1. What is Bonferroni Correction?

The Bonferroni correction is a method to counteract the problem of multiple comparisons by adjusting the significance level. It controls the family-wise error rate by dividing the original alpha level by the number of comparisons being made.

2. How Does the Calculator Work?

The calculator uses the Bonferroni correction formula:

Where:

• \( \alpha \) — Original significance level (typically 0.05)
• \( \text{number\_comparisons} \) — Number of hypothesis tests being performed
• \( \alpha' \) — Adjusted significance level

Explanation: The correction reduces the significance threshold for each individual test to maintain the overall Type I error rate across all tests.

3. Importance of Multiple Comparisons Correction

Details: Without correction, conducting multiple statistical tests increases the probability of false positives (Type I errors). The Bonferroni correction is a conservative method to maintain the overall error rate.

4. Using the Calculator

Tips: Enter the original alpha level (typically 0.05) and the number of comparisons being made. The calculator will output the new significance threshold for each individual test.

5. Frequently Asked Questions (FAQ)

Q1: When should I use Bonferroni correction?
A: Use when conducting multiple hypothesis tests simultaneously to maintain the overall Type I error rate.

Q2: What are alternatives to Bonferroni correction?
A: Less conservative methods include Holm-Bonferroni, Benjamini-Hochberg (FDR), or permutation tests.

Q3: Is Bonferroni always appropriate?
A: No, it can be overly conservative when tests are highly correlated, potentially increasing Type II errors.

Q4: How does this affect power?
A: The correction reduces statistical power for each individual test as the significance threshold becomes stricter.

Q5: Can I use this for confidence intervals?
A: Yes, you can adjust confidence levels similarly (e.g., 95% CI becomes 99% for 5 comparisons).