# Talk:Describing Precision

Herb, 4/19/2015

(1) I'd rename this page "Measuring Precision."

(2) I don't like names "Invariant Measures" vs. "Range Statistics". How about "NSPG Invariant Measures" and "NSPG Variant Measures"? NSPG = Number of Shots Per Group.

- I swizzled names into "Invariant Target Measures" and "Variant Target Measures" which I think defines concept very well.

Herb (talk) 23:18, 9 June 2015 (EDT)

(3) I'd make "NSPG Invariant Measures" and "NSPG Variant Measures" subsections of "Measures". Different kinds of measures sorted appropriately.

(4) Discussion adds x and y as variables. Stick with h and v for horizontal and vertical. No need to have two Cartesian coordinate systems. Especially annoying when you look at horizontal and vertical variance measurement definition.

(5) Second paragraph under Measures - "In the following formulas assume that we are looking at a target reflecting n shots and that we are able to determine the center coordinates x and y for each shot."

Need (h,v) position for all shots only for "NSPG Invariant Measures".

(6) Phrase "group size" is used on this page erroneously to mean the number of shots per group which is contrary to glossary definition.

(7) In Examples section - "Extreme Spread of a 3-shot group, usually at 100 yards. This is statistically almost meaningless, especially when there is no reference to how many 3-shot groups were sampled. (An extended practical, and amusing, critique of the 3-shot group is archived here.)"

3-shot groups are disparaged, yet 2-shot groups have been labeled the "gold standard." Stupid. The average group size for a 3-shot group is a valid statistical estimator. The smallest 3-shot group size is meaningless. 2-shot group sizes are most skewed, three less so, 4 less so and so on. Numb-Numbs using Student's T run into trouble with 2-shot groups because 95% Confidence interval includes negative group sizes which is impossible. The problem is that the distribution is skewed and Student's T doesn't work well for group size for individual groups. If you average 10 2-shot groups, then the standard deviation of the mean would follow Student's T reasonably well.

(8) In Examples section - Excluding a shot as mentioned in 5-shot group line is another subject for a long discussion. Suffice it to say that you'd need to define as model for handling outliers. The 4-shot group left after rejecting a fifth shot still has information. Let's say that 4 shots go into 1", but in one case 5th shot expands groups size to 1.5 inches. That could happen by chance. But what if the 5th shot expands group to 10"? In the case of the 10 inch group size the 4-shot group seems more like a "typical 4-shot" group, not a 5-shot group with just the worse shot thrown away.

(9) In Examples section - "Average, Max, and Min Extreme Spread of five 5-shot groups. (This is the protocol used by the NRA's magazines and is actually rather efficient.)"

"Efficiency" can only be discussed relative to model being tested. The underlying model in this case is the Symmetric Rayleigh Distribution. "Absolute efficiencies" can be determined for 2-shot to n-shots per group if we ignore flyers. Throwing some percentage of flyers into the mix confounds the situation greatly.

(10) In Examples section - NRA method and Ft. Benning method should have references. Don't just allude to vague and unknown authority.

(11) Nothing wrong with RSD meaning Radial Standard Deviation. But much statistical literature uses RSD to mean Relative Standard Deviation, so care is needed with terminology.