Sampling Distribution of Difference in Means

Explore how the difference between sample means behaves when you draw samples from two populations.

Population Parameters

Population 1

Mean (μ₁):

Std Dev (σ₁):

Population 2

Mean (μ₂):

Std Dev (σ₂):

Sample Simulation Settings

Sample Size 1 (n₁):

Sample Size 2 (n₂):

Number of Samples:

Understanding Sampling Distribution of Difference in Means

The sampling distribution of the difference in means is a probability distribution of the differences between the means of samples taken from two populations. It helps us understand how much the means of samples can vary and is crucial for hypothesis testing, especially when comparing the means of two groups. When we repeatedly take samples from two populations and calculate the difference between their means, these differences form a distribution. According to the Central Limit Theorem, this distribution will be approximately normal if the sample sizes are large enough, regardless of the original population distributions. The mean of this sampling distribution is the difference between the population means (μ₁ - μ₂). The standard deviation, often called the standard error of the difference in means, depends on the population standard deviations and sample sizes. This tool visualizes this distribution and calculates its key properties, aiding in understanding statistical inference and comparative data analysis.