Statistics: Meaning of Power

Objectives

• Students will describe power as the relative frequency of “reject the null” conclusions for a given hypothesis test.
• Students will recognize that when the null hypothesis is true, power is exactly the same as alpha.
• Students will recognize that if the null hypothesis is actually false, power measures the ability to detect an existing difference between truth and hypothesis.
• Students will describe how power is influenced (in predictable directions) by sample size, alpha, and difference between actual and hypothesized parameter values.

Vocabulary

• alpha level
• critical value
• power
• significance level
• type I error
• type II error

About the Lesson

In this lesson, samples are generated from a population for a particular hypothesis test, leading to the conjecture that the null hypothesis is actually false.
As a result, students will:

• Observe that most of the sample means fall in the rejection region.
• Examine repeated samples to observe the relative frequency of "reject the null" conclusions -- that is, power or alph --as conditions change.
• Recognize how the sample size, the true population mean, and the alpha, are related to power.
• Relate the value of power to beta.