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This is a question I've wondered about for a long time. In the process of shooting and chronographing literally thousands of rounds it became more and more evident to me that there was a range of velocity variations that would typically represent the AR family.

The reloading sequence is, of course clean if previously shot brass, then size, decap, and prime. The brass is then trimmed and chamfered outside and inside. Neither bullets, cases, or primers are sorted - simply used as they occur. The powder is dispensed with a RCBS ChargeMaster and a Frankford Arsenal Intellidropper. Essentially, every other case is loaded from one then the other - i.e. both are used simultaneously - sort of. :blink:

As of late, I started running only charges of 25 shots. That is, I load 25 rounds with the same charge, the same way, and measure the velocities with a LabRadar. Because I record and keep my results in Excel spreadsheets, I have access to all my tested loads. So, I went through the latest loads of various charges and components and listed the ES for each 25 shot charge. Here are the results. As I added listings, I added two columns, first the case brand used and a little further down, the date the data was collected. The purpose of adding the case brand was to show that cases don't seem to matter, the ES stays within a certain range.



There are several pertinent things here. Numerous gun/barrels are included; different brands and different barrel lengths; different primers, bullets, and cases. The powder is various charges of H4895. I was not my intent to isolate on H4895, but it so happens I had switched to H4895 about the same time I moved to 25 round testing, so I don't have 25 round tests with other powders.

So what do we take away from all this?
First, let's realize this is a sufficient sample size of 27 samples. Typically you see the number 30 tossed around as the minimum sample size among statisticians. Well, this is pretty close and more will be added as I shoot more. As for the statistical analysis that follows, since the sample size is under 30, I used the T statistic to calculate the 95% confidence level and confidence intervals.

Most will experience the glazed-eye effect if I start to explain the math etc. so I won't, but if you are interested, ask.

The table, while essential, is difficult to draw conclusions from, but by massaging the data, we can see some definitive results.

We can calculate the average ES of the 27 samples and the average is 66.9 fps. The standard deviation of the ESs is 10.9 fps. it is important to realize we CANNOT use the data set as a collective, i.e. average the individual velocities of all the sets. The reason that is so, is that different charges were used, different barrel lengths were used, and different bullet weights. All that would spread the ES out tremendously and would not be useful at all. But the ES from group to group does represent a sample that will produce some meaningful results. Having the average ES and SD, we can do a bit more, and that is, calculate the 95% confidence level and intervals.

The confidence level and intervals are a bit tricky. It does not tell us there is a 95% chance the ES of a sample group will be within 5% of the mean. Rather, it means, we can be 95% confident that the mean of the population would lie within the confidence intervals. Glazed eyes yet? :tongue: Hang in there just a bit more; I'll simplify this.

There are two statistical categories, the population and samples of the population. Let's use an example. Suppose I'm measuring the weight of 25 bullets out of of a box of 500 bullets. It may be that 500 is the population, but the sample size is 25. So I'm analyzing the sample to predict the average weight and standard deviation of the entire 500 bullets. So, why did I say the whole 500 "may" be the population? What if I have 4 boxes of 500 of the same lot number? Now what's the population size? Another way it's a bit tricky. :aargh4:

Anyway from the sample size, a confidence value, a T-table, and the SD, we can calculate the confidence interval, in this case for ES the confidence level it's 4.307 fps. The confidence interval is the ES average +/- the confidence level. so the lower value is 63.0 fps and the upper value is 71.6. Again, what this means is that we are 95% confident that the mean of the entire population will lie within the upper and lower bounds.

But what does that mean? It infers that if we all load as I described above and we all go out and shoot a bunch of rounds through ARs and measure the velocities and calculate the ESs, we can expect our average ES to be between 63.0 fps and 71.6 fps. So that's the answer to the question in the title of the thread!

The word "infer" is used because we are using a sample to predict future results of the larger group, or population.

That's my story and I'm stickin' to it! :tongue:
 
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