Sample Size Calculator (β Value)
This guide covers sample size estimation using power analysis (β value), significance level (α), and effect size (d).
1. Sample Size Calculation Table (Using β Value)
This table estimates the required sample size based on power (1-β), significance level (α), and effect size (d).
| Power (1-β) | Significance Level (α) | Effect Size (d) | Required Sample Size (Per Group) |
|---|---|---|---|
| 80% (0.84) | 95% (0.05, Z=1.96) | Small (0.2) | 394 |
| 80% (0.84) | 95% (0.05, Z=1.96) | Medium (0.5) | 64 |
| 80% (0.84) | 95% (0.05, Z=1.96) | Large (0.8) | 26 |
| 90% (1.28) | 95% (0.05, Z=1.96) | Small (0.2) | 526 |
| 90% (1.28) | 95% (0.05, Z=1.96) | Medium (0.5) | 86 |
| 90% (1.28) | 95% (0.05, Z=1.96) | Large (0.8) | 34 |
| 95% (1.645) | 95% (0.05, Z=1.96) | Small (0.2) | 651 |
| 95% (1.645) | 95% (0.05, Z=1.96) | Medium (0.5) | 108 |
| 95% (1.645) | 95% (0.05, Z=1.96) | Large (0.8) | 42 |
2. Key Terms in Sample Size Calculation Using β
| Term | Definition | Typical Values |
|---|---|---|
| Significance Level (α) | Probability of rejecting a true null hypothesis (Type I error). | 0.05 (95%), 0.01 (99%) |
| Power (1-β) | Probability of correctly rejecting a false null hypothesis. | 80%, 90%, 95% |
| Beta (β) | Probability of failing to reject a false null hypothesis (Type II error). | 20% (0.2), 10% (0.1), 5% (0.05) |
| Effect Size (d) | Magnitude of the difference being tested. | Small (0.2), Medium (0.5), Large (0.8) |
| Sample Size (n) | The number of subjects needed to detect an effect at given α and β. | Depends on α, β, and d |