The power of a test depends on which two factors?

The power of a statistical test refers to its ability to correctly reject a null hypothesis when it is false, which is also known as the probability of making a correct decision. The correct answer identifies the two critical factors that determine the power of a test: sample size and effect size.

Sample size plays a significant role because larger sample sizes tend to provide more reliable estimates of population parameters, leading to a better chance of detecting an effect if one exists. As the size of the sample increases, the variability of the sample mean decreases, making it easier to discern a true effect from random noise.

Effect size quantifies the magnitude of the difference or relationship being tested. A larger effect size increases the likelihood that a test will be significant because it is easier to detect a large difference between groups or a strong relationship between variables than a small one. When the actual difference is substantial, even with a modest sample size, the power of the test is enhanced.

Combining these two factors, a larger sample size and a larger effect size significantly improve the power, enabling researchers to draw more accurate conclusions from their data.