Using Statistics in Load Development.
The widespread use of chronographs by shooters has made many of us very familiar with measures such as mean, average, extreme spread and standard deviation, yet I wonder how many shooters actually understand the difference between mean & average, or what a standard deviation actually estimates, or the idea of the validity of data.
Luckily shooters need not get too deeply into the theoretical, but they do need to get a good understanding of some basics, without which at least some of the data they are recording about their loads are actually invalid (i.e. wrong and misleading).
Firstly let us consider sample size. The mathematics of sampling is a field in itself, which need not concern us, other than to appreciate that it is very important if we want valid results.
Consider a simple example. If we needed to find the average height of Australian men, 18 years and over, how many would we need to measure to get a close estimate?
Of course the best result would be to measure every man in the population, but that would be too difficult and very expensive. So how many men would we need to SAMPLE to get a figure which is close enough to the exact number? Would 3 be enough, or maybe 5, or 10 or 100, or 1000?
Obviously the more the better, but what sample size would be large enough to obtain a figure very close to the actual number?
I think most of us realize that we are very unlikely to get a good estimate from a small sample, but how many of us testing our loads, fire and record the velocities of just 3 or 5 shots for each component combination, and then unquestioningly record the SD? Think back on this when you have read about Standard Deviation (SD), next.
Standard Deviation. Your chronograph might calculate (estimate) the SD of a string of shots for you, or if not a scientific calculator will do it for you quite simply. Many articles talk about SD, but in most cases all they say is that the smaller the SD the better.
What actually is a SD & how valid is it in what we do in load testing?
Standard Deviation is an estimate (not a solid value) of the spread of values on either side of the mean. It actually only applies in what is sometimes called a normal distribution, or a bell curve, because when plotted as a graph the result looks like a bell. Velocities from testing a single set of reloading components should qualify
The example above, of the heights of all men in our population, when plotted as a graph would be a bell curve. Probably in most cases, the velocities of a particular set of cartridge components would also form a bell curve.
66% of a set of values (men's heights, shot velocities etc) fall within one SD on either side of the mean, while another 34% of our shots are between 1 & 2 SDs either side of the mean. Shouldn't we also include them in our evaluation of those loads?
When testing our loads we are told that the smaller the SD the more uniform the load, but when the SD calculations are based on only 3 or 5 shots, how reliable can that number be? Just out of interest we could try firing 10 identical loads through a chronograph then calculate the SD for all 10, for just the first 5, for the second five and for randomly chosen sets of three velocities.
The following example should illustrate the points made.
Consider a set of shots (same components) with an average velocity of 3100 ft/s and a SD of 20 ft/s.
66 % of our shots will have a velocity of 3080 to 3120 ft/s (3100 +/- 20).
95 % of our shots will have a velocity of between 3060 ft/s and 3140 ft/s ( 3100 +/- 40).
5 % will have velocities less than 3060 ft/s or greater than 3140 ft/s. (If those numbers don't compare well with the extreme spread of your actual velocities, could it just be an inadequate sample size?)
So, think back to how many shots were actually fired to obtain these figures (our sample size). Was it just 3, or maybe 5? How valid (truthful) is our SD number? Maybe the entrails of a dead chicken would tell us as much?
The point of all this is to not blindly rely on what the chronograph or calculator throws up. Always use as large a sample size as possible and realize the limitations of using statistics meant for large samples when you actually have only small samples, the results of which which will mislead you as often as not.
However, all is not lost! If you use either the Ladder or OCW method, followed by a trial to find the overall cartridge length (OAL) which gives the smallest groups, you will find your optimum loads, regardless.