## Factors Affecting the Power of a Hypothesis Test

The power of a hypothesis test is the probability of notcommitting a Type II error – failing to reject the null hypothesiswhen the null hypothesis is false.

The effect size is the difference between the true value and thevalue specified in the null hypothesis.

Effect size = True value - Hypothesized value

For example, suppose the null hypothesis states that a populationmean is equal to 100. A researcher might ask: What is the probabilityof rejecting the null hypothesis if the true population mean is equalto 90? In this example, the effect size would be 90 - 100, whichequals -10. Obviously if the true value is far from the hypothesisedvalue then the null hypothesis is more likely to be rejected so theprobability of committing a Type II error is reduced. With this madeclear we can make the following summary.

## Factors That Affect Power

The power of a hypothesis test is affected by three factors.

• Sample size (n). Other things being equal, the greater thesample size, the greater the power of the test, since larger samplesizes tend to give more accurate values of the parameter inquestion.

• Significance level (α). The higher the significance level,the higher the power of the test. If you increase the significancelevel, you reduce the region of acceptance. As a result, you aremore likely to reject the null hypothesis. This means you are lesslikely to accept the null hypothesis when it is false; i.e., lesslikely to make a Type II error. Hence, the power of the test isincreased.

• The "true" value of the parameter being tested. Thegreater the difference between the "true" value of aparameter and the value specified in the null hypothesis, thegreater the power of the test. That is, the greater the effect size,the greater the power of the test.

In addition, the probability of committing a Type II errorincreases with decreasing probability of committing a Type I test. Itis impossible to simultaneously decrease the probability of a Type Itest and Type II test. 