Difference between Two Means

What is a sampling distribution?

The probability distribution of a given statistic based on a random sample of size n is called as a sampling distribution.

Sampling distribution of difference between two means:

Statistical analysis are usually based on the difference between means. A distinct example for it is an experiment designed to compare the mean of a control group with the mean of an experimental group. Inferential analysis used depends upon the sampling distribution of the difference between means.

If we perform the below quoted steps repeatedly, the sampling distribution of the difference between means can be the resulting distribution, that is:

• Calculate the sample sizes n₁ and n₂ from Population 1 and Population respectively.
• Estimate the means of the two samples, that is, M₁ and M₂.
• Evaluate the difference between means M₁ - M₂. The resulting distribution is

The sampling distribution of the difference between means.

As one might have expected, the mean of the sampling distribution of the mean is μ_M1-M2 = μ1-μ2. This states that the mean of the distribution of differences between sample means is equal to the difference between population means. From the variance sum law, which states that the variance of the sampling distribution of the difference between means is equal to the variance of the sampling distribution of the mean for Population 1 + the variance of the sampling distribution of the mean for Population 2, we know that:

σ_{M1 - M2²} = σ_M1² + σ_M2²

σ_{M1 - M2²} = σ²/n₁ + σ²/n₂ (since σ_M² = σ²/ N )

The last step is to determine the area that is shaded. Then, using a Z table or the normal calculator, the area can be determined.