Bonferroni Correction Calculator

Adjust a family-wise alpha, correct a raw p-value, compare the Sidak threshold, and estimate the family-wise error rate from any per-comparison alpha.

🧪Multiple-Testing Presets

🔢Correction Inputs

Research setting

Use the setting to label the breakdown and reporting notes.

Family-wise alpha

The total false-positive rate you want across the family.

Number of tests in family (m)

Count planned hypotheses in the same claim family.

Raw p-value to adjust

Enter one unadjusted p-value; repeat for others as needed.

Per-comparison alpha for FWER

Shows FWER if every test is judged at this single-test alpha.

Decision method

Bonferroni is conservative; Sidak assumes independent tests.

P-value role

Role changes interpretation wording, not the correction math.

Displayed precision

Use more decimals when m is large or thresholds are tiny.

Bonferroni alpha 0.004167 family alpha divided by m

Adjusted p-value 0.045600 min(raw p x m, 1)

Sidak alpha 0.004265 independent-test threshold

FWER at alpha per test 45.96% 1 - (1 - alpha per)^m

🧭Current Correction Grid

12Tests m

0.050Family alpha

0.003800Raw p

0.91p / Bonf alpha

2.35%Sidak gap

PassBonferroni

PassSidak

11.4xFWER / alpha

0.004167Needed raw p

CorrectedReport style

📐Formula Breakdown

Bonferroni adjusted alphaα_Bonf = α_family / m. A raw p-value passes when p ≤ α_Bonf.

Bonferroni adjusted p-valuep_adj = min(p x m, 1). A corrected p-value passes when p_adj ≤ α_family.

Sidak adjusted alphaα_Sidak = 1 - (1 - α_family)^1/m. It is slightly less conservative when tests are independent.

Family-wise error rateFWER = 1 - (1 - α_per)^m. This shows false-positive risk when each test uses the entered per-test alpha.

📋Preset Scenario Comparison

Scenario	m	Family Alpha	Raw p	Bonf Alpha	Adj p	Sidak Alpha	Typical Read
Clinical biomarker panel	12	0.05	0.0038	0.004167	0.0456	0.004265	Just passes Bonferroni at 5%
A/B metrics dashboard	8	0.05	0.0120	0.006250	0.0960	0.006391	Raw signal does not survive
Neuroimaging ROI set	64	0.05	0.00090	0.000781	0.0576	0.000801	Close but above corrected threshold
Candidate SNP screen	500	0.05	0.00012	0.000100	0.0600	0.000103	Suggestive candidate signal
RNA pathway sweep	1200	0.05	0.000030	0.0000417	0.0360	0.0000427	Passes a strict family correction
Education item audit	24	0.10	0.0060	0.004167	0.1440	0.004386	Exploratory flag only
Sensor fault bank	40	0.01	0.00031	0.000250	0.0124	0.000251	Misses a 1% family rule
Ecology species contrasts	18	0.05	0.0041	0.002778	0.0738	0.002845	Report as uncorrected evidence
Marketing segment slices	30	0.05	0.0019	0.001667	0.0570	0.001708	Near miss after correction

⚖Bonferroni vs Sidak Reference

Method	Threshold Formula	Assumption	Conservatism	When To Prefer
Bonferroni alpha	α / m	No independence required	Often conservative	Default simple family control
Bonferroni p-value	min(p x m, 1)	Same as Bonferroni alpha	Often conservative	Reporting corrected p-values
Sidak alpha	1 - (1 - α)^(1/m)	Independent tests	Slightly less conservative	Independent planned comparisons
No correction	α per test	Single isolated test	No family control	Only one primary hypothesis
Holm context	Step-down thresholds	Ordered p-values	Less conservative than Bonferroni	Full family p-value lists
FDR context	Controls expected false discoveries	Many discoveries expected	Different error goal	Large screening studies

📈FWER Lookup at Common Per-Test Alpha

Tests m	FWER at 0.05	FWER at 0.01	Bonf Alpha for 0.05	Sidak Alpha for 0.05
2	9.75%	1.99%	0.025000	0.025321
5	22.62%	4.90%	0.010000	0.010206
10	40.13%	9.56%	0.005000	0.005116
20	64.15%	18.21%	0.002500	0.002561
50	92.31%	39.50%	0.001000	0.001026
100	99.41%	63.40%	0.000500	0.000513
500	>99.99%	99.34%	0.000100	0.000103

🔍Multiple-Testing Reporting Checks

Check	Good Practice	Risk Pattern	Why It Matters	Calculator Field
Family definition	Tests answer one planned family	Conveniently excluding tests	Changes the correction threshold	Number of tests m
Alpha chosen first	Family alpha set before analysis	Alpha moved after seeing p-values	Inflates false-positive claims	Family-wise alpha
Raw p precision	Use full unrounded p-value	Only p < 0.05 available	Adjusted p needs numeric detail	Raw p-value
Method stated	Name Bonferroni or Sidak	Only says corrected	Readers need the error rule	Decision method
FWER context	Show risk from uncorrected alpha	Treating many tests as one test	Explains why correction is needed	Per-comparison alpha
Exploratory screen	Label as hypothesis-generating	Claims confirmation from a sweep	Correction does not fix weak design	P-value role

💡Practical Correction Tips

Count the family before testing: Bonferroni protects the family you define. Moving tests in or out after viewing results weakens the false-positive control.

Use adjusted p-values for reporting: p_adj = min(p x m, 1) lets readers compare every result against the same family alpha.

Compare Sidak cautiously: Sidak is mathematically exact for independent tests, while Bonferroni stays valid as a simple upper-bound control.

Separate screening from confirmation: Very large families can need tiny thresholds, so use follow-up validation for discoveries from broad exploratory screens.

Let’s say you’re testing a new drug on three symptoms simultanously. You get important results for only one of those three symptom. Hooray! But then you discover later that running all three together raised the chances of getting a false positive by chance from five percent to fifteen percent. That’s the sneaky pitfall of multiple testing.

If you performs multiple statistical tests within a single study, each additional test multiply your chances of being wrong. Use the Bonferroni correction to fix this inflation.

Why Bonferroni Correction Is Important

Enter your exact number of comparisons into the calculator above. It will crunch the numbers and adjust p-values (or alpha level) to match. This helps you know what you can call a finding rather than just noise pretending to be a signal.

Just calculate your desired family-wise error rate (typically five percent), then divide by the number of comparisons you made. So if you did ten comparisons, now your new threshold for statistical significance is half a percent. Why does that feel so harsh? Because that’s its job. It’s being as conservative as possible. So you increase your confidence in your findings, they’re probably not a fluke! But this comes at the cost of losing some ability to pick up on really small, significant effects. That’s what most researchers is reluctant to sign off on. “I just want my data to speak!” but also “and I want to make sure my data isn’t lying to me.”

This little tool on page makes it easier to understand that changing either the raw p-value or alpha threshold will always result in the same decision. Most people trip up on question of what makes a test. Just because it’s obvious doesn’t mean it should of been counted. Ten biomarker measurements? That’s 10 tests. Now separate each one into genders? You’ve just doubled your family size there. The calculator asks you to specifically define this family. It also provides presets so you can load common study designs, such as A/B testing dashboards and clinical panels. These give the abstract numbers a concrete set of study designs to attach too.

Because the risk of over- (or under-) correcting something based off a small pilot study and doing the same thing with a massive genomic screen is too easy. The penalty for staring harder becomes steeper very quickly, and context matter.

The other thing that’s shown on this calculator (which it compares to the Bonferroni result) is what’s called the Sidak adjustment. It involve a more complicated exponential equation, and it assume that your tests are independent. So in practical terms, the actual numbers you come up with using Bonferroni vs. Sidak will often be pretty similar, particularly if you have only a few test and are doing something like a.05 significance test. But when you’re talking hundreds of variables, even the tiniest mathematical variation in the cutoff might make result go from significant to non-significant. Having both in side-by-side format lets you assess just how vulnerable your results are to the independence assumption.

Last, look at the family-wise error rate output. In this case, it tells you the overall probability that you will make at least one false positive claim without doing any correction. As you keep adding tests, you’ll see the number shoot up from five percent to ninety percent, which can be a sobering reminder about why we’re even doing this in the first place! It makes a concrete risk metric out of something that’s otherwise an abstract statistic. We’re not playing with numbers here: we’re quantifying the likelihood of being wrong.

Whether you’re creating a business report or peer-reviewed paper, the calculator gives you exactness required for accurate reporting. It removes the guessing game from comparing many thing at once. But finally, all of this gets back to how much care is in the discipline to use such a thing rather than in the formula itself. Do you define your hypotheses prior to seeing the data? Are all the comparisons that inform your ultimate conclusions counted? And are you willing to throw away an interesting lead when the numbers prove it wrong? If so, great, but a wrong answer is worse then none at all. The math shields you from yourself, from your optimism.