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# Re: st: Unexpected result from a marginsplot

 From Steve Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: Unexpected result from a marginsplot Date Sat, 28 Jul 2012 10:21:33 -0400

```It's easy to demonstrate the fallacy for independent means.

If s1 is the SE of the 1st mean and s2 is the SE of the second,
the SE of the difference is:  ( s1^2 + s2^2)^.5

Then elementary algebra  shows that:
s1 + s2 > ( s1^2 + s2^2)^.5
(Just square both sides)

Example (two independent means m1 and m2): se1 = se2 = 1

se_dif= (1 + 1)^.5 = 1.414   < 2 =  se1 + se2

Let's take a 2-sided 68.3% CI so that the z multiplier is 1.

CI for mean 1  m1 ± 1
CI for mean 2  m2 ± 1
CI for difference   (m1 - m2) ± 1.414

Then the individual CIs will overlap but the CI for the difference will
exclude zero as long as 1.414 < |m1 - m2| < 2

Steve
sjsamuels@gmail.com

On Jul 28, 2012, at 8:11 AM, Dirk Enzmann wrote:

Jordan wrote:

http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1207/date/article-1062.html

Although not specific to your marginsplot question: It is a general misconception and popular fallacy that confidence intervals should not overlap if the difference is statistically significant.

See:
Cumming, G. & Finch, S. (2005). Inference by eye: Confidence intervals and how to read pictures of data. American Psychologist, 60(2), 170-180.

http://ovidsp.tx.ovid.com/sp-3.5.1a/ovidweb.cgi?&S=JGKCFPKCJLDDMOCBNCPKAEGCOKFAAA00&Abstract=S.sh.15.17.18.23|3|1

Dirk

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