Question

Explain the concept if sample power. How is sample power related to hypotgesis testing? how is a power analysis related to sample power?

Answer 1

The power of a binary hypothesis test is the probability that the test rejects the null hypothesis (H₀) when a specific alternative hypothesis (H₁) is true. The statistical power ranges from 0 to 1, and as statistical power increases, the probability of making a type II error (wrongly failing to reject the null hypothesis) decreases. For a type II error probability of β, the corresponding statistical power is 1 − β.

power= pr( reject H₀ | H₁ is true )

The power of a hypothesis test is the probability of making the correct decision if the alternative hypothesis is true. That is, the power of a hypothesis test is the probability of rejecting the null hypothesis H₀ when the alternative hypothesis H_A is the hypothesis that is true.

Power analysis is directly related to tests of hypotheses. While conducting tests of hypotheses, the researcher can commit two types of errors: Type I error and Type II error. Statistical power mainly deals with Type II errors.