How does sas proc power calculate the sample size?

[saszyc]

In SAS proc power, there is an example for Determining Required Sample Size for a Two-Sample t Test.

Here is the original code from SAS

proc power;

   twosamplemeans

      groupmeans   = (13 14) (13 14.5) (13 15)

      stddev       = 1.2 1.7

      groupweights = 1 | 1 2 3

      power        = 0.9

      ntotal       = .;

run;

I calculate the sample size by using formula, the result is always smaller the one obtained from SAS output.

For example, the first sample size I got is 60.466176 but SAS got 62.507429. Basically,  the fractional n total from SAS is always bigger then the one I calculated based on the common formula which is

n=4*stddev^2*(1.96+1.28)^2/(14-13). I want to know how SAS compute the sample size and base on what formula. I hope someone can help me to find it out. Thanks.

[Reeza]

The documentation has a good description:

SAS/STAT(R) 9.2 User's Guide, Second Edition

Proc Power>Details>Computational Methods and Formulas>Two Sample Means

The results from proc power are the total sample size for both groups that match the results from a web calculator as well:

Power/Sample Size Calculator

Your formula: 60.444

SAS : 64

UBC Calc: 62

All seem within the same ballpark, though not exactly the same. 

[SteveDenham]

One thing to note is that you used the z distribution values (1.96, 1.28) in your calculation.  Use of the t distribution values will result in the more conservative number obtained by SAS.  Note that this is iterative, starting with the asymptotic normals, getting an estimate of sample size, calculating degrees of freedom and then obtaining t distribution values.  (At least I think that is the explanation).

Steve Denham