Hassan Ijaz
Ai, Web & Design
Sample size determination
Power calculator with visual effect size demonstrations showing required samples for statistical significance
Concept Overview
Sample size determination is crucial for ensuring statistical power while maintaining efficiency. Too small samples may miss important effects, while unnecessarily large samples waste resources.
Power Analysis Components
Effect Size
Magnitude of difference we want to detect
Larger effects easier to detect
Significance Level (α)
Probability of Type I error
Typically 0.05
Power (1-β)
Probability of detecting true effect
Typically 0.80 or 0.90
Sample Size (n)
Number of observations needed
What we're trying to determine
Sample Size Formulas
One Sample Mean
n = (z_α/2 + z_β)² × σ² / δ²
δ = effect size, σ = standard deviation
Two Sample Means
n = 2(z_α/2 + z_β)² × σ² / (μ₁ - μ₂)²
For equal group sizes
Proportions
n = (z_α/2 + z_β)² × [p₁(1-p₁) + p₂(1-p₂)] / (p₁ - p₂)²
For comparing two proportions
Practical Considerations
- Pilot Studies: Use preliminary data to estimate parameters
- Multiple Outcomes: Adjust for multiple comparisons
- Dropout Rates: Inflate sample size to account for attrition
- Cost Constraints: Balance statistical power with resources
Key Insight: Sample size requirements grow with the square of precision needed. To halve the margin of error, you need 4 times the sample size!
The power calculator below shows visual demonstrations of effect sizes and required sample sizes. Adjust the parameters to see how they influence statistical significance.
Interactive Visualization
Loading interactive visualization...
Power calculator with visual effect size demonstrations showing required samples for statistical significance