Which element is crucial for determining the expected power of a statistical test?

The sample size plays a critical role in determining the expected power of a statistical test. Power is defined as the probability of correctly rejecting the null hypothesis when it is false. A larger sample size typically increases the test's power because it provides a more accurate estimate of the population parameters, reducing the standard error and making it easier to detect a true effect when it exists. Essentially, with more data, the test can more reliably discern whether observed differences are statistically significant rather than due to random chance.

While factors such as outlier presence, model validity, and the strength of the data can influence results and the robustness of a test, they do not have as direct an impact on power as sample size does. Outliers may skew results, model validity ensures that the assumptions of the statistical test are met, and data strength pertains to the inherent variability and reliability of the data, but it is the sample size that is fundamentally linked to increasing the power of the statistical test.