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## Williams Deisgn 6*3 model, sample size calculation

Hi Everyone,

How can we calculate the sample size for a 6*3 Williams model in non central t-distribution. The equation I have is below code. But I am stuck and is not able to go ahead. Any help would be of great use.

Let σˆ2eσˆe2 denote the residual intrasubject MSE from a historical study; with Method 1, the sample size can be calculated with the following algorithm:

1. Set values for α, φ, and µT/µR (default α = 0.05, φ = 0.80, and µT/µR = 1);

2. Select a range of sample size (N1,N2), for each N ∊ [N1,N2], and do the following:

1. V1=1.5σˆ2e/NV1=1.5σˆe2/N

2. τ1 = [log(µT/µR) – log(▵L) ] / V1

3. τ2 = [log(µT/µR) – log(▵U) ] / V1

4. Calculate PRNT(–tν,α,ν6×3,τ2) – PRNT(–tν,α,ν6×3,τ1), where PRNT(·) is the probability from a noncentral t distribution, and ν6×3 = 2N – 4

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SAS Super FREQ

## Re: Williams Deisgn 6*3 model, sample size calculation

You can use the CDF function to compute the probability of a noncentral t distribution.  I am not an expert in this area, but I know that PROC POWER also has support for noncentral t as part of its CUSTOM statement. An expert like @IanWakeling might be able to give more explicit advice.

## Re: Williams Deisgn 6*3 model, sample size calculation

Just in case somebody is going to proceed with this thread: The article from which @Laiju apparently copied the algorithm can be found here (with much better readable formulas).

In principle, a SAS program implementing the algorithm would consist of only a few lines of code. Most of the terms in the formulas seem to be clearly defined. Moreover, the article contains a table of calculated values (Table 2, p. 245) for comparison. However, I was unable to replicate these values. I even tried to solve the equation for unclear parameters numerically (given a few values from Table 2; without sophisticated tools such as SAS/OR, though), but didn't obtain satisfactory results.

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