Bonferroni Correction Calculator
Adjust the significance level for multiple comparisons.
The Bonferroni correction guards against false positives when running many tests.
How the Math Works
The Bonferroni Correction adjusts the significance level to account for multiple comparisons, reducing the risk of false positives. When conducting multiple statistical tests, the probability of finding at least one significant result by chance increases. To counteract this, the corrected alpha level is calculated by dividing the original significance level (typically 0.05) by the number of tests performed. For example, with 5 comparisons and a 0.05 alpha, the adjusted threshold becomes 0.01 (0.05 / 5). This ensures the overall family-wise error rate remains controlled, maintaining statistical rigor in analyses.
Practical Applications
To apply the Bonferroni Correction, first determine the number of statistical tests being conducted in your analysis. Divide your desired overall significance level (e.g., 0.05) by this number to compute the adjusted alpha for each individual test. Use this stricter threshold when evaluating p-values. For instance, in a clinical trial comparing three treatments, if each comparison uses an adjusted alpha of 0.0167 (0.05 / 3), only results with p-values below this threshold are considered statistically significant. This method is widely used in fields like psychology, medicine, and social sciences to prevent spurious findings from multiple testing.
Day-to-Day Use
While most people don't perform statistical tests daily, the Bonferroni Correction helps interpret research findings they encounter in media or healthcare decisions. When studies report results using this correction, it signals that findings have been rigorously validated to minimize false discoveries. In business or personal decisions involving multiple metrics (e.g., A/B testing website changes), understanding this correction aids in evaluating whether observed differences are truly meaningful or just random noise. It promotes evidence-based choices by emphasizing the importance of statistical rigor in real-world problem-solving.
Worked example
alpha 0.05 over 10 tests gives 0.005.
FAQ
Why correct at all?
Many tests inflate the chance of at least one false positive.