Power Analysis: Calculating Sample Size

Power Analysis Components

  • In power analysis, you solve for one of five components while assuming values for the other four:

    • Power
    • Sample size
    • Effect size
    • Significance level
    • One-sided vs. two-sided tests

  • Typically, power, sample size, or effect size are solved for, while significance level and the type of test (one-sided or two-sided) are assumed.

Example: Testing Mean Difference Between Two Groups

  • Scenario: A study is designed to test for a significant difference in means between a treatment and a control group.
    • Null Hypothesis: No significant difference.
    • Alternative Hypothesis: A significant difference exists (two-sided test).

Solving for Sample Size

  • Assumptions:
    • Minimum power of 80%.
    • Type I error rate (alpha) of 0.05 (reasonable for a single comparison).
    • Two-sided statistical test (prudent to account for the possibility of either group outperforming the other).
    • Cohen's D effect size of 0.5 (moderately sized difference).

Determining Effect Size

  • Options for estimating effect size:
    • Literature review: Look for similar or related studies and their reported effect sizes.
    • Clinical significance: Determine what magnitude of mean difference would be clinically meaningful.

Using G*Power to Calculate Sample Size

  • G*Power is a free, user-friendly, downloadable software for power analysis.
  • Steps:
    1. Select the statistical test: Compare two independent means.
    2. Select the type of power analysis: Compute required sample size given alpha, power, and effect size.
    3. Input parameters:
      • Two-sided test.
      • Cohen's D effect size = 0.5.
      • Alpha error probability = 0.05.
      • Power = 80%.
      • Allocation ratio = 1 (equal group sizes).
    4. Calculate.

Output Interpretation

  • In the example, with the stated assumptions, the power analysis indicates a need for 64 people in each group, totaling 128 participants.

Reporting Sample Size in a Grant Proposal

  • Clearly explain all assumptions made to justify the sample size estimate (e.g., n = 128).

Varying input parameters

  • In the next video, the presenter is going to show what happens when input parameters are changed.