1. What is the Bonferroni Adjustment?

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 tests being performed.

2. How Does the Calculator Work?

The calculator uses the Bonferroni formula:

Where:

• \( α \) — Original significance level (typically 0.05)
• \( k \) — Number of tests being performed

Explanation: The adjustment ensures that the probability of making at least one Type I error (false positive) across all tests remains at the desired significance level.

3. Importance of Multiple Testing Correction

Details: When performing multiple statistical tests, the chance of a false positive increases. The Bonferroni correction is a conservative method to maintain the overall error rate.

4. Using the Calculator

Tips: Enter your original significance level (typically 0.05) and the number of tests you're performing. The calculator will output the adjusted significance level you should use for each individual test.

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Bonferroni correction?
A: Use it when you're performing multiple hypothesis tests and want to control the family-wise error rate (probability of at least one false positive).

Q2: Is Bonferroni the only multiple testing correction?
A: No, other methods include Holm-Bonferroni, Benjamini-Hochberg (FDR), and Šidák corrections. Bonferroni is the most conservative.

Q3: What are the limitations of Bonferroni?
A: It can be overly conservative, especially with many tests, potentially increasing Type II errors (false negatives). It assumes tests are independent.

Q4: Can I use Bonferroni for confidence intervals?
A: Yes, you can adjust confidence levels similarly (e.g., use 99% CIs for 20 tests to maintain 95% family-wise confidence).

Q5: What's a typical adjusted alpha value?
A: For 20 tests with original α=0.05, adjusted α=0.0025. For 100 tests, it would be 0.0005.