Simultaneous Confidence Interval Calculator

Formula Used

Simultaneous confidence interval for multiple means:

CI = Mean ± t * (SD / √n)

Where t is the critical t value adjusted for multiple comparisons using Bonferroni correction:

t = t(1 - α / 2k, n-1)

How to Use This Calculator

• Enter means separated by commas.
• Enter corresponding standard deviations.
• Enter sample size (n) for all groups.
• Set confidence level in percentage (e.g., 95).
• Click "Calculate" to see lower and upper bounds.
• Download results in CSV or PDF as needed.

Example Data Table

FAQs

1. What is a simultaneous confidence interval? It is a range for multiple means calculated together to maintain overall confidence level.

2. How is it different from separate intervals? Separate intervals ignore multiple comparisons and can underestimate error probability.

3. What sample size should I use? Use the same sample size for all groups or adjust formulas if different.

4. How do I interpret the results? Each mean’s true value lies within the interval with given confidence.

5. Can I use this for unequal sample sizes? Modifications are needed; currently it assumes equal n for simplicity.

6. Why use Bonferroni correction? To adjust critical t for multiple comparisons and avoid inflated error rates.

7. Can I download the results? Yes, CSV and PDF download options are provided above the form.

8. Can I change confidence level? Yes, input your desired percentage (e.g., 90 or 99).