Hi Diana,
Sounds really complicated! I would probably simulate the data, with all it's complexities, run the test, and repeat the process many times. The power would be the % of significant p-values.
Darren
Darren Greenwood
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Subject: allstat Digest - 10 Apr 2009 to 12 Apr 2009 (#2009-93)
There is 1 message totalling 77 lines in this issue.
Topics of the day:
1. Power for ordinal regression?
----------------------------------------------------------------------
Date: Sun, 12 Apr 2009 19:13:03 +0100
From: kornbrot <[log in to unmask]>
Subject: Power for ordinal regression?
HELP.=20
Need to calculate power for ordinal regression with factorial explanatory
variables =AD for main effects & interactions
Any advice gratefully received
The Data
8 ordinal variables with values from 1-10 and a 3*2 factorial design. Total
N is 432 [minimum group N is 38]
As is customary in psychology, this horrendously non-normal data has been
analyzed by ANOVA.=20
Have now also run an ORDINAL REGRESSION on the same data, which I believe t=
o
be the =8Ccorrect=B9 analysis.
Non-significant effects are theoretically important.
So have run power analyses using the wonderful g*power, - many thanks to
Axel Buchner, Edgar Erdfelder, Franz Faul:
http://www.psycho.uni-duesseldorf.de/aap/projects/gpower/
http://www.psycho.uni-duesseldorf.de/aap/projects/gpower/user_manual/user_m=
a
nual_02.html#effect_size
Power for ANOVA, assuming normality:
Assume medium effect size [f =3D .25 eta squared =3D.06] assuming equal group
sizes of 38 as a worst case scenario
Power =3D.71
Power for Ordinal Regression [very dubious]
The main effects and interactions are given as chi-squ, with 5 df overall,
so=20
Ran generic chi-square with lamda =3D omega squared *N =3D232 for medium effecg=
t
szie [again worst scenario of 38/group] =3D 20.9 with 5
df for 6 groups.=20
Power =3D .96
This seems over optimistic! It also does not take into account the ordina=
l
nature of the data
So what should one do?
Results for ANOVA & Ordinal Regression
Obtained p-values are similar for main effects and interactions using
ORDINAL regression and ANOVA. There is little overall pattern as to which
analysis gives the lower p-value.
There are 24 possible effects [main1, main2, interaction for 8 variables]. =
9
are significant on both analyses, 14 are not significant on either analysis=
,
just 1 is significant, p =3D /008 for ordinal regression, but just failes ot
be significant on ANOVA, p =3D.055].
Thanks in advance for any advice
Best
Diana
Professor Diana Kornbrot
email:=A0 [log in to unmask]
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Work=20
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End of allstat Digest - 10 Apr 2009 to 12 Apr 2009 (#2009-93)
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