There are a number of problems with the traditional way of evaluating firearm accuracy (it's really precision - accuracy is achieved by adjusting the sights) using the "group size" method. (I recognize this thread is in the handgun section, but group size analysis is really something that is done more seriously with rifles, even though the same procedures work for either.)
The first is that, no matter how large your group, you're essentially only using the information provided by the two shots that fall farthest apart. There's much more information available if you can somehow factor in what the other shots are telling you.
Second, the group size is unavoidably linked to the number of shots you fire - on average, 3-shot groups from the same gun must be smaller than 5-shot groups, which must be smaller than 10-shot groups, etc. Related to that is the fact that the group can never get smaller as you add shots to it, only larger. There's something inherently unsatisfying about that.
Third, and perhaps of lesser concern, you can only compare groups of the same number of shots to each other. If you shoot a 5-shot 1-MOA group with one gun and a 3-shot 1-MOA group with another, which is more accurate? What would you expect either gun to do if you shot a 10-shot group?
Finally, how do you really use the information provided by the group size method for determining practical accuracy in the field? For example, if you have a gun that averages .75-MOA 5-shot groups, what's the statistical probability that a shot taken at 300 yards will strike a target 6 inches in diameter? There's no way of answering that question unless you have more information - and that information is available to you if you want to use it.
Oh - one more. How do you use the information from your group size to adjust your sights so the gun is hitting where you want it to at the distance you're shooting at - not by guess and by gosh, but properly and rationally?
There is a better way, but like most better ways it involves a bit more work. Here's how I evaluate my groups:
Fire a group of any size at an aiming point, then use a ruler (I find digital calipers are actually easier) to measure the distance (i.e., the distance from the aiming point to the center of the shot hole) horizontally (on the x-axis) and vertically (on the y-axis) of every shot. Following the established procedure for cartesian coordinate systems, shots to the left of the aiming point take a negative distance on the x-axis, and shots below the aiming point take a negative distance on the y-axis. You end up with the coordinates of every shot location on a two-dimensional plane.
With that information, you're set up to really evaluate what your gun is doing. The group center is simply the average of the x-axis measurements and the average of the y-axis measurements. So, for example, if you end up with (1.5 inches, -.5 inches) then you know that your gun is shooting, on average and with no guessing, 1.5 inches to the right and a half inch to the left. Using that information you can adjust your sights exactly.
Then, using the Pythagorean theorem, you can calculate the distance of every shot from the group center that you just determined. To do that, you simply subtract the x-axis position of the group center from that of the shot in question, then do the same for the y-axis position, square both quantities and add them together, and then take the square root. All very easy to do with a calculator or, better still, if you set up an Excel spreadsheet.
Once you have the deviation from center for each shot, you can calculate the average deviation, which is a much better evaluation of accuracy than group size, and suffers from none of the problems that I laid out earlier. And, although it's a bit beyond this discussion, using some basic statistics, you can use the standard deviation of the group of deviations from center to determine the probability of striking any size target at any range.