Type I vs Type II Error Simulator

Overview

The Type I vs Type II Error Simulator helps you understand the trade-offs between different types of statistical errors. Type I errors (false positives) occur when you reject a true null hypothesis, while Type II errors (false negatives) occur when you fail to reject a false null hypothesis. This interactive tool visualizes both error types, shows how changing alpha and effect size affects them, and demonstrates the relationship between sample size and statistical power.

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Tips

  • Type I error (α) is the probability of rejecting the null when it’s actually true (false positive)
  • Type II error (β) is the probability of failing to reject the null when it’s actually false (false negative)
  • Power (1-β) is the probability of correctly rejecting a false null hypothesis
  • Lowering alpha reduces Type I errors but increases Type II errors (for fixed sample size)
  • Increasing sample size reduces Type II errors without changing Type I error rate
  • Larger effect sizes make it easier to detect true differences (higher power, lower β)
  • The 2×2 confusion matrix shows all possible outcomes: true/false positive/negative
  • Watch how the distributions separate as you increase effect size or sample size
  • The critical region (rejection region) is determined solely by alpha