics. I'm looking at shooting group analysis. I can identify the center of the group and consider the shots to represent random samples of variances from this center. I can calculate for each sample shot the distance in mm from this sample center. I can calculate the extreme spread of these. Can I calculate the mean and standard deviation in the same, conventional manner?

I'm getting confused because I'm used to only what I will call one dimensional statistics. Velocity data would be an example of this. Each shot has just one velocity number. I can calculate sample mean, SD, ES etc and confidence intervals in these. I can use a t-test to see if I can be confident there's likely a real chance that two sample sets represent different underlying behaviors.

If I think about the cluster of observations on a 2D plane, I think of the 'mean' is the center of the group with sample variances from mean in both distance and angle. The distance from center is almost the first derivative of an (x,y) location on the 2D plane versus the center (a distance ignoring angle). (I think things simplify if we make the assumption that angular variance around the center is random but I'm not sure.)

My goal is to get to confidence intervals and t-test analysis (which I already use on the velocity data). Which group has the smallest variance from center? What's the 95% (or other) confidence interval in this deviation? Can I be x% confident that sample group A represents a different underlying population behavior than sample group B?

I don't care that there might be a shift in the center of each. (This can easily be corrected for by shifting the point of aim.) My only concern is the relative variances/dispersion between the two.

I my description of this makes sense! I appreciate any help.

Regards

Steve