Discuss briefly the concept of power of the test and why it

Discuss briefly the concept of “power of the test” and why it is important in hypothesis testing.

Solution

Type II error. A Type II error occurs when the researcher accepts a null hypothesis that is false. The probability of committing a Type II error is called Beta, and is often denoted by . The probability of not committing a Type II error is called the Power of the test.

To compute the power of the test, one offers an alternative view about the \"true\" value of the population parameter, assuming that the null hypothesis is false. The effect size is the difference between the true value and the value specified in the null hypothesis.

Effect size = True value - Hypothesized value

For example, suppose the null hypothesis states that a population mean is equal to 100. A researcher might ask: What is the probability of rejecting the null hypothesis if the true population mean is equal to 90? In this example, the effect size would be 90 - 100, which equals -10.