# Do I have a correlation here or not?

I am writing my thesis at the moment and I am pretty new with statistics. I tired to google around but I don’t know what to do anymore, since I don’t really find an answer in this case. I hope you can help me…

I want to calculate a bivariate correlation, but as I read everywhere the variables I use for this have to be normally distributed and one should be able to see a linear connection between them in a scatterplot. They are normally distributed but one of them is ordinal though and my graph looks like this:

It gets even worse when I have two ordinal variables. Then it looks like this:

I get significant (but weak) r values in both cases you see above, when I calculate a correlation, but I am not sure if I am allowed to use my results, since I cannot see any linearity in my graphs in the first place. And as I read it this should be a pre-requirement for a correlation. But the fact that mz avriables are ordinal make it hard to see if there might be some linearity, alsothough I am not able to see it. So, basically I don't know if I have a correlation now or not...

I also read that I could use Spearman's correlation instead, but isn't it that I need to have some kind of connection in the graph for this one as well? I my case I don’t see anything in my scatter plots.

• I've been having the exact same issue. Have you come with any ideas!? Thanks
– user123879
Jul 20, 2016 at 11:07
• I'm not going to put this as an answer, because I'm not sure about the linearity assumption underlying these statistics, but for the first analysis (ordinal vs. interval) you may want to investigate polyserial correlation. For the second analysis (ordinal vs. ordinal) polychoric correlation may be appropriate. Jul 20, 2016 at 11:10

You cannot use Pearson's correlation with ordinal variables. You can use Spearman's rank correlation and there are other measures of association as well.

But correlation does not assume the variables are normally distributed.

• Since the question asker seems more concerned with linearity than normality, it may be worth pointing out that Spearman's rank correlation does not assume linearity (although it does assess monotonicity) Jul 20, 2016 at 11:23