Enter the standard deviations and sample sizes for two samples into the calculator to determine the standard error of the difference between the two sample means. This calculator helps in estimating the variability between the sample means.

Standard Error of Difference Formula

The following formula is used to calculate the standard error of the difference between two sample means. 

SED = √((σ₁² / n₁) + (σ₂² / n₂))

Variables:

  • SED is the standard error of the difference between two sample means
  • σ₁ is the standard deviation of sample 1
  • n₁ is the sample size of sample 1
  • σ₂ is the standard deviation of sample 2
  • n₂ is the sample size of sample 2

To calculate the standard error of the difference, square the standard deviations of both samples, divide each by their respective sample sizes, add the two values, and take the square root of the sum.

What is Standard Error of Difference?

The standard error of the difference (SED) is a measure of how much the difference between two sample means is expected to vary due to sampling variability. It is used in hypothesis testing, particularly in the context of comparing two independent sample means. A smaller SED suggests that the sample means are more likely to be close to the true population means, while a larger SED indicates more variability and less certainty about the true difference between population means.

How to Calculate Standard Error of Difference?

The following steps outline how to calculate the Standard Error of Difference.

  1. First, determine the standard deviation of sample 1 (σ₁).
  2. Next, determine the sample size of sample 1 (n₁).
  3. Then, determine the standard deviation of sample 2 (σ₂).
  4. Next, determine the sample size of sample 2 (n₂).
  5. Use the formula SED = √((σ₁² / n₁) + (σ₂² / n₂)) to calculate the Standard Error of Difference.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Standard deviation of sample 1 (σ₁) = 5

Sample size of sample 1 (n₁) = 30

Standard deviation of sample 2 (σ₂) = 4

Sample size of sample 2 (n₂) = 40