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?