# Thread: Sample size with G power

1. ## Sample size with G power

Hello

I ran some sample size calculations using Gpower, in order to find the minimum required sample size for the Fisher exact test, since I need to compare proportions between two groups, with rare events.

This is the output I got:

Exact - Proportions: Inequality, two independent groups (Fisher's exact test)
Options: Exact distribution
Analysis: A priori: Compute required sample size
Input:
Tail(s) = One
Proportion p1 = 0.1
Proportion p2 = 0.02
α err prob = 0.05
Power (1-β err prob) = 0.8
Allocation ratio N2/N1 = 1
Output:
Sample size group 1 = 124
Sample size group 2 = 124
Total sample size = 248
Actual power = 0.8019416
Actual α = 0.0114122

I noticed that the actual α is much lower than 0.05. Does it mean that I can choose a larger α, without crossing the 5% type I error probability ? Will regulation bodies like FDA accept this "trick" ?
(am trying to reduce the sample size from 124 per group to around 100)

2. ## Re: Sample size with G power

one more thing I found weird, and I guess you guys won't be able to explain it to me, when I ran this calculation with SAS, I got n=123 per group, and when I tried PASS, I got n=132

3. ## Re: Sample size with G power

Hi, NN_Power,

Typically when you see differences between statistical packages, it often stems from differences in default options. Note that in G*power, you've selected a one-sided test: in SAS 9.2 PROC POWER, the default is a two-sided test. I haven't used PASS, so I can't attest to its default options. Since the difference between G*Power and SAS is N=1, I'd imagine that difference may be round off error. If the options specified are the same and PASS still gives you a different result, the program may be using another approximation which is more conservative.

If you do a simulation, you will actually find that Fisher's Exact Test may be a bit conservative: the real type I error rate is actually below the nominal rate. This is why there's a difference between the nominal rate you entered (0.05) and the actual rate (0.011). You could raise your nominal type I error rate while preserving the actual type I error rate, but I don't know if regulatory agencies will accept such practices.

Hope that helps.

4. ## The Following 2 Users Say Thank You to Asymptotically Unbiased For This Useful Post:

GretaGarbo (03-28-2013), trinker (03-27-2013)

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