Using N=178, and a power of 0.8 (beta), with the function 'pwr.r.test' in R (http://www.r-project.org), I get:

r=0.208 for alpha = 0.05

r=0.253 for alpha = 0.01

r=0.303 for alpha = 0.001

All spearman rank. Google spearman rank or rank correlation.

Using N=178, and a power of 0.8 (beta), with the function 'pwr.r.test' in R (http://www.r-project.org), I get:

r=0.208 for alpha = 0.05

r=0.253 for alpha = 0.01

r=0.303 for alpha = 0.001

Note for a correlation df = N -2 as far as I can remember. So the N should be 179. Why you would like to do such a calculation eludes me though.. You can also back calculate from the t distribution.

For the formula google or see: http://vassarstats.net/rsig.html

Thanks Pepijn, and yes Mirre for df=177, N would be 179 .

You can also use critical values tables such as ...

http://www.gifted.uconn.edu/siegle/research/correlation/corrchrt.htm

http://www.bws.wilts.sch.uk/Curriculum/pdfs/geog_SpearmanExplained.pdf

http://webspace.ship.edu/pgmarr/Geo441/Tables/Spearman%20Ranked%20Correlation%20Table.pdf

http://www.uwe.ac.uk/hlss/llas/statistics-in-linguistics/Appenix1.pdf