Bonferroni Correction Calculator
Adjust significance levels for multiple comparisons to control family-wise error rate
Multiple Comparison Correction
Total number of statistical tests or comparisons
Original significance level (typically 5%)
Correction Results
Method: Classic Bonferroni Correction
Formula: α_corrected = 5% / 0 = 0.0000%
Power Reduction: 0.0% decrease in statistical power
Interpretation
Example Calculation
Medical Study Example
Scenario: Testing 4 different treatments
Original significance level: 5%
Number of tests: 4
Problem: Multiple comparisons increase false positive rate
Classic Bonferroni
Corrected α = 5% / 4 = 1.25%
Each test needs p < 0.0125 to be significant
Family-wise error rate ≤ 5%
Šidák Correction
Corrected α = 1 - (1 - 0.05)^(1/4)
= 1 - 0.95^0.25 = 0.0127 = 1.27%
Slightly less conservative
Multiple Comparison Methods
Bonferroni
Most conservative
Controls FWER strongly
Šidák
Less conservative
Assumes independence
Holm-Bonferroni
Step-down method
More powerful alternative
When to Use
Multiple hypothesis testing
Post-hoc analysis in ANOVA
Exploratory data analysis
Clinical trial safety analyses
Understanding Bonferroni Correction
What is Bonferroni Correction?
The Bonferroni correction is a statistical method used to address the multiple comparisons problem. When performing multiple statistical tests simultaneously, the probability of obtaining at least one false-positive result (Type I error) increases. The Bonferroni correction controls this family-wise error rate.
Why is it Important?
- •Controls false-positive results in multiple testing
- •Maintains overall Type I error rate
- •Ensures meaningful statistical significance
- •Required in many scientific publications
Correction Formulas
Classic Bonferroni
α_corrected = α / m
Where α is the original significance level and m is the number of tests
Šidák Correction
α_corrected = 1 - (1 - p)^(1/m)
Less conservative, assumes independence between tests
Advantages
- ✓Simple and straightforward to apply
- ✓Strongly controls family-wise error rate
- ✓Works with any statistical test
- ✓Widely accepted in scientific literature
Limitations
- •Can be overly conservative
- •Increases risk of false negatives
- •Reduces statistical power significantly
- •May miss important true effects
Alternatives
- →Holm-Bonferroni method
- →Benjamini-Hochberg (FDR)
- →False Discovery Rate methods
- →Westfall-Young procedures