Power of a Test (College Board AP® Statistics)

Study Guide

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Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

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 p equals 1 half but actually p equals 1 third

    • 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 straight H subscript 0 when it is false

    • A Type II error means not rejecting straight H subscript 0 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

Examiner Tips and Tricks

You should learn the relationship that power is 1 - P(Type II error) as it is not given in the exam.

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, n, increases

      • The significance level, alpha, increases

      • The standard error of the hypothesis test decreases

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

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Mark Curtis

Author: Mark Curtis

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.