# Understanding very high p value with Spearman's rank correlation

I've been using an Excel add-on to calculate Spearman's rank correlation coefficients between two variables (bone density and bone survivorship / preservation) with and without a potentially problematic data point. My outputs have been as follows:

• Bone Density 1: $\rho$ -0.050 p-value 0.784
• Bone Density 1 with problem data: $\rho$ 0.020 p-value 0.9117
• Bone Density 2: $\rho$ -0.039 p-value 0.8314
• Bone Density 2 with problem data: $\rho$ 0.007 p-value 0.9705

If I understand correctly, all of the $\rho$ values indicate very weak correlations. However, the very high p-values indicate that I cannot reject the null hypothesis.

• What does this mean for the interpretation of the $\rho$ values?
• Should I say that the rho values indicate weak correlations, but the p-values indicate that I cannot reject the null hypothesis?
• There is no but here: the correlations are around zero; the P-values are $\gg$ conventional thresholds such as 0.05; therefore you cannot reject the null hypothesis that they are zero. I would suggest that even the term "weak" is wishful thinking: the highest correlation absolutely is 0.05, which is negligible. Also, the problem data don't make much of a difference. What you should always do if you are not doing it already is plot the data so that you can judge whether the correlation is consistent with what you see. – Nick Cox Sep 4 '17 at 16:08
• What you should report depends on how you're expected to report. If a relationship with bone density is what you're expecting, then that hypothesis has a problem. For further guidance, tell us where this lies on the spectrum from high school report, university term paper, etc., to intending to submit this work to a leading journal. – Nick Cox Sep 4 '17 at 16:10
• This is archaeological data, which is part of my dissertation. I'm looking at how well preserved certain skeletal elements are based on the density of the bones. The commonly held hypothesis is that the denser the bone, the more likely it is to survive erosional processes that slowly destroy stuff. We run these tests to see if the bones in the assemblage reflect a pattern where only the densest survive, which indicates we are dealing with a skewed assemblage. If there's no indication that bone density determines preservation, then it means the assemblage is less affected (biased) by erosion. – J E Sep 4 '17 at 16:22
• OK, so a weak relationship is (unusually) good news. Watch out that "skewed" in statistics refers to asymmetric distributions, not problems with sample selection. – Nick Cox Sep 4 '17 at 16:27
• how did you rank bonesurvivor-ship? – Martijn Weterings Jul 14 '18 at 12:16