Spearman or Pearson

[Tommaso Salvitti]

Good morning everyone, I need to test the correlation between two variables. Neither of these two variables is normally distributed so it is incorrect to use the Pearson correlation coefficient. I opted for the spearman correlation coefficient but the two variables do not satisfy the monotonicity relationship. Which test to use? do I still use spearman? or pearson? which one is more correct..thank you very much in advance

[Nick Cox]

Correlation coefficients primarily measure how far data approximate whatever is ideal for each flavour of correlation. Or so I assert.

Thus Pearson correlation measures approximation to linearity; Spearman measures approximation to monotonicity.

It is no more a requirement for Spearman that data are monotonically related than it is a requirement for use of a thermometer that temperatures are hot. That confuses what you are trying to find out with what is needed to do that.

Where normality enters is as a secondary assumption for one test of whether Pearson correlations are really zero. If that test is needed, and bivariate normality is greatly in doubt, I would bootstrap to get confidence intervals for the correlation and get a test that way.

You'd get a better answer if you showed the data in question, at least as a scatter plot.

Oddly, or otherwise, many texts and courses obsess about normal distributions as a supposed prerequisite for various procedures, but lack of independence is a bigger threat to rock-solid inferences with those procedures but is often not discussed at all.

[Tommaso Salvitti]

Graph1.gphHere the graph

[Tommaso Salvitti]

thanks a lot!!

[Nick Cox]

Please don't post .gph attachments. Post .png. This is explained in the FAQ Advice at #12.

[Tommaso Salvitti]

Here the graph!!

[Nick Cox]

Thanks for the graph. I don't see there either a linear or a monotonic relationship that would produce a strong correlation of any kind.

I can't decode what the variables are and if I could I suspect I don't have specialist knowledge on what to expect.

The outcome seems to have a hard lower limit of 50.

The predictor doesn't show any values above 25.

All values seem to be reported as integers. There could be a great deal of overplotting of identical points.

[Tommaso Salvitti]

Thanks and so it's better pearson or spearman???

[Nick Cox]

As in your case neither measure seems helpful I would not want to declare either better. If you had strong grounds to think the relationship linear -- or that is likely be nonlinear but monotonic -- then those grounds determine which answers your question.

Which is a better answer therefore depends on what the question is.