Standard Error Of Difference Calculator

The Standard Error of Difference is used to measure the precision of the difference between two sample means. It is especially useful in hypothesis testing to determine if the difference between two groups is statistically significant.

Formula

The standard error of difference is calculated using the formula:

\[ SE_{\text{diff}} = \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}} \]

Where:

• \(\sigma_1\) and \(\sigma_2\) are the standard deviations of the two groups.
• \(n_1\) and \(n_2\) are the sample sizes of the two groups.

Example Calculation

If Group 1 has a standard deviation of 5 with a sample size of 30, and Group 2 has a standard deviation of 7 with a sample size of 25, the standard error of difference would be:

\[ SE_{\text{diff}} = \sqrt{\frac{5^2}{30} + \frac{7^2}{25}} \approx 1.9031 \]

Applications

This calculation is commonly used in comparing two different population means, such as in clinical trials, social science research, and other experimental studies.