# Definition of monotonic, and implications for using Spearman's correlation

I have two variables: one labeled D is my dependent variable, and one labeled as I is my independent variable (according to my hypothesis). In order to test my hypothesis that a respondent's attitude towards "D" is dependent on their attitude to "I", I want to test it with a statistical measure. Since it is an ordinal scale, I supposed Spearman to be the right choice.

I've read that in order to do a Spearman your variables must have a monotonic relationship. I made a scatterplot and I don't really know if the result is monotonic (see picture)

It does not look like the "school-book" picture of a monotonic relationship, but maybe it is all right? The scatterplot seems to indicate some form of relationship between the two variables.

I made Spearman and it turned out like this:

Are the results from this Spearman test useable at all? Does my variables meet the condition of being monotonic?

(The data I am analyzing are survey data from a survey which went out to 141 people with 72 answering.)

• The authors claim that you must assume that "there is a monotonic relationship" is certainly a strange way to put things. I suppose what they have in mind is that, if there is a (stochastically) monotonic relationship then the coefficient will tell you how strong and in which direction it is. That makes it similar to the more familiar correlation coefficient that tells you how strong the linear relationship part of a relationship is, cheerfully ignoring any non-linear structure that might be there. – conjugateprior Jul 14 '15 at 15:20

I'm not sure where you read that a relationship must already be monotone before you look at Spearman's $\rho$, but the whole point of calculating a rank correlation is to see if it is (i.e., you don't already know a priori). So yes, the value you calculated has meaning independent of any assumptions one might have about the data.