[marginalia_nu]

That's not really how measurements work though. All real-world measurements have precision associated with them. It's not a matter of measurements being correct or being wrong.

As GP hints at, since you don't measure an arm the same way you measure an ear, it's reasonable to expect the errors to have different characteristics.

[ckdot2]

Of course we can expect errors, I don't doubt that. That's what I mean with "wrong". But still, how should the author consider that if he doesn't know about the precision nor quantity of errors? I just don't think that's the topic of the article. The article is about correlations in the dataset, no matter, if the dataset may contain errors.

[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).

[crackedbassoon]

Intuition tells me it would be harder to achieve a precise measurement of ear protrusion than of a larger body part. This could be wrong of course, but it is generally good scientific practice to think about measurement errors when comparing sets of correlations. This may be especially true for a Bayesian, since Bayesian statistics (when placed in opposition to frequentist) strongly emphasises a deep consideration of all sources of uncertainty.

[pessimizer]

https://en.wikipedia.org/wiki/Significance_arithmetic

> Significance arithmetic is a set of rules (sometimes called significant figure rules) for approximating the propagation of uncertainty in scientific or statistical calculations. These rules can be used to find the appropriate number of significant figures to use to represent the result of a calculation. If a calculation is done without analysis of the uncertainty involved, a result that is written with too many significant figures can be taken to imply a higher precision than is known, and a result that is written with too few significant figures results in an avoidable loss of precision. Understanding these rules requires a good understanding of the concept of significant and insignificant figures.

[crackedbassoon]

Yes exactly this. And with noisier measures come lower correlations.