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From |
Dirk Enzmann <dirk.enzmann@uni-hamburg.de> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: confidence intervals overlap [was: positive interaction - negative covariance] |

Date |
Tue, 26 Feb 2013 15:55:23 +0100 |

* ==== Start Stata commands: =========================================== * Example "Comparing Proportions" (Schenker & Gentleman, 2001, p. 183) input samp y freq 1 0 88 1 1 112 2 0 112 2 1 88 end logistic y samp [fw=freq] mat meanci = J(2,4,.) forvalues i = 1/2 { ci y if samp==`i' [fw=freq], b w mat meanci[`i',1] = r(mean) mat meanci[`i',2] = r(lb) mat meanci[`i',3] = r(ub) mat meanci[`i',4] = `i' } svmat meanci label variable meanci1 "proportion" label variable meanci2 "ci_l" label variable meanci3 "ci_u" label variable meanci4 "sample" twoway (scatter meanci1 meanci4 in 1/2) /// (rcap meanci2 meanci3 meanci4 in 1/2), ytitle("y") /// ylab(, angle(0)) xscale(range(0.5 2.5)) xlabel(1(1)2) /// title("Example Schenker & Gentleman (95% Wilson CIs)", /// size(medium)) legend(cols(1) position(4)) * ==== End Stata commands. =============================================

References:

http://www.apastyle.org/manual/related/cumming-and-finch.pdf http://psycnet.apa.org/journals/amp/60/2/170/

http://www.tandfonline.com/doi/abs/10.1198/000313001317097960 Dirk Sat, 23 Feb 2013 15:34:39 -0500, David Hoaglin <dchoaglin@gmail.com> wrote:

Subject: Re: st: positive interaction - negative covariance The problems that arise from trying to compare confidence intervals are more general. They arise in situations where the estimates are independent. Thus, the covariance in the sampling distribution of b1 and b3 is not the real issue. To assess the difference between two estimates, it is usually a mistake to compare their confidence intervals. The correct approach is to form the appropriate confidence interval for the difference and ask whether that confidence interval includes zero. I often encounter people who think that they can determine whether two estimates (e.g., the means of two independent samples) are different by checking whether the two confidence intervals overlap. They are simply wrong. The article by Schenker and Gentleman (2001) explains. (I said "usually" above to exclude intervals that are constructed specifically for use in assessing the significance of pairwise comparisons.) David Hoaglin Nathaniel Schenker and Jane F. Gentleman, On judging the significance of differences by examining the overlap between confidence intervals. The American Statistician 2001; 55(3):182-186.

-- ======================================== Dr. Dirk Enzmann Institute of Criminal Sciences Dept. of Criminology Rothenbaumchaussee 33 D-20148 Hamburg Germany phone: +49-(0)40-42838.7498 (office) +49-(0)40-42838.4591 (Mrs Billon) fax: +49-(0)40-42838.2344 email: dirk.enzmann@uni-hamburg.de http://www2.jura.uni-hamburg.de/instkrim/kriminologie/Mitarbeiter/Enzmann/Enzmann.html ======================================== * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

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