Statistical power is the probability that a test will detect an effect if one truly exists. A power of 80% means there's an 80% chance of finding a significant result when the effect is real. Low power leads to missed discoveries (Type II errors).
| Parameter | Description | Typical Value |
|---|---|---|
| Power (1-β) | Probability of detecting true effect | 0.80 |
| Alpha (α) | Significance level | 0.05 |
| Effect Size (w) | Cohen's w for chi-square | 0.1-0.5 |
| Sample Size (n) | Number of observations | Varies |
| Effect Size (w) | Interpretation |
|---|---|
| 0.10 | Small effect |
| 0.30 | Medium effect |
| 0.50 | Large effect |
Before your study (a priori): Determine required sample size
After your study (post hoc): Assess power of completed study
A priori power analysis is strongly preferred for study planning.
Our calculator uses the exact non-central chi-square distribution (not approximations) to provide accurate power calculations:
For chi-square tests, sample size depends on desired power, alpha level, effect size, and degrees of freedom. CrossTabs.com calculates the minimum sample size needed to achieve 80% power for your specific effect size.
Upload your data to CrossTabs.com to instantly see:
Scenario: You plan a study testing whether a training program affects pass/fail rates. You expect a medium effect size (w = 0.3) and want 80% power at α = 0.05 with df = 1.
Required sample size: Using the formula N = (z_α + z_β)² / w², where z_α = 1.96 (for α = 0.05) and z_β = 0.84 (for 80% power):
N = (1.96 + 0.84)² / 0.3² = 7.84 / 0.09 = 87 participants
CrossTabs uses the exact non-central chi-square distribution for more precise calculations, which may give slightly different results than this approximation.
| Effect Size (w) | df = 1 (2×2) | df = 2 (3×2) | df = 4 (3×3) |
|---|---|---|---|
| 0.1 (small) | 785 | 964 | 1,091 |
| 0.3 (medium) | 88 | 108 | 122 |
| 0.5 (large) | 32 | 39 | 44 |
All values for 80% power at α = 0.05.