Type I Error Calculator — 公式
## 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.
### 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.
计算示例
You run 5 independent tests at alpha = 0.05. What is the chance of at least one false positive?
- P(no error in 1 test) = 1 - 0.05 = 0.95
- P(no error in all 5) = 0.95^5 = 0.7738
- P(at least 1 error) = 1 - 0.7738 = 0.2262
- Family-wise error rate = 22.6%
- Bonferroni correction: 0.05 / 5 = 0.01 per test