Power analysis and effect size in mixed effects models: A tutorial

Type II Error

Increasing Statistical Power

Computing Statistical Power Online

Relationship Between Statistical Power and Type II Error

Adequate Statistical Power

Relationship Between Statistical Power and Relationship Strength

Which of the following best defines the statistical power of a research design?

A researcher designs a study with a statistical power of .80. This means there is a 20% probability that the study will fail to detect a real effect that actually exists in the population.

A researcher is refining their study design to improve the probability of detecting a real relationship between variables. Match each design decision with its specific impact on the study's statistical power.

A researcher is designing a study to examine how social media use affects attention span. Arrange these four study configurations in order from the lowest statistical power (at the top) to the highest statistical power (at the bottom) by analyzing how their parameters influence the probability of detecting a real relationship.

A researcher is developing a study to detect a subtle relationship between sleep duration and cognitive performance ($r = .15$). With a fixed budget that limits the sample size to $150$ participants, which of the following research plans correctly synthesizes the necessary design elements to maximize statistical power?

Example of Sample Size Requirements for High Statistical Power

Assuming a real effect exists in the population, arrange the following study designs in order based on their probability of failing to detect that effect (Type II error), from the highest risk of error (at the top) to the lowest risk of error (at the bottom).

A researcher is evaluating two proposed study designs for a clinical trial. Design A has a reported statistical power of .75, while Design B is estimated to have a .15 probability of failing to detect a real effect that exists in the population. To ensure the highest probability of correctly identifying a relationship, the researcher should select the design with a power of _____.

Match each term related to statistical power with its correct description.

A clinical psychologist is designing an experiment to test a new therapy for anxiety. If the study is configured to have a statistical power of 0.75, then the probability that the study will fail to reject the null hypothesis when a real therapeutic effect exists in the population is 0.25.

An investigator is reviewing two proposed experimental designs for a study on peer pressure and decision-making:

• Design A is planned with a sample size and significance level ($\alpha = .05$) that yields a statistical power of .80.
• Design B is planned with a different configuration that yields a statistical power of .65.

Assuming a real effect of the hypothesized strength exists in the population, Design A has a _____ probability of making a Type II error compared to Design B (enter 'higher' or 'lower').

Which of the following best describes the statistical power of a research design?

If a research design has a statistical power of 0.80, this indicates that there is an 80% chance of making a Type II error.

A researcher designs a study to test a new cognitive therapy and determines that the probability of making a Type II error ($\beta$) is 0.12. Expressed as a decimal, the statistical power of this research design is ____.

Analyze the components of statistical power by matching each research concept or mathematical representation to its correct definition or role in a study design.

Evaluate the following research design scenarios based on their expected ability to detect a true effect. Arrange them in order from the lowest statistical power to the highest statistical power.

Statistical power is mathematically defined as the complement of the probability of making which of the following errors?

Match each statistical concept to its correct description in the context of statistical power.

To reduce the likelihood of missing a real clinical effect, a researcher modifies their study's design to increase its statistical power from 0.60 to 0.85. By making this change, the researcher has successfully decreased the probability of making a Type II error from 40% to 15%.

A peer reviewer is evaluating a research manuscript and notices a mathematical discrepancy. The authors state that their study has an 80% chance of missing a real effect in the population, yet they also conclude that their research design has a high statistical power of 0.80. Based on the components of statistical power, why is this combination of claims logically flawed?

A grant panel evaluates two competing studies investigating the same phenomenon. Study A reports a statistical power of 0.70. Study B reports a Type II error probability ($\beta$) of 0.15. If the panel's primary goal is to fund the design most likely to correctly reject the null hypothesis when the relationship exists in the population, they should select Study ____.