Power of a Test (College Board AP® Statistics)

Power of a test

What is the power of a test?

• The power of a test is the probability of correctly rejecting the null hypothesis when it was, in reality, false

  • A better hypothesis test has a higher power

• In practice, you need to be given the actual (true) population parameter to calculate the power
  

  • For example, H₀ assumed  but actually 

  • Power is P(in the critical region, given the actual population parameter is true)

How does power relate to Type II errors?

• The power of a test is 1 - P(Type II error) 

  • Power is the probability of correctly rejecting when it is false

  • A Type II error means not rejecting when it is false

    • These probabilities are complements of each other (so sum to 1)

• You ideally want the power of a test to be greater than 0.5 

  • That way it's less likely to produce a Type II error

    • And more likely to reach the correct conclusion

How do I increase the power of a test?

• As the power is 1 - P(Type II error), to increase the power of the test you need to reduce the probability of a Type II error

  • This happens when one of the following is changed (and the others are kept the same):

    • The sample size, , increases

    • The significance level, , increases

    • The standard error of the hypothesis test decreases

    • The actual (true) population parameter is farther from the null population parameter