[555watch]

I think the previous poster claims that different measurement process yields different measurement errors (spread). Since correlation coefficient is a function of spread, if the measurement errors are random, even if the underlying relation is the same, it suffices to increase the spread a little bit and get a subsequently smaller correlation coefficient.

Confidence bounds for every correlation coefficient would add value and _might_ change some of the interpretations.

E.g.: "its average correlation with the other measurements is only 0.03, which is not just small, it is substantially smaller than the next smallest, which is ear breadth, with an average correlation of 0.13."

If the former is 0.03 +- 0.02 and the latter is 0.13 +- 0.07, we could claim that both are equal to 0 (or just equal).