Does increasing partial correlation covariates affect power? I'm trying to characterise the relationship between variable A and B. I know the relationship is confounded by age, and maybe also variable C.
The partial Spearman correlation coefficient between A and B controlled for age is 0.33, p=0.02. The partial Spearman correlation coefficient between A and B controlled for age + variable C is 0.29, p=0.06.
Can someone please help me interpret this? The p-val has become non-significant p>0.05 but the coefficient doesn't appear to have changed much; have I lost power to detect statistical significance or is there a genuine interaction with variable C being measured here? Any help with understanding/more appropriate tests would be much appreciated. Thank you!

Confounders can create spurious correlation that is not actually due to a causal effect of A on B. So, in principle, your result that controlling for C makes the correlation disappear is very well possible.
In your case, the p-value is near your level of significance which is not a very clear result. So I would check if there are other methods with which I could improve the results. Here are some possibilities:
First, maybe you can investigate more closely whether C is really a confounder and not actually a mediator. Or you might have missed other confounders you need to control for.
Furthermore, maybe you find non-confounding variables that, when controlled for, decrease noise.
Finally, maybe you can find another way to measure the correlation and compare the results. There are many possible approaches, you could use regression with powerful packages like brms or matching methods (e.g. Matching) or hybrids thereof as implemented in MatchIt.
