Visualize the trade-offs between false positives and false negatives
P(Type I Error) = α = Rejecting true H₀
Distance between H₀ and H₁ distributions
Larger samples increase power and reduce β
Type I Error (α): False Positive - Rejecting the null hypothesis when it is actually true. This is the significance level you set (e.g., 0.05 means 5% chance of false positive).
Type II Error (β): False Negative - Failing to reject the null hypothesis when it is actually false. This depends on effect size, sample size, and alpha.
Statistical Power (1-β): The probability of correctly detecting a true effect. Higher power means lower chance of missing a real difference.
The Trade-off: For a fixed sample size, lowering α (being more conservative) increases β (more likely to miss real effects). The solution is to increase sample size!
| H₀ is True | H₀ is False | |
|---|---|---|
| Reject H₀ | Type I Error (α) | Correct (Power) |
| Fail to Reject H₀ | Correct (1-α) | Type II Error (β) |