Type I and Type II Errors Math Example 3

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Example 3

easy
If we set α=0.01\alpha = 0.01 (stricter) instead of α=0.05\alpha = 0.05, what happens to Type I error rate? What likely happens to Type II error rate?

Solution

  1. 1
    Type I error rate: decreases from 0.05 to 0.01 — we are less likely to falsely reject H0H_0
  2. 2
    Type II error rate: increases — by requiring stronger evidence to reject H0H_0, we miss more true effects
  3. 3
    Trade-off: stricter α makes it harder to reject H₀, protecting against false discoveries but missing real effects

Answer

Stricter α\alpha → lower Type I rate, higher Type II rate. Classic trade-off.
The trade-off between Type I and II errors is fundamental. A stricter decision rule (smaller α) reduces false positives but misses more true effects. This trade-off is why significance levels must be chosen based on the relative costs of each error type.

About Type I and Type II Errors

Type I error (α\alpha): rejecting H0H_0 when it is actually true (false positive). Type II error (β\beta): failing to reject H0H_0 when it is actually false (false negative).

Learn more about Type I and Type II Errors →

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