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Power

Power Analysis — Sample Size for Independent t-test

Determine required sample size to detect d=0.5 with 80% power (α=.05). G*Power formula and interpretation.

📊 n = 52 per group (total N = 104)
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⚡ 10 · Power Analysis & Sample Size

How large must my sample be to detect d=0.5 with 80% power?
Power
Scenario: Planning a two-group RCT. Expected effect size d = 0.5 (medium), α = .05, desired power = 80%.
Cohen's formula for two independent groups
$$n = \frac{(z_{\alpha/2} + z_\beta)^2 \times 2}{d^2}$$ $$z_{\alpha/2} = z_{.025} = 1.96, \quad z_\beta = z_{.20} = 0.842$$ $$n = \frac{(1.96 + 0.842)^2 \times 2}{0.5^2} = \frac{(2.802)^2 \times 2}{0.25} = \frac{7.851 \times 2}{0.25} = \frac{15.70}{0.25} = 62.8 \approx \mathbf{63 \text{ per group}}$$
dPower 80%Power 90%Power 95%
0.2 (small)197265327
0.5 (medium)6385105
0.8 (large)263442
1.0 (very large)172227
63
n per group
126
Total N
80%
Power
APA-7
An a priori power analysis (G*Power framework) indicated that 63 participants per group (N = 126) were required to detect a medium effect (d = 0.50) with 80% power at α = .05 (two-tailed).

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