Aim: To Calculate Sample Size required when your aim is to estimate difference between two sample means with specified precision.

Formula Used

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μ₁ = Estimated first sample mean.

μ₂ = Estimated second sample mean.

SD₁ = Estimated standard deviation in first sample.

SD₂ = Estimated standard deviation in second sample.

r = Ratio of sample sizes in two groups (N2:N1)

Z _1-α/2 = the standard normal deviate corresponding the confidence level

ε = Precision

Example 1:

A researcher wants to estimate the mean difference in SBP reduction by two antihypertensive drugs, A and B. There will be two groups and each group will receive either of the drugs. He wants to estimate this difference in mean reduction in SBP within 2 mm of Hg of true value. The mean reductions in SBP with first and second drug are expected to be 28 mm of Hg and 25 mm of Hg with SD of 6 for both the groups. How much sample size shall be required at confidence level of 95%. (equal sample size in two groups).

Solution:

Here

μ₁ = 28, μ₂ = 25, SD₁ = 6,SD₂=6, confidence level = 95%, ε = 2

After putting these values, we get required sample size in each group = 49.