By David Machin; et al
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Qxd 5 9/8/08 10:21 Page 47 Comparing two independent groups for continuous data SUMMARY This chapter considers sample-size calculations for comparisons between two groups where the outcome of concern is continuous. The situations when the data can be assumed to have a Normal distribution form and when they do not are described. 1 Introduction A continuous variable is one that, in principle, can take any value within a range of values. For example, in a trial comparing anti-hypertensive drugs one might record the level of blood pressure once a course of treatment has been completed and use this measure to compare different treatments.
For a given total sample size m ϕm m⎝ ϕ ⎠ N = m + n this standard error is minimised when m = n, that is when ϕ = 1. This standard error can also be written as s 2 ⎛1 + ϕ ⎞ ⎜ ⎟ and since, in general, the required m ⎝ 2ϕ ⎠ sample size is directly proportional to the variance (the square of the standard error) this leads to a simple expression to modify the formula for a sample size for equal sized groups to give that for when the allocation ratio ϕ ≠ 1. Thus if we define mUnequal as the sample size in the first group and nUnequal (= ϕmUnequal) the sample size in the second group, then mUnequal = (1 + ϕ) mEqual .
2816. 9 or 239 operations. 1 gives 474 operations but since πKnown (= π2) is assumed known, we halve this to 474/2 = 237 operations which is very close to 239. In practice, a final recruitment target for such a clinical study would be rounded to, say, N = 250 operations. 10 are small, a more cautious approach would be to use the tabular values for Fisher’s exact test in SSS which gives 513 (rather than 474) leading to N = 513/2 or approximately 260 operations in this case. 7 References Ang ES-W, Lee S-T, Gan CS-G, See PG-J, Chan Y-H, Ng L-H and Machin D (2001).