First, for anyone confused, what James is evaluating is precision, not accuracy. The chart below shows the difference. Precision is group size, and accuracy is group placement. Unless the sight is loose, a good load for a gun will show good precision. Good accuracy can then be achieved by adjusting the sights.
James handed me the basic data in the form of how many millimeters (mm) from the point of aim (POA) that each bullet hole was vertically, and how many mm from the POA each hole was horizontally. I used the convention of up and up and right as positive and down and left as negative. Below is a plot of the average points of impact (POI's) for each of the 3-shot groups. You just average all the horizontal numbers for each group and average all the vertical numbers for each group and use this as the average POI. I also found the average POI for all 15 rounds combined (red X) and inserted a bullseye as the aiming center indicator. Since James was shooting at 100 meters (m) rather than the 100 yards we usually used, I converted these to minutes of angle (moa) which both ranges would have in common.
At: 100 m, 29.09 mm = 1.00 moa
My original intent was to combine the groups in sets of three to improve statistical significance, but with only five groups and the fact there is a 0.5 grain jump between groups 2 and 3 rather than the 0.4 grain step used in the other changes, that seems unproductive. Instead I used Student's t-test to evaluate significance of differences in group size and location. More on that in a moment.
I also found the difference in radial distance of each group average from the average location for all groups and plotted this below (blue line and points). The flat spot (least change between loads) then becomes exaggerated. The second plot (red) is just another way of showing the same thing. This time the line is the slope of change in distance from the overall average divided by change in powder charge at each group. It is plotted against charges between the two used to find the slope. This exaggerates the information even more. Since the OCW criteria is to find a spot where mean POI's change least, the nominal charge weight would be where this red line is nearest to zero in value. That turned out to be 40.95 grains, so 41 grains looks best in this evaluation.
The averages behave like an Auddette ladder in this case, and the first image is what such a ladder would look like, except we are using 3-shot averages instead of single rounds to plot the trendline. The flat spot is where barrel harmonics appear to be most in sync with bullet ejection from the muzzle's recoil deflection ringing phase. That is, a load centered on 41 grains is expected to change POI least with charge errors or changes in temperature and other change influences.
The t-test suggests the horizontal displacement differences between the average centers of groups 1-3 are not significant, so the fact group 3 went left of group 2, for example, has a very good chance of being just due to random error and might reverse the next time the same test was shot. The same holds true for the horizontal difference between groups 4 and 5. Only the jump between 3 and 4 is likely to be more than random, and that's enough that we can conclude there is a slight rightward trend as powder charge increases.
The t-test suggests the vertical difference between group centers is probably real to better than 93% confidence for all but the difference between groups 3 and 4. The vertical difference between 3 and 4 has less than 50% confidence, so the vertical change between 3 and 4 has a good chance of just being random and might go flat or reverse if the same test were run again.
The t-stest results also show group sizes for groups 2 through 5 are not different to a very good degree of statistical significance. In other words, with just 3 shots per sample, again, the difference in their size may just be random rather than load tuning differences. However, group one is statistically likely to be smaller, and that's unlikely to be random.
So, there are two tasks to straighten out. One is to fire the test with better resolution (more charge steps and uniform charge steps) so a 3 group trend analysis would be meaningful and get us around 3-shot uncertainty levels. The other is to get enough shots either side of group one to see if there's a genuine additional sweet spot there or to learn if the tight group was a random event (still possible; just not highly probable).
I recommend three rounds each in 0.3 grain increments. You will not need 9 or more of each if we have enough to combine three consecutive shots without stepping way outside of the accuracy bounds. The loads I would shoot would be:
39.8 grs
40.1 grs
40.4 grs
40.7 grs
41.0 grs
41.3 grs
41.6 grs
41.9 grs
Nick