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st: RE: sample size for correlation, and for Cronbach's alpha


From   "Newson, Roger B" <r.newson@imperial.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: sample size for correlation, and for Cronbach's alpha
Date   Tue, 19 Sep 2006 09:41:26 +0100

You might like to try my -powercal- routine (Newson, 2004), downloadable
from SSC using the -ssc- command. -powercal- can do generalized power
and sample size calculations, based on standard errors from a pilot
study and on the principal that quadrupling the sample size halves the
standard error. The last example from this paper demonstrates power
calculations for Somers' D, based on a pilot study, and you could
probably do the same for Cronbach;s alpha, correlation coefficients etc.
You might like to use either -jackknife- or -bootstrap- to calculate a
standard error for whatever statistic you want to use, based on a pilot
study.

I hope this helps.

Roger


References

Newson R. Generalized power calculations for generalized linear models
and more. The Stata Journal 2004; 4(4): 379-401. Pre-publication draft
downloadable from my website (see my signature below).

Roger Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk 
www.imperial.ac.uk/nhli/r.newson/

Opinions expressed are those of the author, not of the institution.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Christopher
W. Ryan
Sent: 18 September 2006 23:26
To: Statalist
Subject: st: sample size for correlation, and for Cronbach's alpha

I am attempting to create a summated rating scale to detect functional
fecal retention (ffr) in children.  The scale contains 15 items (v1-v16,
but no v10 (which is an unrated distractor)).  12 Items are rated 0-2; 3
items are rated 0-4.  I had planned to sum the scores on the individual
items; sum can range 0-36.  Higher scores mean more constipated.

I hope to correlate the score on the scale with visual assessments of
constipation on plain radiographs.

Two questions come to mind:

Does Stata have a sample size routine for correlations?

How does sample size relate to Cronbach's alpha?  I've been told that
roughly ten subjects per item would yield a reasonable sample size for
reliability testing; this would be 150 in my case.  I have little hope
of recruiting more than 50-60 subjects for this initial study, unless I
extend it to a longer duration, which I'd like to avoid.

To my knowledge, no such survey instrument exists, so these are
relatively uncharted waters.  I've only tried out the survey on 8
subjects, just to see if they could understand the questions:

.slist v1-v16

 v1  v2  v3  v4  v5  v6  v7  v8  v9  v11  v12  v13  v14  v15  v16
  0   0   0   0   0   0   0   0   0    0    0    0    1    2    0
  1   0   0   0   0   0   0   0   0    0    0    0    1    1    1
  0   0   0   0   0   0   1   0   0    0    0    0    1    3    .
  1   0   0   0   0   1   0   0   0    0    0    0    2    2    1
  2   1   1   2   0   1   2   1   2    1    0    2    3    2    2
  1   0   0   1   0   0   1   0   2    0    1    1    3    1    0
  2   2   2   2   1   1   2   2   0    0    0    2    1    .    .
  2   1   1   1   2   1   2   1   1    1    2    2    2    2    0

I feel silly calculating it for just 8 cases, but alpha for the
instrument as a whole was


.  alpha v1-v16

Test scale = mean(unstandardized items)

Average interitem covariance:      .274784
Number of items in the scale:           15
Scale reliability coefficient:      0.9211

What conclusions could I draw from this, about the likelihood of
obtaining a respectable alpha with less than 150 subjects?  Or is that a
nonsensical question?

Thanks.

--Chris
-- 
Christopher W. Ryan, MD
SUNY Upstate Medical University Clinical Campus at Binghamton
and Wilson Family Practice Residency, Johnson City, NY
cryanatbinghamtondotedu
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"If you want to build a ship, don't drum up the men to gather wood,
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