Power Analysis with Known Sample Size

Known Sample Size

Existing Data Source: Using a pre-existing dataset for secondary analysis where the sample size is already determined.
Fixed Number of Subjects: Limited number of subjects available for data collection within a specific timeframe.
- Example: Gathering data on patients in a clinic with a low rate of specific cases (e.g., one or two patients per week).
Specialized Patient Populations: Working with uncommon groups where obtaining a large sample is difficult.
Smaller Studies: Conducting research with inherent limitations on sample size.

When to Use: Appropriate when the sample size is known.
Scenarios:
- Repurposing an existing intervention for a new study population where the effect size is uncertain.
- Investigating a truly novel effect where there's no prior estimate.
- Literature reports a wide range of effect sizes across multiple studies.
Assumptions:
- Known sample size.
- Power (e.g., 80% or 90%).
- Type I error rate (alpha) of 0.05.
- Two-sided test.
Process: Calculate the smallest effect size that can be detected given the assumptions.
Value: Provides context on the sensitivity of the study.

When to Use: Appropriate when the sample size and expected effect size are known.
Process: Calculate the statistical power based on the known sample size and estimated effect size.
Interpretation:
- Sufficient Power (>= 80%): Confidence in proceeding with the study.
- Insufficient Power (< 80%): Re-evaluate the study design, and consider increasing the sample size if possible.

A Priori Power Analysis:
- Definition: Power calculations performed before data collection or analysis.
- Recommendation: Crucial for proper study design.
Post Hoc Power Analysis (Observed Power):
- Definition: Power calculations performed after data analysis.
- Criticism: Widely criticized and not recommended.
- Issue: Often requested by reviewers/editors but provides limited value.

Perform power calculations routinely during the planning and design phases of research studies.