I will eventually get around to some testing. I don't have the time at the moment.
I think we could all take a breath & reset as this has spiralled into something that none us wanted.
I'll try to explain as best I can why I like to see robust statistical testing conducted. To be clear, I haven't singled out barrel tuners. I look at every device & the claims about those devices from the same perspective.
I don't know how much you know about statistics but, I'll try to put some perspective on why stats are used. If you're unfamiliar with stats, particularly stats involved with rifle accuracy testing, I suggest you look up some info on Google.
With regard to the questions & answers pertaining to this very thread, stats are used to test individual rifles used by armies world wide. For example, the Chinese commissioned a bunch of their own scientists who conducted a huge test which was primarily focussed on working out the minimum number of test samples required to accuracy test all their rifles while maintaining statistically robust data. This is quite important because the Chinese military hierarchy would need to substantiate the massive expenditure in time & ammunition to test millions of rifles. If memory serves, the Chinese scientists came up with 5 x 8 shot groups ( don't quote me) to determine a rifles "cone of fire" while maintaining statistical relevance.
The statistical relevance or robustness of any test is dependent upon the SD of the variation measured.
Grubbs conducted very similar experiments with a total of 10,000 shots fired by army marksmen. The position of each & every shot was plotted using Bivariate coordinates & the centre of the POI of the combined shots calculated.
To cut a long story, Grubbs test was ground breaking in that it provided a sound scientific & statistical basis for the information Grubbs & others have since used to determine the future probability of an outcome.
All I can assure is that statistics, when properly applied, do matter. Statistics are employed in just about every business & Government to help & guide outcomes from manufacturing QC to population demographics to market stock speculation & everything else imaginable.
Statistics isn't just a word used to demoralize & confuse those who disagree with us in their tracks. Stats are a very real, analytical, verifiable, repeatable, mathematical systems with rules & boundaries. It is usually the misapplication & or misuse of stats which are the cause if misunderstanding or outright distrust.
It was the past British Prime Minister Benjamin Disraeli who has been attributed to the famous quip; "There are 3 kinds of lies: Lies, Damned Lies & Statistics" the philosophical truth of which can be vigorously debated because, it is not statistics in their pure form which lie but, the application & mathematical rigidity adhered to which is the lie.
We see this kind of statistical skulduggery, misapplication & outright lies, in news polls which try to convince the mostly ignorant masses that everyone around them possesses a particular political or other view. How do these polls twist the truth & create the narrative?
I'm glad you asked. The most common method is to use very small sample numbers, focussed in a particular area or demographic. The small sample number helps to ensure that the answers to the poll questions will be held within the requirements of the narrative &, the demographic or area is chosen with the previous knowledge of a certain concentration of view points, in the case of political polling.
Accuracy testing can be undertaken in much the same way whereby, a small sample number, focussed in a particular way, reinforces a pre-existing belief.
For example; Tuner testing 2 or 3 shot group then changing the setting then, another 2 or 3 shot group & etc assumes that a minute change in the centre of mass of the barrel WILL reveal a measurable change. So, right from the outset, the results will be skewed with the assumption driving the result, rather than allowing the raw data to be interpreted as it stands. So, it's not only the sample number which is a problem but also, the way in which a test is conducted which, can & usually will impact the results or, the interpretation of those results.
In conclusion, statistical testing must have a logical, repeatable focus in concert with a resolution of the variance which can be measured & plotted & an appropriate sample number calculated to achieve a stable standard deviation (SD) with which to use as the basis of the required statistical calculations.
If you want to extrapolate into the future by shooting a sample of groups then, rigid statistical analysis is THE only way we have of reaching a reliable outcome. Everything else is just noise, twisted to appear realistic.