I Is an R-Value of 0.93 Considered Strong in Social Sciences?

[qspeechc]

Hello everyone.

I stumbled across an article in the social sciences that had a correlation coefficient of r=0.93.

Being from a maths background and knowing nothing about things like social sciences, psychology, etc., is this r-value in these types of fields considered fairly strong, strong, weak...? Or what?

Cheers

 

[Vanadium 50]

If you have two variables, x, and y, with a correlation of r, that means that r^2 of the variation in y can be explained by the variation in x. For example, height and weight have an r around 0.8 or so.

 

[qspeechc]

Haha, I know what the correlation coefficient means, I'm asking in the field of social sciences, psychology etc., is r=0.93 considered high? Mediocre? What?

 

[FactChecker]

It's high. It means that most of the variation of the y values can be explained by the regression equation. The fraction of variation that is explained is r² = 0.86.

You should be judicious when drawing conclusions about relationships with a high r value. Two variables can have very similar trends even if there is no connection between them. The population of the Earth and the age of the Solar system both increase, but that does not mean that they are related.

I think it is reasonable to say that variation of y which looks random, but can be largely explained by variation of x is more likely to indicate a connection between the two variables.

 

[Vanadium 50]

That's roughly the same correlation as the number of honey bee colonies in the US and the marriage rate in Vermont.

 

[qspeechc]

Ah, so the r² value is more important?

 

[FactChecker]

That's roughly the same correlation as the number of honey bee colonies in the US and the marriage rate in Vermont.

View attachment 211777

This is a good example of two variables with general downward trends giving a high r² regression value. But it also shows a periodic component that looks synchronized, driving the r² value even higher. This is where the scientist must be judicious in his conclusions. If he searched the world for something to match to the bee hive numbers, then he is bound to find something. If he had some a priori reason to relate bee hive numbers to the marriage rate, then this is some supporting information. (I can't imagine any a priori reason.)

PS. I wonder if the data shown is real or is fictitious to make a point?

 

[Vanadium 50]

I wonder if the data shown is real or is fictitious to make a point?

As far as I know, it is real. It is from the "Spurious Correlations" page at www.tylervigen.com. It has other great ones - "Divorce rate in Maine" and "Per capita consumption of margarine" at r = .9926.

 

[StoneTemplePython]

If it's in psychology, and there haven't been replication attempts yet, I'd ignore it. There's something of a replication crisis still brewing out there.