1. What is Standard Error Difference?

The Standard Error Difference (SED) measures the standard deviation of the sampling distribution of the difference between two sample means. It's used in hypothesis testing to compare two independent groups.

2. How Does the Calculator Work?

The calculator uses the Standard Error Difference formula:

Where:

• \( s1 \) — Standard deviation of group 1
• \( n1 \) — Sample size of group 1
• \( s2 \) — Standard deviation of group 2
• \( n2 \) — Sample size of group 2

Explanation: The formula combines the standard errors of both groups to estimate the variability in the difference between their means.

3. Importance of SED Calculation

Details: SED is crucial for constructing confidence intervals and performing t-tests when comparing two independent sample means. It helps determine if observed differences are statistically significant.

4. Using the Calculator

Tips: Enter standard deviations and sample sizes for both groups. All values must be valid (standard deviations ≥ 0, sample sizes > 0).

5. Frequently Asked Questions (FAQ)

Q1: When should I use this calculation?
A: Use it when comparing means from two independent groups, typically before performing an independent samples t-test.

Q2: What's the difference between SE and SED?
A: SE measures variability in a single sample mean, while SED measures variability in the difference between two sample means.

Q3: Does this assume equal variances?
A: No, this is the formula for unequal variances (Welch's t-test approach). For equal variances, a pooled variance approach would be used.

Q4: Can I use this for dependent samples?
A: No, for paired/dependent samples, you would use the standard error of the mean differences.

Q5: How does sample size affect SED?
A: Larger sample sizes reduce SED, making it easier to detect significant differences between groups.