Dale – the simple answer is look up the Power/Sample size formula
for the difference of 2 proportions and the z-test for the difference of 2
proportions. You will notice that the “z”-term in the Power/Sample size
formula is of the form z(beta)+z(alpha/2), while in the z-test it is of the
form z(alpha/2).
Hth.
pl
From: SPSSX(r) Discussion
[mailto:[hidden email]] On Behalf Of Dale Glaser
Sent: Friday, July 25, 2014 9:08 AM
To: [hidden email]
Subject: Re: [SPSSX-L] Power, estimated sample size and conundrum!
Thank you Bruce....yes, that
is exactly what I got with Stata when I initially ran the power analysis
two years ago (i.e., n = 596 per group). However, the discussion I've
been having is when one runs a z-test for two proportions (whether using the
SPSS macro or Stata option) n = 300 per group will suffice to obtain
significance for 4.5% vs. 8.5% (z = 1.99, p = .047).
I do understand that with power, in part being based on the
noncentral distribution, in conjunction with the rigors of the desired power
(e.g., .8) may make sample size estimates larger than what one needs to obtain
significance via simulation (as I did with the SPSS macro for z test of
proportions). However, it seems that there is a nontrivial difference between n
= 300 per group sufficing to have p < .05 (per the z test) as opposed to n =
596 per group as per the power analysis (with desired power of .8, two tailed
test, and alpha = .05)
So though I understand the statistical difference between
conducting power and running the actual z-test, I'm having difficulties
reconciling the large sample size differences when discussing this with the PI
(and making the ultimate recommendation). Any feedback how you all broach
the subject re: difference of sample size estimate via power analysis as
opposed to simulation obtaining the actual test statistic (and p-value) would
be much appreciated.
Thank you....Dale
Dale Glaser, Ph.D.
Principal--Glaser Consulting
Lecturer/Adjunct Faculty--SDSU/USD/Alliant
3115 4th Avenue
San Diego, CA 92103
phone: 619-220-0602
fax: 619-220-0412
email: [hidden email]
website: www.glaserconsult.com
From: Bruce
Weaver <[hidden email]>
To: [hidden email]
Sent: Thursday, July 24, 2014 6:38 PM
Subject: Re: Power, estimated sample size and conundrum!
Speaking of Stata, here's what I get for your original question (i.e., sample
size for proportions of .085 & .045):
. power twoproportions .085 .045
Performing iteration ...
Estimated sample sizes for a two-sample proportions test
Pearson's chi-squared test
Ho: p2 = p1 versus Ha: p2 != p1
Study parameters:
alpha = 0.0500
power = 0.8000
delta = -0.0400 (difference)
p1 = 0.0850
p2 = 0.0450
Estimated sample sizes:
N = 1192
N per group = 596
I found this site helpful in working out how to do that:
http://www.stata-press.com/manuals/power-sample-size-reference-manual/
HTH.
Dale Glaser wrote
> Greetings all....I have a
> question/situation that on the surface seems very transparent but I am
> having
> difficulties navigating. So any feedback will be much appreciated.
>
>
> For a study two years
> ago I conducted a power analysis comparing two proportions (p1 = .085 vs.
> p2 =
> .045). Whether I used G*Power, Stata, or Power and Precision they
all
> gave me
> sample size estimates ranging from 600 to 640 (contingent if continuity
> correction was incorporated) per group for alpha = .05 and power of .80.
>
>
>
> However, when I ran the
> SPSS macro for z test of proportions for two groups comparing .045 vs.
> .085, I found that n = 300 per
> group was sufficient to obtain significance: z = -1.99, p = .047. I also
> confirmed this in Stata using the following syntax: prtesti 300 .045 300
> .085.
>
> Hence, can I assume that
> the difference (i.e., n = 600 per group per power analysis vs. n = 300 per
> group being sufficient to obtain significance) is a function of the
> desired
> power insofar with the conventional power of .80 you are setting the bar
> high
> enough so as to find the optimal nexus of Type I and Type II error?
>
> The conundrum is such
> that our study ended up with p1 = .027 vs. p2 =.047 and p = .194
with the
> recommended sample
> size being n = 300 per group given the simulation I ran in SPSS and
> Stata. Note that post hoc power analysis indicates I
> would have needed n = 1496 per group (alpha =.05, power = .80) to obtain
> significance
> for delta of 2%, though when I run .027 vs. .047 in Stata and SPSS with n
> = 685
> per group z = 1.96, p = .05.
>
> Anyway, this has become
> an interesting/challenging discussion with PI and reviewers alike.
We
> went with the sample size (n = 300 per
> group) since that was sufficient for obtaining significance, but they are
> indicting we
> should have gone with the larger sample size based on the power estimate
> (i.e.,
> n = 600 per group).
>
> Has anyone encountered
> such a dilemma and how did you deal with it?
>
> Thank you….Dale
>
>
>
>
>
>
> Dale Glaser, Ph.D.
> Principal--Glaser Consulting
> Lecturer/Adjunct Faculty--SDSU/USD/Alliant
> 3115 4th Avenue
> San Diego, CA 92103
> phone: 619-220-0602
> fax: 619-220-0412
> email:
> glaserconsult@
> website: www.glaserconsult.com
>
>
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>
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-----
--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/
"When all else fails, RTFM."
NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.
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