## The Power of a Test

**Overview:**

When you hope your hypothesis test is strong enough to reject the null hypothesis and you’d like to know how likely you are to succeed in finding that out, then the power of a test will give a way to think about that. The power of a test is the probability that it correctly rejects a false null hypothesis. When the power is high, you can be confident you’ve looked hard enough.

**The Power**

β is the probability that a test fails to reject a false null hypothesis, so the power of a test is the probability that it does reject: 1 – β.

**Effect Size**

The value of the power depends on how far the truth lies from the null hypothesis value, and the truth, ρ,

**the effect size**or “How big a difference would matter?” The power depends directly on the effect size. Power is calculated for a particular effect size, and it changes depending on the size of the effect we want to detect.

**Example 1:**

An increase in the sample size will affect the power of the test in what way?

*Solution: There is less chance of error, increasing the power of the test.*