Sensitivity analysis is a critical component of power analysis, allowing researchers to evaluate how the variation in input parameters can impact the power of a statistical test. By conducting sensitivity analysis, researchers can assess the robustness of their findings and ensure that their study design is properly calibrated to detect effects of interest. Below are three practical examples that illustrate the application of sensitivity analysis in power analysis across different contexts.
In clinical trials, determining the appropriate sample size is essential for detecting treatment effects. Researchers often conduct sensitivity analysis to see how changes in sample size influence the power of their study.
When planning a study comparing a new drug to a placebo, researchers hypothesize that the drug will reduce symptoms significantly. They want to ensure that their sample size is sufficient to detect this effect with high probability.
The researchers initially calculate the required sample size to achieve 80% power at an alpha level of 0.05, assuming a medium effect size (Cohen’s d = 0.5). After determining the sample size, they perform a sensitivity analysis to see how increasing or decreasing the sample size affects the power.
In this analysis, the researchers find that decreasing the sample size significantly lowers the power, suggesting that they should aim for at least 64 participants to confidently detect the drug’s effects.
In educational research, estimating the effect of a new teaching method on student performance is crucial. Researchers often face uncertainty regarding the expected effect size, which can vary based on prior studies or pilot data.
For this example, a study is planned to evaluate a new teaching method’s effectiveness. The researchers initially estimate an effect size of 0.4 (Cohen’s d) based on previous literature. However, they recognize that this estimate may not hold true for their specific population.
To perform a sensitivity analysis, they simulate different effect sizes (0.3, 0.4, 0.5) and observe how the power changes with each scenario for a fixed sample size of 100 students.
This sensitivity analysis demonstrates that even small changes in the effect size have a significant impact on the study’s power.
In psychological research, the significance level (alpha) is typically set at 0.05. However, researchers may want to explore different thresholds to understand how they affect the power of their study.
In this scenario, a study aims to determine whether a new cognitive-behavioral therapy reduces anxiety symptoms more effectively than a control group. Researchers initially set alpha at 0.05 and calculate power based on this threshold. They then conduct sensitivity analysis by varying the alpha level to see how it influences power.
The analysis reveals that increasing the alpha level improves power, but at the risk of increasing the likelihood of Type I errors. Researchers must weigh the trade-offs between power and the probability of false positives.
By utilizing sensitivity analysis in power analysis, researchers gain valuable insights into how various factors affect their study designs and outcomes, ultimately enhancing the reliability of their findings.