5.4.3 - The Relationship Between Power, \(\beta\), and \(\alpha\)

Recall that \(\alpha \) is the probability of committing a Type I error. It is the value that is preset by the researcher. Therefore, the researcher has control over the probability of this type of error. But what about \(\beta \), the probability of a Type II error? How much control do we have over the probability of committing this error? Similarly, we want power, the probability we correctly reject a false null hypothesis, to be high (close to 1). Is there anything we can do to have a high power?

The relationship between power and \(\beta \) is an inverse relationship, namely...

\(Power = 1-\beta\)
\(\beta\) = probability of committing a Type II Error.

If we increase power, then we decrease \(\beta \). But how do we increase power? One way to increase power is to increase the sample size.  Sample size calculations are included in your textbook but not covered in the course.  Remember, it is possible to answer the question of “how many ___ do I have to study” by learning about sample size estimates.

The concepts, logic, and terminology of hypothesis testing can take some time to master. It is worth it! Hypothesis testing is a very powerful statistical tool.

Next, we will move onto situations where we compare more than one population parameter.