Interpreting the p-value in Spearman's rank correlation I have a dataset of 50 values. The data is not normally distributed. Executing the spearman function returned the result below.
Is this a strong relation? Was the association caused by a random variation or some level of monotonic relationship?
Spearman's rank correlation rho
data:  x and y
S = 10718, p-value = 0.0004159
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho
0.4853301

 A: Welcome to Cross Validated! :-)

I have a dataset of 50 values

How small or large is this sample size depends on what it is. If it's a school class, for example, and you're trying to assess the relationship between two variables regarding this specific group, that's fine. If it's a small sample from a much larger population, maybe you shouldn't rely too much on this correlation.

The data is not normally distributed.

This is fine. Different from the p-value calculation of Pearson's correlation coefficient (PCC), the calculation of the p-value for Spearman's correlation does not depend on normality.

Is this a strong relation?

Well, it is 0.48 in which the minimum is -1 (rarely -1 in practice, though) and the maximum is 1 (rarely 1 in practice, though). So it's about halfway through in absolute terms [or if it's a positive relationship]. In some fields, this is considered to be a strong correlation, in some other fields not so much. You should check studies in your field and get a grasp of what is considered a strong correlation there. In psychology, for example, I have the impression that 0.4 would be considered a strong correlation, but that's based on what some psychologist friends have told me in the past. I can't say for sure.

Was the association caused by a random variation or some level of monotonic relationship?

With two variables only, it's very hard (not to say almost unreasonable) to know if an estimated correlation is actually due to random chance or unmeasured variables. There are mainly two exceptions, though:

*

*Check the scatter plot of the two variables you're estimating the correlation. If it's a linear correlation (PCC), you would expect to see the points resembling a line. If it's Spearman's correlation, resembling a monotonic function. Sometimes, you can have "visually random" points that give you a good $r$ or $\rho$. That would be a bad sign.

*Background knowledge. You know from background knowledge that actually the two variables you're estimating the correlation, $A$ and $B$, are actually caused by $C$, and then you expect them to be independent given $C$. You can check this with partial Spearman's correlation in your case, for example.

Regarding the interpretation of the p-value, it should go just like any other p-value interpretation. You should have your significance level, based on contextual knowledge, and compare the obtained p-value to it. A small p-value with small sample size is usually a good sign.
