Aim: To Calculate Sample Size required to test whether two sample means are significantly different.

Formula Used

For two tailed hypothesis

---

For one tailed hypothesis

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 = the standard normal deviate corresponding the confidence level

β = 1 – Power (Out of 1) (e.g. 80% = 0.8)

Z _1-β = the standard normal deviate corresponding to 1- β.

Example 1:

Two antihypertensive drugs are to be compared to test whether mean reduction in SBP with these drugs are significantly different.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% and power of 80% (equal sample size in two groups).

Solution:

Here

μ₁ = 28, μ₂ = 25, SD₁ = 6,SD₂=6, confidence level = 95%, power = 80%, two tailed ("significantly different")

After putting these values, we get required sample size in each group = 63.

Example 2:

Two antihypertensive drugs are to be compared to test whether mean reduction in SBP with first drug is significantly more than the mean reduction with second drug.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% and power of 80% (equal sample size in two groups).

Solution:

Here

μ₁ = 28, μ₂ = 25, SD₁ = 6,SD₂=6, confidence level = 95%, power = 80%, one tailed ("significantly more")

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