Type II Error and Power of the Test
Understand the probability of failing to reject a false null hypothesis and how to design more powerful tests.
Type II Error ()
Type II Error: Failing to reject when the alternative hypothesis is actually true.
The probability of a Type II error () depends on:
- •The actual value of the parameter under
- •The sample size
- •The level of significance
Power of the Test
Power: The probability of correctly rejecting a false null hypothesis. It's the probability of detecting an effect when one actually exists.
Low Power
High chance of missing a real effect
High Power
Likely to detect a real effect
Factors Affecting Power
Increase Sample Size ()
Larger samples reduce variability → higher power
Increase Significance Level ()
Larger α makes rejection easier → higher power (but higher Type I risk)
Larger Effect Size
Bigger difference from is easier to detect
Lower Variability ()
Less noise in data makes effects easier to detect
Common Pitfalls
Confusing α and β
α = P(Type I) = P(reject true H₀). β = P(Type II) = P(fail to reject false H₀).
Thinking Power = 1 - α
Power = 1 - β, not 1 - α. These are different concepts.
Ignoring Power in Study Design
Low-powered studies often fail to detect real effects, wasting resources.
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