What is another way to call the probability of rejecting a null hypothesis that is false? (A) Type I error (B) Type II error (C) Type III error (D) Power of the test
Answer (1)
The question is about statistical hypothesis testing, a crucial concept in statistics. When conducting a hypothesis test, you take a sample and use its data to determine whether to reject a null hypothesis. The null hypothesis, typically denoted as H 0 , is the default assumption that there is no effect or no difference.
In this context, the probability of rejecting a null hypothesis that is false is called the 'Power of the test.' This is option (D).
Let's break down the relevant terms:
Type I Error : This occurs when you incorrectly reject a true null hypothesis. It is also known as a 'false positive,' and the probability of making a Type I error is denoted by the Greek letter alpha ( α ).
Type II Error : This happens when you fail to reject a false null hypothesis, also called a 'false negative.' The probability of making a Type II error is denoted by the Greek letter beta ( β ).
Type III Error : This term is not standard in traditional hypothesis testing and usually refers to situations where you've addressed the wrong question or problem.
Power of the test : The power of a test is the probability that it correctly rejects a false null hypothesis. It is calculated as 1 − β [ t e x ] , w h ere [ / t e x ] β is the probability of a Type II error. Therefore, a high-powered test is more reliable in detecting a true effect or difference when it exists.
To summarize, the 'Power of the test' is a critical measure in hypothesis testing that indicates how well the test can identify a false null hypothesis and is the probability of making the correct decision when the null hypothesis is false.
