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

 From "Christopher W. Ryan" To statalist@hsphsun2.harvard.edu Subject Re: st: sample size for correlation, and for Cronbach's alpha Date Tue, 19 Sep 2006 13:03:51 -0400

```Thanks, this helps a lot.

It also led me to the -cialpha- package, of which I was unaware.  It
seems very useful.

. alpha v1-v16

Test scale = mean(unstandardized items)

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

. cialpha

Cronbach's alpha one-sided confidence interval
--------------------------------------------------
Items   |   alpha            [95% Conf.Interval]
---------+----------------------------------------
Test    |   .92106827   >=       .81485882
--------------------------------------------------

If I'm interpreting this output correctly, with just the 8 cases on my
15-item scale, I can say with 95% confidence that the alpha is above 0.8?

--Chris
--
Christopher W. Ryan, MD
SUNY Upstate Medical University Clinical Campus at Binghamton
and Wilson Family Practice Residency, Johnson City, NY
cryanatbinghamtondotedu
GnuPG and PGP public keys available at http://pgp.mit.edu

"If you want to build a ship, don't drum up the men to gather wood,
divide the work and give orders. Instead, teach them to yearn for the
vast and endless sea."  [Antoine de St. Exupery]

frone@ria.buffalo.edu wrote:
> 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
> 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
> statalist@hsphsun2.harvard.edu
>
>
> To
> Statalist <statalist@hsphsun2.harvard.edu>
> cc
>
> 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
>
> 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
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