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# st: Identifying the best scale without a "gold standard"

 From "Seed, Paul" To "statalist@hsphsun2.harvard.edu" Subject st: Identifying the best scale without a "gold standard" Date Fri, 11 Nov 2011 11:49:57 +0000

```Dear Statalist,

I have six scales, all of which are supposed to measure the same thing (breathlessness)
Factor analysis confirms a single large factor, with different weightings by the different scales.
I can now say in general terms, which scales are best & which worst, but I am
would like to confirm that the observed differences are not due to chance.

Method 1: Extract the main factor & use Richard Goldstein's -corcor- to compare
correlations between the scales & factors

Method 2 : take the simple average of the scales & use -corcor- as before.

This gives me very different answers:

******** example code ****************
version 11.2
webuse bg2
factor bg2cost1-bg2cost6

* Method 1
predict f1
foreach v in varlist bg2cost1- bg2cost5 {
corcor f1 `v' bg2cost6
}

* Method 2
gen mean_bgcost = ( bg2cost1+ bg2cost2+ bg2cost3+ bg2cost4+ bg2cost5+ bg2cost6)/6
foreach v in varlist bg2cost1- bg2cost5 {
corcor  mean_bgcost `v' bg2cost6
}

******** end example ****************

I am fairly sure that method 2 is better, as
in method 1 there is a circularity about
using the weighted average; and then showing that
the variable with the biggest weighting also has
the biggest correlation.

However, is there also a flaw in method 2?
(apart from the multiple testing issues)
Is there a better approach?
Any thoughts, references,  programs appreciated.

Paul T Seed, Senior Lecturer in Medical Statistics,
Division of Women's Health, King's College London
020 7188 3642.

"I see no reason to address the comments of your anonymous expert ... I prefer to publish the paper elsewhere" - Albert Einstein

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```