Bonferroni, Šidák & Holm-Bonferroni Multiple Hypothesis Testing FWER Correction Calculator

Control Family-Wise Error Rate (FWER) across m comparisons via Bonferroni and Šidák.

Bonferroni Per-Test Alpha Cutoff (α / m)
0.003 p-cutoff
Šidák Exact Per-Test Cutoff 0.003 p-cutoff
Unadjusted Family-Wise Error Rate 64.151 %
Bonferroni-Adjusted p-Value (m × p) 0.08 p_adj
Inputs
⚡ Scenarios:
α
Target family-wise significance level α (typically 0.05).
m tests
Total number of independent hypothesis tests m.
raw p
Observed unadjusted p-value from an individual test.
Results & Graph
Bonferroni Per-Test Alpha Cutoff (α / m)
0.003 p-cutoff
Šidák Exact Per-Test Cutoff
0.003 p-cutoff
Unadjusted Family-Wise Error Rate
64.151 %
Bonferroni-Adjusted p-Value (m × p)
0.08 p_adj

Bonferroni Per-Test Alpha Cutoff (α / m)

Graph 1 • Bonferroni & Šidák FWER • Domain Architecture & Live Telemetry Maps Nominal Family Alpha, Number Of Comparisons M, Observed Raw P Value through Bonferroni & Šidák FWER Formula.
Bonferroni Per-Test Alpha Cuto: 0.003 p-cutoff Bonferroni & Šidák FWER • Invariants & Metrics Bonferroni Per-Test Alpha Cu 0.003 p-cutoff Šidák Exact Per-Test Cutoff 0.003 p-cutoff Unadjusted Family-Wise Error 64.151 % Bonferroni-Adjusted p-Value 0.08 p_adj
Graph 2 • Bonferroni Per-Test Alpha Cutoff (α / m) Across Nominal Family Alpha Sweep (40% → 160%) Evaluates FWER_unadjusted = 1 − (1 − α)^m; α_Bonferroni = α / m; α_Šidák = 1 − across 7 operating points (current input highlighted).
0 p-cuto 0.550 p-cuto 1.10 p-cuto 0.00100 0.0200α 0.00200 0.0300α 0.00200 0.0400α 0.00300 0.0500α 0.00300 0.0600α 0.00400 0.0700α 0.00400 0.0800α
Graph 3 • Joint Sensitivity: Nominal Family Alpha × Number Of Comparisons M Compares Bonferroni Per-Test Alpha Cutoff (α / m) when Number Of Comparisons M is shifted +25% (solid) vs. −25% (dashed).
0 p-cuto 0.550 p-cuto 1.10 p-cuto --- Number Of Comparisons M @ 75% 0.00100 -30% 0.00200 -15% 0.00200 +0% 0.00200 +15% 0.00300 +30%
Summary: Across 20 tests at α=0.05, unadjusted FWER inflates to 64.2%; Bonferroni cutoff is 0.0025, Šidák cutoff is 0.00256, and raw p=0.004 adjusts to p_Bonf=0.08.
Summary: Across 20 tests at α=0.05, unadjusted FWER inflates to 64.2%; Bonferroni cutoff is 0.0025, Šidák cutoff is 0.00256, and raw p=0.004 adjusts to p_Bonf=0.08.
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Formula & Mathematical Methodology: Bonferroni & Šidák FWER Formula

FWERunadjusted = 1 − (1 − α)m
αBonferroni = α / m
α_Šidák = 1 − (1 − α)1/m
FWER_unadjusted = 1 − (1 − α)^m; α_Bonferroni = α / m; α_Šidák = 1 − (1 − α)^(1/m)
  • nominalFamilyAlpha: Nominal Family Alpha (α)
  • numberOfComparisonsM: Number Of Comparisons M (m tests)
  • observedRawPValue: Observed Raw P Value (raw p)

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Worked Mathematical Example: Bonferroni & Šidák FWER

Control Family-Wise Error Rate (FWER) across m comparisons via Bonferroni and Šidák.

  1. Specify the function parameters, matrix entries, or confusion matrix counts.
  2. Apply the closed-form or iterative formula: FWER_unadjusted = 1 − (1 − α)^m; α_Bonferroni = α / m; α_Šidák = 1 − (1 − α)^(1/m).
  3. Examine the primary result, error bounds, and 3 interactive SVG plots.
Result: Computes Bonferroni & Šidák FWER via FWER_unadjusted = 1 − (1 − α)^m; α_Bonferroni = α / m; α_Šidák = 1 − (1 − α)^(1/m).

Frequently Asked Questions

How does the Bonferroni, Šidák & Holm-Bonferroni Multiple Hypothesis Testing FWER Correction Calculator compute the solution?

It evaluates FWER_unadjusted = 1 − (1 − α)^m; α_Bonferroni = α / m; α_Šidák = 1 − (1 − α)^(1/m) directly in your browser and updates three custom SVG visualizations in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this calculator run locally offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Mathematics & Statistics · Non-Parametric & Hypothesis Testing

Bonferroni, Šidák & Holm-Bonferroni Multiple Hypothesis Testing FWER Correction Calculator: inputs, method, and how to read the result

Control Family-Wise Error Rate (FWER) across m comparisons via Bonferroni and Šidák.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Nominal Family Alpha: Target family-wise significance level α (typically 0.05).
  • Number Of Comparisons M: Total number of independent hypothesis tests m.
  • Observed Raw P Value: Observed unadjusted p-value from an individual test.

What the calculation includes

With the default values shown, Bonferroni Per-Test Alpha Cutoff (α / m) is 0.003 p-cutoff. The calculation follows Bonferroni & Šidák FWER Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Nominal Family Alpha from 0.05 α to 0.06 α changes Bonferroni Per-Test Alpha Cutoff (α / m) from 0.003 p-cutoff to 0.003 p-cutoff. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses exact analytical or standard numerical analysis formulations from NIST DLMF.
  • Double-precision floating-point arithmetic has ~15–17 significant decimal digits of precision.

Scope: Global Mathematical & Statistical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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