Type I and Type II Errors › Summary
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Type I and Type II errors are the two ways hypothesis tests can fail. Understanding them is essential for designing studies and interpreting results:
Type I Error (α): Rejecting a true null hypothesis, a false positive. You conclude an effect exists when it doesn't.
- Probability equals your chosen significance level
- You control α directly by your choice of significance threshold
- Consequences: wasted resources, false claims, harm from unnecessary interventions
Type II Error (β): Failing to reject a false null hypothesis, a false negative. You miss a real effect.
- Probability depends on effect size, sample size, significance level, and population variance
- You influence β through study design, primarily sample size
- Consequences: missed discoveries, failed treatments, wasted research effort
Power (1 - β): The probability of correctly detecting a true effect.
- Conventional target: 80% (β = 0.20)
- Higher power requires larger samples, larger effects, or higher α
- Underpowered studies are one of the most serious problems in research
The Fundamental Tradeoff: For a fixed sample size, decreasing α increases β. The only way to reduce both simultaneously is to increase the sample size.
The key insight is that these error rates are not just abstract probabilities: they affect patients and businesses, as well as scientific progress. Thoughtful study design requires explicitly considering these tradeoffs in the context of your specific application.