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From |
tiago.pereira@incor.usp.br |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Generating random variable with specified effect size between groups |

Date |
Mon, 21 Jul 2008 02:11:23 -0300 (BRT) |

Barth, I did not understand exactly what you are looking for. If you want to generate two independent, normally distributed variables, but, at the same time, want to specify an effect size, I think you can only vary the difference between observations (mu1-mu2) to have also a specific pooled standard deviation. For example, suppose you want to simulate two normally distributed variables, whose effect size [based on your conjecture] is ((mu1-mu2)/sd_pooled) = 0.2 with a pooled SD of 2. d = mu1-mu2 = sd_pooled*effect_size d = 2*0.2 = 0.4 Since both groups are of equal size, sd_pooled == sd of mu1 == sd of mu2 */----- example 1 ----------------- clear set memory 600m set obs 1000000 scalar sd1 = 2 scalar sd2 = 2 matrix SDS = (sd1,sd2) drawnorm mu1 mu2, means(120 119.6) sds(SDS) scalar sd_pooled = sqrt((((_N-1)*(sd1^2))+((_N-1)*(sd2^2)))/(_N+_N-2)) gene effect_size = (mu1-mu2)/sd_pooled sum effect_size, detail */----- example 1 ----------------- */----- example 2 ----------------- clear set memory 600m set obs 1000000 scalar sd1 = 2 scalar sd2 = 2 matrix SDS = (sd1,sd2) drawnorm mu1 mu2, means(-0.6 -1) sds(SDS) scalar sd_pooled = sqrt((((_N-1)*(sd1^2))+((_N-1)*(sd2^2)))/(_N+_N-2)) gene effect_size = (mu1-mu2)/sd_pooled sum effect_size, detail */----- example 2 ----------------- In the examples below, it does not matter the values of mu1 and mu2 as long as their mean difference is 0.4 If you want that effect_size==d, it will be necessary to set one of the values equal to zero and to have sd_pooled equal to 1. Furthermore, you have to check if you are already simulating data correctly, but get some variation due to the fact you are not working with the population (i.e. you have actually the sampling variation), so your effect size will rarely be equal to the population effect size that you input. Hope this helps. Cheers! Tiago * * 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/

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