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Re: st: Unexpected result from a marginsplot
From
Steve Samuels <[email protected]>
To
[email protected]
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
[email protected]
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
========================================
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: [email protected]
http://www2.jura.uni-hamburg.de/instkrim/kriminologie/Mitarbeiter/Enzmann/Enzmann.html
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