Re: PROC POWER Does Not Agree With Sample Size Calculation

Robin, thank you very much for your explanation. I too was suspicious of a
similar correction, however the on-line documentation does not provide such
technical details (at least that I am aware of).

As for the other question on the equivalent of MDC in PROC POWER, I came
across the following note in the on-line docs:

Some of the analyses in the POWER procedure focus on precision rather than
power. An analysis of confidence interval precision is analogous to a
traditional power analysis, with "CI Half-Width" taking the place of effect
size and "Prob(Width)" taking the place of power. The CI Half-Width is the
margin of error associated with the confidence interval, the distance
between the point estimate and an endpoint. The Prob(Width) is the
probability of obtaining a confidence interval with at most a target
half-width.

--> Do you think HALFWIDTH= option in the TWOSAMPLEMEANS / ONESAMPLEMEANS
statements is the equivalent of MDC?

--> The HALFWIDTH= option is not available for the TWOSAMPLEFREQ /
ONESAMPLEFREQ statements. So how should we proceed there?

Cheers,

Bora Y.



|---------+------------------------------->
| | |
| | Robin High |
| | <robinh@unlserve.unl|
| | .edu> |
| | |
| | 26/06/2006 21:07 |
| | |
|---------+------------------------------->
>---------------------------------------------------------------------------------------------------------------------------|
| |
| To: Bora Yavuz <BoraYavuz@HSBC.COM.TR> |
| cc: SAS-L@LISTSERV.UGA.EDU |
|Subject: Re: PROC POWER Does Not Agree With Sample Size Calculation Formula? |
>---------------------------------------------------------------------------------------------------------------------------|







> I'm trying to do a standard sample size calculation to detect the
> difference between two proportions, and to check whether the result
agrees
> with PROC POWER.
>
> The usual formula is:
>
> n = (Zæ + Zß)^2 * (p1*q1 + p2*q2) / MDC^2
>
> where
>
> n = Minimum sample size (to be calculated)
> Zæ = Z-coefficient for the Type-I error rate
> Zß = Z-coefficient for the Type-II error rate
> p1 = Estimate of population proportion 1
> q1 = 1 - p1.
> p2 = Estimate of population proportion 2
> q2 = 1 - p2
> MDC = Minimum detectable change (defined in absolute terms)
>
> Let's create an example:
>
> One-Sided or Two-Sided? --> Two-Sided
> Alpha (Type-I Error) --> 0.05
> Beta (Type-II Error) --> 0.50
> Population-1 Proportion Estimate --> 0.25
> Population-2 Proportion Estimate --> 0.20
> MDC (Change You Want to Detect) --> 0.05
>
> The formula yields:
>
> n = (1.96 + 0)^2 * (.25 * .75 + .20 *. 80) / (0.05)^2 = 534. This is
> presumably the minimum sample size that one should get from each
> population.
>
> However, the following PROC POWER code gives n = 574:
>
> PROC POWER;
> TWOSAMPLEFREQ
> TEST = fisher /*lrchi*/ /*pchi*/ /*fisher lrchi*/
> SIDES = 2
> ALPHA = .05
> GROUPPROPORTIONS = (.25 .2)
> NPERGROUP = .
> POWER = .50
> ;
> RUN;
>
> My questions are:
>
> 1) Why do the two results not agree?


The following DATA step closely replicates your PROC POWER and hand
calculations.

DATA xy; drop pb qb;
LABEL n = "Minimum sample size" Za = "Z Type-I" zb = "Z Type-II"
p1 = "proportion 1" p2 = "proportion 2"
MDC = "Minimum detectable change";

p1=.25; p2=.2; q1 = 1 - p1; q2 = 1 - p2;
mdc = ABS(p1-p2);
za=probit(.975); zb=probit(.5);

n = ((Za + Zb)**2) * (p1*q1 + p2*q2) / MDC**2;

* sample size formula from Fleiss, "Statistical Methods for Rates and
Proportions, 3rd ed. , p. 72 basically replicates this result
They give a source how this formula gives values that are too low ;

pb=(p1+p2)/2; qb=1-pb;
nn = ((za*sqrt(2*pb*qb)) + (zb* (sqrt((p1*q1) + (p2*q2)))))**2
/ ( (p2-p1)**2 );

* to result SAS provides with PROC POWER is close to the following
which incorporates a continuity correction also given on p. 72 ;

npg =ROUND((nn/4) * (1+ SQRT(1+ (4/(nn*ABS(p2-p1)))))**2+.5,1);

* which is close to what SAS PROC POWER gives;

PROC PRINT LABEL; run;

Minimum
proportion proportion detectable
1 2 q1 q2 change

0.25 0.2 0.75 0.8 0.05

Minimum
Z sample
Type-I Z Type-II size nn npg

1.95996 -4.0638E-17 533.963 535.884 576
^^^^^^^ ^^^
your Fleiss continuity
formula result corrected n

So I assume SAS includes a "correction" to increase the sample size.

HTH,

Robin High
Univ. of Oregon