1. What is a Confidence Interval for Two Samples?

A confidence interval for two samples provides a range of values within which the true difference between two population parameters is likely to fall, with a certain level of confidence (typically 95%).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \text{diff} \) — The observed difference between the two sample means
• \( \text{ME} \) — The margin of error for the difference

Explanation: The confidence interval is centered around the observed difference and extends equally in both directions by the margin of error.

3. Importance of Confidence Intervals

Details: Confidence intervals provide more information than simple hypothesis tests by showing the range of plausible values for the population parameter difference and the precision of the estimate.

4. Using the Calculator

Tips: Enter the observed difference between your two samples and the calculated margin of error. The calculator will provide the lower and upper bounds of the confidence interval.

5. Frequently Asked Questions (FAQ)

Q1: What confidence level does this calculator use?
A: This calculator is general and works with any confidence level, as long as you input the appropriate margin of error for your desired confidence level.

Q2: How is the margin of error determined?
A: The margin of error depends on the standard error of the difference and the critical value from the appropriate distribution (usually t or z).

Q3: What does a 95% confidence interval mean?
A: If the same study were repeated many times, 95% of the calculated confidence intervals would contain the true population difference.

Q4: What if my confidence interval includes zero?
A: If the interval includes zero, there may be no statistically significant difference between the two groups at your chosen confidence level.

Q5: Can I use this for proportions as well as means?
A: Yes, the same basic formula applies to differences between proportions, though the margin of error calculation differs.