Bonferroni Correction Alpha Calculator

Calculator

Family Alpha

Common values are 0.05, 0.01, or 0.10.

Number of Comparisons

Use the number of tests in the same family.

Decimal Places

Controls displayed precision.

Decision Rule

Most reports use the first rule.

Raw P Values

Separate values by lines, commas, spaces, or semicolons.

Test Labels

Optional. Use one label per line.

Study Notes

Add project, outcome, or model notes.

Comparison Count Option

Use entered p-value count as comparisons

This is useful when each p value is one test.

Output Includes

Corrected alpha
Adjusted p values
Family error estimates
CSV and PDF export

Example Data Table

Family Alpha	Comparisons	Corrected Alpha	Example Raw p	Decision
0.05	5	0.01	0.008	Significant
0.05	10	0.005	0.008	Not significant
0.01	4	0.0025	0.003	Not significant
0.10	20	0.005	0.004	Significant

Formula Used

Bonferroni corrected alpha:

Corrected alpha = family alpha / number of comparisons

Adjusted p value:

Adjusted p = min(raw p value × number of comparisons, 1)

Uncorrected family error estimate:

FWER = 1 - (1 - alpha)^m

Corrected family error estimate:

Corrected FWER = 1 - (1 - corrected alpha)^m

Here, m means the number of comparisons. Alpha is the accepted Type I error rate for the full test family.

How to Use This Calculator

Enter the family alpha for your study.
Enter the number of planned comparisons.
Add raw p values if you want test-level decisions.
Add optional labels for clearer exported reports.
Choose the decision rule used by your report.
Press the calculate button.
Review the corrected alpha and adjusted p values.
Download the CSV or PDF summary.

Understanding Alpha In Bonferroni Correction

Alpha is the error limit chosen before testing. It is often written as α. In many studies, alpha is 0.05. That means the researcher accepts a five percent chance of a false positive for one planned test. The problem grows when many tests are run together. Each test creates another chance to flag a result by luck.

Why Bonferroni Helps

The Bonferroni correction protects the family of tests. It divides the family alpha by the number of comparisons. The new value becomes the per-test alpha. A p value must be below that smaller value to be called significant. This method is simple, strict, and easy to explain. It is useful when false positives are costly.

What The Calculator Does

This calculator takes your family alpha and comparison count. It then returns the corrected alpha. It also multiplies each entered p value by the number of tests. That gives an adjusted p value. The tool compares raw p values with the corrected threshold. It also compares adjusted p values with the family alpha. Both views should give the same decision.

Choosing The Comparison Count

The comparison count should match your planned family of tests. It may be the number of pairwise group contrasts. It may be the number of outcomes tested. It may also be the number of models compared. The best choice depends on your analysis plan. Define it before looking at results. This keeps the decision fair.

Reading The Output

A smaller corrected alpha makes significance harder to reach. For example, a family alpha of 0.05 with ten comparisons gives 0.005. A raw p value of 0.004 passes. A raw p value of 0.012 does not pass. The adjusted p value view shows the same logic in another way.

Practical Notes

Bonferroni is conservative when tests are correlated. It can reduce power. Some projects may prefer Holm or false discovery rate methods. Still, Bonferroni remains a trusted first check. It is clear, fast, and suitable for confirmatory work. Use the exported summary for audit trails.

Report original alpha, method, count, and corrected alpha. Include raw p values and adjusted p values. Add final decisions in your notes clearly.

FAQs

What is alpha?

Alpha is the chosen chance of a Type I error. It is the risk of calling a result significant when no true effect exists.

What is Bonferroni corrected alpha?

It is the family alpha divided by the number of comparisons. It gives a stricter threshold for each individual test.

When should I use Bonferroni correction?

Use it when you run several related tests and want to control the chance of any false positive across the full family.

What comparison count should I enter?

Enter the number of planned tests in the same analysis family. This may be pairwise contrasts, outcomes, or model comparisons.

Can Bonferroni be too strict?

Yes. It can be conservative, especially when tests are correlated. This may reduce power and hide real effects.

How are adjusted p values calculated?

Each raw p value is multiplied by the number of comparisons. Values above one are capped at one.

Should I use p less than or equal to alpha?

Many reports use p less than or equal to alpha. Use the rule required by your study plan, journal, or reviewer.

Does significance prove the result is true?

No. Significance only means the p value passed the chosen threshold. Study design, assumptions, and effect size still matter.