Power

Definition

Power is a statistical concept that refers to the ability of a statistical test to detect an effect or difference if it truly exists in the population. It is a measure of the likelihood that a statistical test will reject the null hypothesis when the alternative hypothesis is true.

5 Must Know Facts For Your Next Test

1. Power is directly related to the probability of detecting an effect or difference if it truly exists in the population.
2. Power is influenced by the significance level ('$\alpha$'), the effect size, and the sample size of the study.
3. Increasing the sample size or the effect size can increase the power of a statistical test, while increasing the significance level can decrease the power.
4. Power is an important consideration in the design of statistical studies, as it helps researchers determine the appropriate sample size to ensure that the study has a high likelihood of detecting an effect if it exists.
5. Low power can lead to a failure to detect an effect that is truly present, which is known as a Type II error.

Review Questions

• Explain how power is related to the probability of detecting an effect or difference in a population proportion test (8.3 A Population Proportion).
  • In the context of a population proportion test (8.3 A Population Proportion), power refers to the likelihood that the statistical test will correctly reject the null hypothesis when the alternative hypothesis is true. The power of the test is directly related to the probability of detecting a difference in the population proportion if such a difference truly exists. Higher power means a greater chance of detecting an effect, while lower power increases the risk of a Type II error, where the test fails to detect a difference that is actually present in the population.
• Describe how power is connected to the concepts of Type I and Type II errors (9.2 Outcomes and the Type I and Type II Errors).
  • Power is closely related to the concepts of Type I and Type II errors. Type I errors occur when the null hypothesis is true, but it is incorrectly rejected, leading to a false positive result. Type II errors occur when the null hypothesis is false, but it is not rejected, leading to a false negative result. Power is the complement of the probability of a Type II error, meaning that higher power corresponds to a lower probability of a Type II error. Researchers aim to design studies with sufficient power to minimize the risk of both Type I and Type II errors, as these errors can have significant implications for the conclusions drawn from the statistical analysis.
• Analyze how the factors of significance level, effect size, and sample size influence the power of a statistical test.
  • The power of a statistical test is influenced by three key factors: the significance level ('$\alpha$'), the effect size, and the sample size. Increasing the significance level (i.e., allowing for a higher probability of a Type I error) can decrease the power of the test. Conversely, increasing the effect size or the sample size can increase the power of the test. Researchers must carefully balance these factors when designing a study to ensure that the test has sufficient power to detect an effect or difference if it truly exists in the population. By understanding the relationships between these factors and power, researchers can make informed decisions about the appropriate study design and sample size to maximize the likelihood of detecting meaningful effects.

Related terms

Type I Error: A Type I error occurs when the null hypothesis is true, but it is incorrectly rejected, leading to a false positive result.

Type II Error: A Type II error occurs when the null hypothesis is false, but it is not rejected, leading to a false negative result.

Significance Level: The significance level, denoted as '$\alpha$', is the probability of making a Type I error, or the maximum acceptable probability of rejecting the null hypothesis when it is true.