## Question 900:

1## Answer:

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For a placebo-controlled trial we are working with different subjects in each treatment group so the sample size we calculate is between-subjects (as opposed to withing subjects).We would use the 2-sample t-test to compute the difference between means so the sample size calculation is basically working backwards from 2-sample t-test.

There are actually a few different ways of computing power (SAS and Stata provide slightly different methods). My approach is close to the SAS results.

The formula is n = s

^{2}* t

^{2}/ d

^{2}

where s is the standard deviation

t is the sum of the critical value for the level of confidence (95%) and 1-sided critical value for power (80%)

d is the difference we want to detect (15)

We fill the values in the formula and get an initial estimate of the sample size. We then update it using an iterative approach for the t-distribution.

See the attached excel file for the computations and the iterations.

We get an initial estimate of 174.4, then iterate using the t-distribution until the sample size no longer increases. This gets us with a total sample size of 176.3 but it's best top round any remainder up to the next whole person and we get 177 in each group or 354 people in total.