Type I Error Calculator

Calculate the probability of Type I error (false positive) across multiple independent tests, and the Bonferroni-corrected significance level.

Family-wise Error Rate

0.226219

FW Error Rate (%)22.6219
Bonferroni-Corrected Alpha0.010000
P(No Error in 1 Test)0.9500

Family-wise Error Rate vs Significance Level (alpha)

सूत्र देखें →

सूत्र

## Understanding Type I Error ### Formula **Family-wise Error Rate = 1 - (1 - alpha)^k** **Bonferroni Correction: alpha_corrected = alpha / k** A Type I error occurs when you reject a true null hypothesis (false positive). When performing multiple tests, the probability of at least one false positive increases rapidly. The Bonferroni correction divides alpha by the number of tests to control the family-wise error rate.

हल किया गया उदाहरण

You run 5 independent tests at alpha = 0.05. What is the chance of at least one false positive?

  1. 01P(no error in 1 test) = 1 - 0.05 = 0.95
  2. 02P(no error in all 5) = 0.95^5 = 0.7738
  3. 03P(at least 1 error) = 1 - 0.7738 = 0.2262
  4. 04Family-wise error rate = 22.6%
  5. 05Bonferroni correction: 0.05 / 5 = 0.01 per test