Chronograph outliers

[Cascade1911]

Not wanting to hijack this thread: Can someone tell me my Standard Deviation for this Load? I have a questions related to the following post:

If you have a spreadsheet, just plug in your shot data in a list ...
1200
1250
1230
1400
1210
...

then in a cell do =STDEV(A1:A40) and you have it. What is nice is you can eyeball your data and threw out (if needed) an obvious 'error' such as the 1400 in the above list of values.

My question, at what point do you decide its a chronograph error rather than a flaw in the load be it charge, variation in case, bullet, crimp, bad primer, seating depth or a combination. I've had ten shot strings that may have had an extreme spread of 10-15 fps if I threw out the high and low that were maybe 20-30 above or below the truncated 8 round average. Something like:

1230
1222
1268
1234
1229
1224
1231
1226
1202
1223

Do I throw out the 1268 and the 1202?

I certainly would throw out a 1400 or a 1000 but where do you draw the line? I'm going from memory but the above was a .357 load I was playing with.

[Wyoredman]

1230
1222
1268
1234
1229 66 ES
1224
1231 16.32618891 SD
1226
1202
1223

I wouldn't throw any of them out. Your Extreme spread is only 66 (5%). Your SD of 16 is quite good for only 10 shots. I would say that more than anything it is chrony error. I would be happy with that data for that load. just my opinion.

[Wyoredman]

Last weekend I was working up some loads for my .220 and IMR 4064 and a 50gr bullet. The first loads I had were six rounds with 37.5 gr. The first four fired measured in th 2400 fps range. I knew that was wrong, so I colored the last two with a felt tip marker and got readings of 3700fps. I couldnt get a sd because I only had two good readings. Thats the way it goes. Load more and test again!

[Cascade1911]

I agree, my question is where do you draw the line? OK, 150-200 +/- is probably a chrony error, 20-30 +/- may not be. +/- 40,50, 60, 100?

[rclark]

To me it is 'intuitive' thing. Most times I shoot 15 rounds and sometimes on a promising load I'll re-shoot 30 shots for a longer string just for curiosity sake. Scanning 15 to 30 values it 'usually' is obvious the bad value(s). If it isn't obvious or doesn't feel right then I leave them in the string. I have no set 'rule' of thumb other than usually the bad values stick out like a sore thumb ... . In the case you stated, I'd leave alone because you have 'minimum' data set (10 shots) and ES isn't really bad. If you got the same results in 15 shots, then I would be 'tempted' to throw out the high and low. Definitely in 30 shots. Confidence is a lot higher in what you are seeing with more shots. Sorry I don't have a 'straight' answer for you but I don't think there is one! It's really your call on what data to keep and throw away. FWIW....

[Cascade1911]

Thanks rclark. I also am going on intuition. In my stated example I loaded up fifty more rounds of which I'll probably scare my chrony with 20 of them and see if I can hit a garbage can lid at seven feet with the rest .

[rclark]

Sounds good to me . BTW, you should set up a target out at say 15-25 yards beyond your bench with the chronograph in between. That way 1) you'll have something to aim at, 2) you will shooting the same height over your chronograph every time, and 3) also test for accuracy. Probably already doing this, but just thought I'd mention it! Good luck!

[FlyFish]

Identification and treatment of outliers is a hotly debated topic among statisticians and there is no universally accepted way of doing either. That said, it is possible to do better than simply looking at your chronograph data and throwing out numbers that are suspiciously high or low or, (much worse, and never valid regardless of how many measurements you have) simply deleting the highest and lowest numbers.

A reasonably valid way of doing so is to use the properties of the normal distribution (the so-called "bell-shaped curve"). I've tested a number of sets of chronograph data and all of them have approximated a normal distribution. Statistical theory tells us that approximately two-thirds of the measurements in a normal distribution will fall within plus or minus one standard deviation of the mean (average), about 95% will be within two SDs, and about 99% will be within 3 SDs. That is to say, only about one percent of the data will be 3 SDs or more away from the mean.

To determine if a particular measurement is a [likely] outlier, calculate how far away from the mean it is (subtract the average of the string from the measurement) and divide the result by the standard deviation - ignore any negative signs). This is pretty simple to do because the chronograph will give you the mean and SD. That result equals how many standard deviations away from the mean that particular data point is - this value is known as it's "z-score." If that number is 3 or greater, there is less than a 1% chance that the particular measurement comes from the same population as the others, and it can be considered an outlier. Note that you can't be 100% sure that it is an outlier, only that it's highly likely that it is.

Like any test, the more data points in the string the better the test will be. It's possible to correct for small sample sizes somewhat by using what's called a t-distribution (really a family of distributions) rather than the normal distribution, but that's probably more sophistication than is necessary for this application.

[Cascade1911]

rclark, thanks, yes, I set up a target but find I pay too much attention to the chronograph and don't get the same accuracy that I do when the chrony is packed up.

FlyFish, good info, I'll apply your suggestion to some of my data and see what shakes out.

[rclark]

and don't get the same accuracy that I do when the chrony is packed up.

Glad I am not the only one . I try anyway as I might as well 'practice' while chronographing .

Flyfish, I'll add that to my 'spread sheet' . My chronograph just gives velocities which I write in my log. At home, I then type the data into a spreadsheet and go from there.

[ballardw]

For rclark and others who may shoot longer strings: The next statistic you you want to look at is skewness. Another one of those not often used statistics but skewness tells you if you have some bias to high or low of the mean value in your data or none if 0.

[Cascade1911]

I'm guessing here that you're saying of a 20 shot string 10 are above and 10 are below the average is a skewness of 0, no? To what use do you put this?

[FlyFish]

No, that's not what's meant by skewness. Think of a normal bell-shaped curve. Now imagine taking one of the tails of that curve and stretching it along the axis so that the hump of the bell is no longer centered. The distribution is no longer normal - it's now skewed left or right depending upon which end you pulled.

I think the value of knowing the skewness of a distribution is limited for the typical reloader, but one practical use is that the outlier identification test I posted above would be invalid for a highly skewed distribution.

[rclark]

FYI, here is some info on skewness : http://en.wikipedia.org/wiki/Skewness ... Still digesting it. Note I never did like stats back in college.... but here I am 'relearning' some of it .