I will work through the math and come back here with an opinion as to whether the stated proximity is to be expected (also, please put an email address in the body of your text). Just a couple of points to be clarified first:
larc wrote:
Focus, Thank you for your thoughts. Let me provide a little more detail [..] Also it was possible to add the fifty other ratings and correlate this total
larc, there are many measures ("metrics") for correlation, as I'm confident you are aware. The additive method of arriving at a "rest of population" score table is IMO most meaningful if the correlation coefficient being computed is one of rank - is it, and what formula is being used? Also, who says a 0 and a 9 score for a particular food item are "worth" as much as a 4 and a 5? Where one is computing a sum (or mean; same end result here) of 50 scores, this point is very moot. Linearity is an assumption.
square root
I take it if the correlation coefficient was -ve, the logic you use would require the "square root" to be defined as the negative square root of the absolute value of the coefficient (rather than i times the positive value thereof?)
I want to congratulate you on your first point of contention. You are absolutely right about similiar but wrong judgements producing overestimates. No one among the reviewers or the editor mentioned this. In measurement theory for 90 years, they have assumed that [..] Thanks again, for your comments they were well thought out.
Note that you can use a Monte Carlo (stochastic) technique yourself (just in Excel, say) to bypass the math and see whether pseudo-random evaluations still produce the closeness you have stated.
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Focus
(Thinking for oneself occasionally is a profitable exercise Class)