# Power calculation for Spearman correlation

Suppose, I am generating data from bivariate normal distribution with means 0 and variances 1 and correlation coefficient 0,0.5 and 1. I need to calculate power for different correlations. I am doing this simulation in R but when I change my correlation coefficient to 0.5, my power is always one. I think I am missing something here. For correlation coefficient 0, i get my power to be around 0.05 which makes sense but for others it is not.

• try r = 0.1 see if it give you the power between 0.05 and 1. maybe r = 0.5 results in power is nearly 1. – user158565 Oct 24 '18 at 15:45
• Actually I just ran 500 simulations for 0.1 and 0.2. With 0.1 the power is 0.858 and with 0.2 it is 1. There must be something wrong here. – Hello Oct 24 '18 at 16:44
• sample size? Maybe the sample size is so large such that tiny difference from 0 will be detected. – user158565 Oct 24 '18 at 16:46
• Maybe, I am using sample size of 1000. – Hello Oct 24 '18 at 16:47
• When sample size > 10000, everything is significant, cited from a professor.So decrease the sample size to 100, to prove that your program is correct. – user158565 Oct 24 '18 at 16:51

The standard error of a Spearman sample correlation under the null of no correlation will be about $$1/\sqrt{n}\approx 0.0316$$ and the null distribution of the correlation is approximately normal. A correlation near $$0.5$$ will be about $$15.8$$ such standard errors from $$0$$; i.e. with such a large sample size giving a large standardized effect size, you expect to have power essentially at $$1$$.