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From |
"Yulia Marchenko" <ymarchenko@stata.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: calculation of sample size |

Date |
Fri, 8 Oct 2004 09:11:51 -0500 |

Aijing Shang wrote: >Dear all, >Recently when I calculate power using sampsi, a strange thing happened. I >want to compare two propotions, one is 0.001, another is 0.002. As what I >know, the bigger the sample size is, the more power it is. However, the >results sampsi gave are reversed. See the results following. >. sampsi 0.001 0.002, n1(10) n2(10) alpha(0.05) >Estimated power: power = 0.9999 >. sampsi 0.001 0.002, n1(100) n2(100) alpha(0.05) >Estimated power: power = 0.3762 >. sampsi 0.001 0.002, n1(1000) n2(1000) alpha(0.05) >Estimated power: power = 0.0250 >Can anybody tell me what is wrong? Thank you very much. Stata -sampsi- command use approximate large sample test on proportions for power and sample size calculations. The distribution of the test statistic is approximated by Normal distribution for large n. One has to check if all of the following equalities hold before using large sample test (in order for Central limit theorem to work): n1p1>=10, n1(1-p1)>=10 n2p2>=10, n2(1-p2)>=10 In your case the sample size is not big enough. For example, 0.001*100=0.1 and 0.002*100=0.2. If you start even with n1=n2=5000, 7000, 10000 you'll see that power is increasing. Here is an example: *********************************************************************** . sampsi 0.001 0.002, n1(5000) n2(5000) alpha(0.05) Estimated power for two-sample comparison of proportions Test Ho: p1 = p2, where p1 is the proportion in population 1 and p2 is the proportion in population 2 Assumptions: alpha = 0.0500 (two-sided) p1 = 0.0010 p2 = 0.0020 sample size n1 = 5000 n2 = 5000 n2/n1 = 1.00 Estimated power: power = 0.1771 . sampsi 0.001 0.002, n1(7000) n2(7000) alpha(0.05) Estimated power for two-sample comparison of proportions Test Ho: p1 = p2, where p1 is the proportion in population 1 and p2 is the proportion in population 2 Assumptions: alpha = 0.0500 (two-sided) p1 = 0.0010 p2 = 0.0020 sample size n1 = 7000 n2 = 7000 n2/n1 = 1.00 Estimated power: power = 0.2579 . sampsi 0.001 0.002, n1(10000) n2(10000) alpha(0.05) Estimated power for two-sample comparison of proportions Test Ho: p1 = p2, where p1 is the proportion in population 1 and p2 is the proportion in population 2 Assumptions: alpha = 0.0500 (two-sided) p1 = 0.0010 p2 = 0.0020 sample size n1 = 10000 n2 = 10000 n2/n1 = 1.00 Estimated power: power = 0.3762 --Yulia ymarchenko@stata.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: calculation of sample size***From:*"Aijing Shang" <shang@ispm.unibe.ch>

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