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Bonferroni Correction Formula:
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The Bonferroni correction is a method to counteract the problem of multiple comparisons in statistical analysis. It adjusts the significance level by dividing it by the number of comparisons being made, or equivalently multiplies the original p-values by the number of tests.
The calculator uses the Bonferroni formula:
Where:
Explanation: The correction controls the family-wise error rate by making the criteria for statistical significance more stringent when multiple tests are performed.
Details: Without correction, performing multiple statistical tests increases the probability of obtaining false positive results (Type I errors). The Bonferroni correction is a conservative method to maintain the overall error rate.
Tips: Enter the original p-value (between 0 and 1) and the number of statistical tests performed. The calculator will output the adjusted p-value.
Q1: When should I use Bonferroni correction?
A: Use when performing multiple hypothesis tests simultaneously and you want to control the family-wise error rate.
Q2: What are the limitations of Bonferroni correction?
A: It can be overly conservative, especially with large numbers of tests, potentially increasing Type II errors (false negatives).
Q3: Are there alternatives to Bonferroni correction?
A: Yes, methods like Holm-Bonferroni, Benjamini-Hochberg (FDR), or permutation tests may be more powerful in some situations.
Q4: What's the difference between Bonferroni and Holm-Bonferroni?
A: Holm's method is a step-down procedure that is less conservative while still controlling family-wise error rate.
Q5: How do I interpret the adjusted p-value?
A: Compare it to your original significance level (typically 0.05). If p_adjusted ≤ 0.05, the result remains significant after correction.