EXAMPLE 7.24

Planning a new study of calcium versus placebo groups. In Example 7.19 (page 451), we examined the effect of calcium on blood pressure by comparing the means of a treatment group and a placebo group using a pooled two-sample t test. The P-value was 0.059, failing to achieve the usual standard of 0.05 for statistical significance. Suppose that we wanted to plan a new study that would provide convincing evidence—say, at the 0.01 level—with high probability. Let’s examine a study design with 45 subjects in each group (n₁ = n₂ = 45) to see if this meets our goals.

Step 1. Based on our previous results, we choose μ₁ −μ₂ = 5 as an alternative that we would like to be able to detect with α = 0.01. For σ we use 7.4, our pooled estimate from Example 7.19.

Step 2. The degrees of freedom are n₁ + n₂ − 2 = 88, which leads to t* = 2.37 for the significance test.

Step 3. The noncentrality parameter is

Step 4. Software gives the power as 0.7965, or 80%. The Normal approximation gives 0.7983, a very accurate result.

With this choice of sample sizes, we are just barely below 80% power. If we judge this to be large enough power, we can proceed to the recruitment of our samples.