Standard Error of Difference Calculator

Formula

The formula to calculate the Standard Error of Difference (SED) is:

\[ SED = \sqrt{\left(\frac{\sigma_1^2}{n_1}\right) + \left(\frac{\sigma_2^2}{n_2}\right)} \]

Where:

\( SED \) is the standard error of the difference between two sample means
\( \sigma_1 \) is the standard deviation of sample 1
\( n_1 \) is the sample size of sample 1
\( \sigma_2 \) is the standard deviation of sample 2
\( n_2 \) is the sample size of sample 2

What is the 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.

Example Calculation

Let's assume the following values:

Standard Deviation of Sample 1 (σ₁): 4
Sample Size of Sample 1 (n₁): 50
Standard Deviation of Sample 2 (σ₂): 5
Sample Size of Sample 2 (n₂): 60

Step 1: Calculate the Standard Error of Difference (SED):

\[ SED = \sqrt{\left(\frac{4^2}{50}\right) + \left(\frac{5^2}{60}\right)} = \sqrt{\left(\frac{16}{50}\right) + \left(\frac{25}{60}\right)} = \sqrt{0.32 + 0.4167} = \sqrt{0.7367} \approx 0.86 \]

The standard error of the difference is approximately 0.86.