The eighth wonder of the world, the Garmin Xero C1 Pro chronograph
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Saw this video comparing the Garmin vs the Labradar:
Garmin Xero C1 Pro vs LabRadar (youtube.com)
Interestingly, it seems the Garmin uses the population SD formula while the Labradar uses the sample SD formula. In my view a string of shots is a sample where the population is all shots fired by the rifle. Any statisticians care to comment?
Garmin Xero C1 Pro vs LabRadar (youtube.com)
Interestingly, it seems the Garmin uses the population SD formula while the Labradar uses the sample SD formula. In my view a string of shots is a sample where the population is all shots fired by the rifle. Any statisticians care to comment?
Interesting.
I agree with you and disagree with the video guy about which formula is ‘right’. I’d rather keep myself honest by knowing my rifle will shoot more than a handful of shots, so I prefer the higher SD calculated with the sample formula. It’ll be closer to what I may get on any given day.
I guess if I ever wanted to puff out my chest I could shoot a 5 shot group and use the population formula for a 10-20% reduction in SD numbers. lol!
Yes I saw that video, and I subscribe to his channel. He's very knowledgeable and experienced, has a great channel, and I have learned alot from his videos.
He (Bryan) is correct for the SD statistics rule, i.e. the SD from a single range shooting session is the entire population method. It is NOT a sub-sample of a larger population (e.g. all the velocity data records from that rifle over hundreds or thousands of shots on different days, with different enviro variables, possibly different lots of brass, powder, primers, bullets, different winds, barometric pressure, throat erosion on the barrel, shooter error, etc). Therefore one has to use the population SD calculation method for that one session.
This is because in shooting, we know that there are many different variables (some of which we cannot control), affecting our velocities every single range session.
The stats-101 textbooks often use the student heights example for explaining population vs subsample. E.g. All the data for student heights in grade 12 in Canada are in this spreadsheet. That national data set uses the entire population SD method. Now I want to compare my school's subsample heights mean and SD with the National population height mean and SD, so therefore I would use the sub-sample SD method, and compare it to the national mean and SD. In this example there are no uncontrolled variables. Its a simple height measurement that cannot be affected by other variables.
HOWEVER: In this video he made a critical mistake and violated the fundamental rules of statistics, which makes all his SD numbers invalid in this video: He calculated SD's from each individual 3-shot velocity group. In Statistics, there is no such thing as an SD from a sample size of 3. An SD is only valid if the sample size is large enough, AND has a normal distribution (i.e. a relatively symmetrical bell curve). Generally the rule of thumb is that a sample has to be at least 30, or approaching 30, for any hope in generating a normal distribution. You can sometimes cheat a little with smaller sample sizes than 30, and graph these results in histograms, choosing the bin size, to show that its approximately approaching a normal distribution, close enough-ish so to speak.
The velocity number is a one-dimensional data type. It has no pre-determined mean or distribution until you shoot the rounds for that session. All else being equal, any one-dimensional outcome data type will generate a normal distribution of variance around the mean (in the center hump of the bell curve). Therefore one must generate a sufficient sample size first, to generate a normal distribution, before doing the SD calculation. However, we can skip (at our peril) the technical step of proving the normal distribution first, and just generate the SD from the raw data. If we do this, we are making the assumption that our sample size was large enough and we shot every round under the same conditions, etc.
Ironically, he has all the raw data to do this correctly. He shot fourteen 3-shot groups with each chronograph, and showed these 3-shot means on screen. Therefore he has a true sample size of 42 velocities for each chronograph. This should easily produce a normal distribution for each chronograph, and then he could do one Mean, ES and SD statistical calculation to compare his two samples (both of which would be the population method).
I wanted to add a comment to his video with an encouragement to him do this with is raw data (which is really good data), and do one SD comparison. But he has comments turned off.
On screen he shows he had already sub-pooled his raw data into 3-shot group means, (masking the true variation across the entire sample), so I am unable to run the correct SD calculation on his 42 data points per chronograph. SD absolutely relies on true distribution along the X axis in order to generate a bell curve and reliable SD.
For a good backgrounder on Standard Deviation, Wikipedia does a good job of explaining it in general language. Link: https://en.wikipedia.org/wiki/Standard_deviation
(Aside: There are other variants of SD calculations for skewed distributions that are generated from 2-dimensional (coordinate X and Y) variables, such as bullet hit distance from bullseye center, which generate a density cloud around the bull center. These distributions show more (denser) hits closer to the center of the bull and fewer (less dense) hits further away (i.e. bell curve heavily skewed to the left with a long shallow tail to the right). These are types of distributions that require a special SD depending on their amount of skewness. These 2 or 3 dimensional types of data distributions get complicated very fast because the type of the distribution has to be determined first, and then the proper SD method chosen).
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I can confirm his theory with old Labradar data I have that were exported to CSV files (with 5 shot groups minimum, not the 3 he initially used). Looks like the Labradar is using some variation of STDEV (rather than STDEVP). This is within LibreOffice Calc.
After looking at the data I had previously recorded, I created a manual dataset of 100 points and as per expectations STDEV and STDEVP were very close to the same with the larger population size.
https://www.youtube.com/watch?v=w4ZwuZSePEg
His comments in Part 2 of that video would also be correct in that if all my load development has been done with the Labradar, then comparing SD's would still be OK looking for the lowest SD. Statistically the numbers are not correct, but comparing only Labradar generated SD's the development data is still valid.
It would only fall apart if some data were collected with the Labradar and SD's were compared to data collected on the Garmin....
I know as per Biologist above that the rule of thumb on sample size for SD is at minimum 30 points, but for what we are trying to achieve in small sample load development I can't see what else they can use.
After looking at the data I had previously recorded, I created a manual dataset of 100 points and as per expectations STDEV and STDEVP were very close to the same with the larger population size.
https://www.youtube.com/watch?v=w4ZwuZSePEg
His comments in Part 2 of that video would also be correct in that if all my load development has been done with the Labradar, then comparing SD's would still be OK looking for the lowest SD. Statistically the numbers are not correct, but comparing only Labradar generated SD's the development data is still valid.
It would only fall apart if some data were collected with the Labradar and SD's were compared to data collected on the Garmin....
I know as per Biologist above that the rule of thumb on sample size for SD is at minimum 30 points, but for what we are trying to achieve in small sample load development I can't see what else they can use.
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I contemplated ordering one on line but waited until this week when Prophet River got more in $799 plunked one in my basket and picked it up yesterday morning at the store, it's nice living 3 blocks from their store, I even dropped Clay another bag of jerky when I picked it up. I have not yet tried it out as I was busy today getting the shed ready for our target delivery on Monday, the next week or so is going to be to cold so I'll wait, the good thing is I have it ready to go whenever I want.
I agree that in load development, things get expensive and time consuming very fast!
Often 30 samples per load variable is not reasonable for our budgets (e.g. bullet weight and brand, powder charge and brand, seating depth, primer brand, brass brand, all add up to an enormous number of combinations and permutations). Good news: There is a better method for small sample sizes (less than 30, in the 20-ish sample size range). Its the "Box and Whisker" method, which orders the data points smallest to largest, into "quartiles", which are four 25% groupings. The ES are the whiskers, which are the 1st and 100th percentile. The median is the 50th percentile. The mean is calculated the usual way as the average, but the median is often the better indicator. And the "inter-quartile range" is the "box" of the plot that spans the middle 50% of the distribution, from the 25th to the 75th percentile. This statistical analysis works very well every time and there is no bell curve needed to validate the statistics. There is no requirement for a normal distribution bell curve. It is a simple linear grouping method from smallest to largest value, divided into percentiles.
The inter-quartile range box of 50% for interpretation for us shooters is sort of analogous to the concept of the 1st SD, which is 34% on either side of the mean, totaling 68% of the variation in the SD method using the normal distribution. Both of these are the inner bulk of the distribution closest to the mean or median. The Box and Whisker method is a linear distribution of smallest to largest (which is intuitive without a stats knowledge background), and everyone knows what percentages are.
Excel has the Box and Whisker stats method in its standard software. Its easy to use. And as a bonus, Box and Whisker has a function which identifies "outliers".
Personally, I think Box and Whisker analysis is far more intuitive and useful for the shooting sports. BTW, I am in the process of working up some rimfire chronograph data given to me by a friend, and I was going to work this up into a Box and Whisker data presentation in a new thread on CGN, and compare and contrast it to the SD method. However that is another topic for another day.
Personally, I think Box and Whisker analysis is far more intuitive and useful for the shooting sports. BTW, I am in the process of working up some rimfire chronograph data given to me by a friend, and I was going to work this up into a Box and Whisker data presentation in a new thread on CGN, and compare and contrast it to the SD method. However that is another topic for another day.
I'd very much like to see that when you start the thread. Thanks.
Now back to the Garmin is great thread
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- Lloydminster, Alberta
So the guy who made that video had his head handed to him by an actual statistician and proceeded to have an epic meltdown on a shooting forum and got banned. The whole Garmin / Labradar debate is a bit like the Mac / PC debate (Holy war). Personally, I've never had issues getting results from the Labradar, so I have no interest in spending more money on a newer device.
As a proud A+ in Stats 3T3 (some years ago), sample is correct. After all, you don't have the entire population unless you never shoot that rifle/load combination again.
https://www.khanacademy.org/math/st...pulation-and-sample-standard-deviation-review
So the Garmin is going to make people happy because their 3-shot groups will have really good SDs
As a proud A+ in Stats 3T3 (some years ago), sample is correct. ...
So the Garmin is going to make people happy because their 3-shot groups will have really good SDs
Speaking as someone who passed a Sadistics course mumble years ago, I do still have the sense that you need a sadistically significant number of shots in your sample set. My Garmin runs so far are mostly over 10-20 rounds.
(and yes, my coursemates and I called it that)
You do. I was making a dig at the wild SD claims that some people make, where we don't know how many shots were deleted from the string to get the number. SD is the new group size. Instead of bragging about the .145" group their hunting rifle makes with handloads, now it's the 2.4fps SD they got just by switching primers.
The Garmin still produces too small a number because it uses Population instead of Sample for the calculation. Which doesn't matter for most things, but does when predicting the ES of a large number of rounds downrange, which might matter to an ELR shooter or just someone who is detail-oriented. It does have the positive effect of giving people a smaller number to brag about, like a woman bragging that she fits a size 2 dress which has been cut a little large.
I'm letting the target tell me how good my groups are. Primary motivation for the Garmin is reassurance that velocity is in the lane with what the loading manual suggests I should see. Especially if I'm thinking of launching an expedition for the next faster node, I want to be sure I'm not pushing too hard.
I did see that my .223 reloads with Black Sheep processed mix-headstamp brass were giving a notably wider velocity spread than either factory .223 or my single-headstamp 6.5CM reloads, so that's an interesting tipoff from the Garmin that I ought to try selecting a single headstamp to see if my groups get better.
I did see that my .223 reloads with Black Sheep processed mix-headstamp brass were giving a notably wider velocity spread than either factory .223 or my single-headstamp 6.5CM reloads, so that's an interesting tipoff from the Garmin that I ought to try selecting a single headstamp to see if my groups get better.
I've 8een.. lookin...lookin...readin...lookin...readin... lookin some more...dammmm all these great reviews !!!!
NOWWWWW...I REALLY WANT one...I NEED one...sold my V3 kit 2 days ago for over half what the Xero costs. This will help the wallet pain su8side much quicker..LOL
...looks like a call to Peter at Hirsch Precision is in order !!!
Thanks for driving the final nail in my decision wall...LOL
NOWWWWW...I REALLY WANT one...I NEED one...sold my V3 kit 2 days ago for over half what the Xero costs. This will help the wallet pain su8side much quicker..LOL
...looks like a call to Peter at Hirsch Precision is in order !!!
Thanks for driving the final nail in my decision wall...LOL
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I agree that spread and SD numbers don’t tell the whole story. I just developed a 6.5CM hunting load. Here’s the result…
This is a ten shot unaltered string. The spread and SD values aren’t that dazzling. But the group size at 100m for those ten shots was .390” (.344moa). It really doesn’t get any better than that for a hunting rifle. I confirmed the accuracy all the way out to 700m afterwards. (Even though this will only be used to a maximum range of 400 metres.)
Could I have shot a larger group…? Maybe. But how many is large enough?
This is a ten shot unaltered string. The spread and SD values aren’t that dazzling. But the group size at 100m for those ten shots was .390” (.344moa). It really doesn’t get any better than that for a hunting rifle. I confirmed the accuracy all the way out to 700m afterwards. (Even though this will only be used to a maximum range of 400 metres.)
Could I have shot a larger group…? Maybe. But how many is large enough?
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I agree that spread and SD numbers don’t tell the whole story. I just developed a 6.5CM hunting load. Here’s the result…
This is a ten shot unaltered string. The spread and SD values aren’t that dazzling. But the group size at 100m for those ten shots was .390” (.344moa). It really doesn’t get any better than that for a hunting rifle. I confirmed the accuracy all the way out to 700m afterwards. (Even though this will only be used to a maximum range of 400 metres.)
Could I have shot a larger group…? Maybe. But how many is large enough?
You shot a ten shot group out of a hunting rifle that measures less than.5 MOA??
OUTSTANDING accuracy!!
Who cares what the SD , or ES is with accuracy like that from a hunting rig?
Cat
