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From |
"E. Paul Wileyto" <[email protected]> |

To |
[email protected], [email protected] |

Subject |
Re: st: Effect size / sample size / power calculation |

Date |
Thu, 07 Jan 2010 08:48:32 -0500 |

The formula to get standardized effect size for a one sample test is: . di sqrt((invnorm(.975)+invnorm(.9))^2)/sqrt(150) .26466864 But actually, I cheated and used PASS software. P Miranda Kim wrote:

Thank you for your responses Steve and Paul. I will illustrate myproblem with an example…For example, previous research on a given association yields acorrelation coefficient 0.41 with p-value 0.131 and n=15.Initially I was looking at what sample size n would be required tohave 90% power to detect a correlation coefficient 0.41 using a testat the 5% level of significance.I used the fact that the correlation coefficient of two variables withunit standard deviation is the same as the regression coefficientbetween those two variables.So in effect, I wish to perform a sample size calculation for aregression coefficient of two variables with unit standard deviation.In this case the standard error of the regression coefficient issqrt((1-(b*b))/(n-2)), so standard deviation of the regressioncoefficient is approximately sqrt(1-(b*b)).For this example, this gives a standard deviation of 0.91. I then used the command sampsi 0.41 0, p(0.9) sd(0.91) onesam which yielded n=52.I now know that I will have approximately n=150 in the study, and wantto know how this affects this correlation coefficient at 90% power and80% power (5% significance)?I have a dataset with approximately 20 correlation coefficients, so Iwas hoping to automate the calculation.Paul, what formula did you use to obtain 0.265 in your response? Best wishes and many thanks for your help, Miranda [email protected] wrote:Miranda, -sampsi- is not the right command to do the initial calculation, for the effect size for multiple linear regression is not beta, but delta = r/sqrt( 1 - r^2) where r = partial correlation of Y and X, adjusted for the other predictors Z. and beta = r SD(X|Z) /SD(Y|Z)) To solve for the detectable beta, use Russ Lenth's online Java calculator (Linear regression) at: http://www.stat.uiowa.edu/%7Erlenth/Power/ . You have to enter the Variance Inflation Factor VIF. ding, since the -Steve On Wed, Jan 6, 2010 at 9:27 AM, Miranda Kim <[email protected]> wrote:Could anyone help me with this...To detect a regression coefficient of 0.41 with standard deviation0.91 Ican compute a sample size (using a 5% level of significance with 90%power)with the following command: sampsi 0.41 0, p(0.9) sd(0.91) onesamHow could I work out what regression coefficient (effect size) isdetectablewith a sample size of 150, based on this information? I need to do this with about 20 regression coefficients. I am using stata 11. Many thanks, Miranda * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

-- E. Paul Wileyto, Ph.D. Assistant Professor of Biostatistics Tobacco Use Research Center School of Medicine, U. of Pennsylvania 3535 Market Street, Suite 4100 Philadelphia, PA 19104-3309 215-746-7147 Fax: 215-746-7140

* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Effect size / sample size / power calculation***From:*Miranda Kim <[email protected]>

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