Christopher,
Regarding your second question, you might find the following article a
useful summary:
Duhachek, A., Coughlan, A.T., & Iacobucci, D. (2005). Results on the
Standard Error of the Coefficient Alpha Index of Reliability. Marketing
Science, Vol. 24, No. 2, pp. 294–301.
They discuss the impact of scale length (p), average inter-item
correlation (r), and sample size (n) on the point estimate of coefficient
alphas and it standard error.
Both p and r impact the point estimate, but n does not. So its not
unreasonable to obtain a high alpha with a small sample.
In contrast, p, r, and n affect its precision (i.e., standard error).
In their conclusions they state:
"Analysis 1 also proves analytically that p and r are substitutes in their
beneficial (positive) effects on alpha, and that p, r, and n are
substitutes in their beneficial (negative) effects on alpha’s standard
error."
Perhaps the best thing would be to report the point estimate with its
standard error.
Mike Frone
****************************************************************
Michael R. Frone, Ph.D.
Senior Research Scientist
Research Institute on Addictions
State University of New York at Buffalo
1021 Main Street
Buffalo, New York 14203
Office: 716-887-2519
Fax: 716-887-2477
E-mail: frone@ria.buffalo.edu
Internet: http://www.ria.buffalo.edu/profiles/frone.html
****************************************************************
"Christopher W. Ryan" <cryan@binghamton.edu>
Sent by: owner-statalist@hsphsun2.harvard.edu
09/18/2006 06:26 PM
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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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