Re: Power, estimated sample size and conundrum!

Posted by Bruce Weaver on Jul 25, 2014; 1:38am
URL: http://spssx-discussion.165.s1.nabble.com/Power-estimated-sample-size-and-conundrum-tp5726815p5726821.html

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: [phone]
fax: [phone]
email: [hidden email]
website: www.glaserconsult.com


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