{smcl}
{* 11 Apr 2011}{...}
{cmd:help sampsi_rho}
{hline}

{title:Title}

    {hi: Calculates Sample Size or Power for Pearson Correlation}

{title:Syntax}

{p 8 17 2}
{cmdab:sampsi_rho}
[{cmd:,} {it:options}]

{synoptset 20 tabbed}{...}
{synopthdr}
{synoptline}
{syntab:Main}
{synopt:{opt null(#)}} specifies the null value of the Pearson correlation, the default is 0.{p_end}
{synopt:{opt alt(#)}} specifies the alternative value of the correlation, the default is 0.5.{p_end}
{synopt:{opt n:1(#)}} specifies the sample size, the default is 100.{p_end}
{synopt:{opt a:lpha(#)}} specifies the significance level, the default is 0.05.{p_end}
{synopt:{opt p:ower(#)}} specifies the power, the default is 0.9.{p_end}
{synopt:{opt s:olve()}} specifies whether to calculate the sample size or the power, the default is n.{p_end}
{synopt:{opt onesided:}} specifies whether the alternative hypothesis is onesided, the default is a two-sided test.{p_end}
{synoptline}
{p2colreset}{...}

{title:Description}

{pstd}
{cmd:sampsi_rho} calculates either the sample size or power for a Pearson correlation. The formula
for sample size is ((Za+Zb)/(delta))^2 + 3 where delta is the difference between test value and
the null value, Za is the signficance Z-value and Zb is the power Z-value. The correlations are transformed
using the Fisher z transformation  1/2ln((1+rho)/(1-rho)) this z is normally distributed with a standard deviation
of 1/sqrt(N-3).

{title:Options}

{dlgtab:Main}

{phang}
{opt null(#)} specifies the null value of the Pearson correlation, the default is 0.

{phang}
{opt alt(#)} specifies the alternative value of the correlation, the default is 0.5.

{phang}
{opt n:1(#)} specifies the sample size, the default is 100.

{phang}
{opt a:lpha(#)} specifies the significance level, the default is 0.05.

{phang}
{opt p:ower(#)} specifies the power, the default is 0.9.

{phang}
{opt s:olve()} specifies whether to calculate the sample size or the power, the default is n.

{phang}
{opt onesided:} specifies whether the alternative hypothesis is onesided, the default is a two-sided test.


{title:Examples}

{phang}
{stata sampsi_rho}

{phang}
{stata sampsi_rho, solve(power)}

{phang}
{stata sampsi_rho, solve(power) n(10) alt(0.2)}

{phang}
{stata sampsi_rho, p(0.8) onesided}


{title:Author}

Adrian Mander, MRC Biostatistics Unit, Cambridge, UK.

Email {browse "mailto:adrian.mander@mrc-bsu.cam.ac.uk":adrian.mander@mrc-bsu.cam.ac.uk}

{title:See Also}

Related commands:

{help sampsi} (if installed)
{help samplesize} (if installed)   {stata ssc install samplesize} (to install this command)
{help sampsi_reg} (if installed)   {stata ssc install sampsi_reg} (to install this command)
{help sampsi_mcc} (if installed)   {stata ssc install sampsi_mcc} (to install this command)