Power of a test
Power is the probability of rejecting the null when a real effect exists: power = 1 - beta. Power rises with a larger sample, a bigger true effect and a larger alpha.
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Analogy
How good a metal detector is at finding a coin that really is buried.
Example
H0: mean 100, true mean 104sigma 15, n 100, alpha 0.05 one-sidedReject if mean > 100 + 1.645 x 1.5 = 102.47Power = P(Z > (102.47 - 104)/1.5)= P(Z > -1.02) = 0.85
In practice
Studies are planned for about 80 percent power so a real effect is likely to show up.
Practice
Flashcards
- What is power?1 minus beta: the chance of detecting a real effect.
Interview questions
- Explain Type I and Type II errors using a medical screening example, and say how sample size affects them.
- Type I is a false alarm
- Type II is a missed case
- Alpha is the Type I rate
- More data raises power
- Lowering alpha raises beta
Questions people ask
How can I increase the power of a study?
Collect more data, since this shrinks the standard error. Reduce measurement noise, aim for a larger effect, or accept a higher alpha. Of these, sample size is usually the practical lever, which is why power is calculated before data collection.
What is the link between power and Type II error?
Power equals 1 minus the Type II error probability beta. If beta is 0.15, power is 0.85, meaning an 85 percent chance of detecting the effect when it exists. Low power means real effects are often missed, so a study with 30 percent power wastes time and money.