# Sample Size for Correlation Testing

A research team wishes to test the null hypothesis: $H_0, r=0$ at $\alpha = 0.025$ against the alternative: $H_1, r>0$ using Fisher’s transformation of the Pearson product moment correlation coefficient as the test statistic. They have asked their consulting statistician for a sample size $n$ such that $\beta = 0.05$ when $r= 0.10$ (that is, $r^2 = 0.01$ ). What is this value?

I used the following equation:

$$n=\frac{Z_{\alpha}+Z_{\beta}}{(0.5\ln(\frac{1+r}{1-r}))}^2+3$$

and got $n\ge1303$, this is different from the answer my professor provided which is $n\ge1320$.

Am I using the correct equation and just plugging in the wrong values or do I have the wrong equation?

• Welcome to MSE! To correctly format equations use dolar signs and greek letters with back slashes eg $\alpha = \beta$ which renders $\alpha = \beta$. – Ali Caglayan Aug 4 '14 at 19:17
• Do you mean expand as in expand out to a series? If so no I did not try that. – Sepatau Aug 4 '14 at 19:43
• Still works out to the same value of 1303. I'm beginning to think it's a typo on the provided solution we were given. – Sepatau Aug 4 '14 at 19:57
• @chinny84 seems like the answer is correct and it's a difference caused by rounding off. Thanks for help Chinny. – Sepatau Aug 4 '14 at 20:25
• Ah the rounding error it sounds like that given the divisor. But great stuff. Write up an answer and accept it to close it off :). – Chinny84 Aug 4 '14 at 20:32