# Correlation Range Misconception (-1; +1)

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?

• Please see stats.stackexchange.com/… for one set of examples. Among the top hits there is the thread at stats.stackexchange.com/questions/82105 which explicitly answers your question in one context.
– whuber
Jul 2, 2020 at 15:58
• 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.) Jul 2, 2020 at 17:36
• 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. Jul 2, 2020 at 17:39
• @whuber, thank you again for the great help as always. He proposes an exercise: 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". Jul 2, 2020 at 20:06
• @nick cox, thanks for the comments, I shared a link about an exercise of the misconception Jul 2, 2020 at 20:06