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Mathematically, a correlation coefficient can range from –1.0 to 1.0.

The book 'statistical misconceptions' by S. W. Huck says this is a misconception people have.

... What is the parallel frame of reference for correlation coefficients? Under certain conditions, some correlational procedures produce correlation coefficients that must land on a continuum that extends from –1.0 to +1.0. Note, however, that the previous sentence began with the phrase “under certain conditions.”...

If a person thinks that correlation coefficients always end up on a continuum that extends from –1.00 to +1.00, he or she will be unable to judge accurately the relationship strength. What looks to be moderate may actually be strong. Worse yet, a correlation that makes a relationship look weak and meaningless may actually be as high as it can possibly be!

But from the book is not clear when a correlation, let's say of 0.5 would be a strong correlation. Could someone help clarify this to me?

João Vitor Gomes
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    Please see https://stats.stackexchange.com/search?q=logistic+regression+r+squared+votes%3A1 for one set of examples. Among the top hits there is the thread at https://stats.stackexchange.com/questions/82105 which explicitly answers your question in one context. – whuber Jul 02 '20 at 15:58
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    Sure, there are correlation-like measures that cannot vary over the entire interval $[-1, 1]$ and some correlation-like measures that can stray outside it.... But. I wouldn't say that the first sentence you quote describes a misconception; it is part of a definition! (I own the book in question but under lockdown cannot access my copy.) – Nick Cox Jul 02 '20 at 17:36
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    A strong correlation is one that experts in the field of the data agree to be strong. Sounds facetious, but strength is relative to what is possible, plausible and interesting. – Nick Cox Jul 02 '20 at 17:39
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    @whuber, thank you again for the great help as always. He proposes an exercise: http://www.statisticalmisconceptions.com/Instruct03a.html . I tried to organize the data to see what he means, I managed to get a r = -1 and r = ~0.83 , not r= +1. I think what he means is that with some data you can't get sometimes -1;+1, but a 0.83 wouldnt still be stronger than say 0.5 ? What puzzled me was the phrase "What looks to be moderate may actually be strong". – João Vitor Gomes Jul 02 '20 at 20:06
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    @nick cox, thanks for the comments, I shared a link about an exercise of the misconception – João Vitor Gomes Jul 02 '20 at 20:06
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    The idea behind that exercise is that when two distributions are not equivalent under a change of location and scale, then it is impossible for any variables with those distributions to be perfectly correlated. It's only indirectly related to the another concept that seems to be on the table, which is that in some *application domains* a population correlation coefficient of, say, $0.2$ might not only be interesting and meaningful but also extraordinary large among any comparable population. The "What looks ... strong" phrase indeed is ambiguous. – whuber Jul 02 '20 at 20:11
  • Sorry for my ignorance, but what is 'application domains' ? – João Vitor Gomes Jul 02 '20 at 21:13

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