Estimating Sample Size and Statistical Power

Overview

• Estimating sample size is also known as power analysis or power calculations.
• Determines the number of samples needed to achieve a certain level of statistical power in an analysis.
• Aims to estimate the minimum sample size to detect a meaningful difference when it exists.
• Meaningful difference can vary: clinically significant, socially meaningful, etc.
• Consideration for minimum detectable effect size if participant recruitment is limited.

Defining a Meaningful Difference

• Derived by examining scientific literature, expert opinions, or pilot studies.
• Example: Clinically significant change in cholesterol levels.

Key Components of Sample Size Determination

1. Significance Level (Alpha)

   • Typically set at 0.05, but adjustable based on context.

2. Type of Test

   • One-sided or two-sided alternative.

3. Level of Power (1-Beta)

   • Probability of detecting an effect; typically set at 80% but flexible.

4. Effect Size

   • Difference intended to detect; crucial for sample size calculations.

Importance in Grant Applications

• Essential to include sample size/power calculations in grant proposals to increase chances of approval.

Statistical Decision Considerations

• Maximize correct decisions while minimizing false positives (Type 1 Error) and false negatives (Type 2 Error).
• Balance Alpha and Beta levels appropriately.

Example: Paired T-Test

• Variables Needed: Alpha level, alternative hypothesis, power, Delta (difference to detect), standard deviation.
• Use of pilot data or published work for standard deviation.
• Equations differ based on one-sided or two-sided test.
• Example Calculation: Estimating sample size for a paired t-test in a study on intraocular pressure.

Example: Independent Samples T-Test

• Similar to paired t-test but requires variance in two groups.
• Equations account for differences in variances between groups.
• Example Calculation: Determining sample size for testing blood pressure differences between oral contraceptive users and non-users.

Additional Considerations

• Balanced Design: Equal number of subjects in each group.
• Unbalanced Designs: More complex calculations, not covered in this class.
• Power Tables and Curves: Assist in visualizing and presenting power and sample size estimates.

Software and Calculations

• Software like nQuery, PASS, SAS, SPSS can perform advanced sample size/power calculations.
• Note: Hand calculations may differ slightly from software results due to approximations.

Conclusion

• Understanding sample size and power is crucial for effective study design and securing grants.
• Concludes the module and the week's lectures.