How to Calculate Sample Size for Power

Sample Size Formula for Two-Sample Means:

\[ n = \frac{(Z_{1-\alpha/2} + Z_{1-\beta})^2 \times 2\sigma^2}{\delta^2} \]

Significance Level (α):

(e.g., 0.05)

Power (1-β):

(e.g., 0.8)

Standard Deviation (σ):

units

Effect Size (δ):

units

Sample Size per Group (n):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Sample Size Calculation for Power?

Sample size calculation for power determines the number of participants needed in each group to detect a specified effect size with a given level of statistical power and significance. This ensures studies are adequately powered to detect meaningful differences.

2. How Does the Calculator Work?

The calculator uses the formula for two-sample means:

\[ n = \frac{(Z_{1-\alpha/2} + Z_{1-\beta})^2 \times 2\sigma^2}{\delta^2} \]

Where:

\( n \) — Sample size per group
\( Z_{1-\alpha/2} \) — Z-score for significance level
\( Z_{1-\beta} \) — Z-score for power
\( \sigma \) — Standard deviation
\( \delta \) — Effect size (difference to detect)

Explanation: The formula balances Type I error (α), Type II error (β), variability (σ), and the minimum effect size considered important (δ).

3. Importance of Sample Size Calculation

Details: Proper sample size calculation prevents underpowered studies (missing real effects) and overpowered studies (wasting resources). It's essential for ethical research and valid statistical conclusions.

4. Using the Calculator

Tips: Enter significance level (typically 0.05), desired power (typically 0.8 or 0.9), estimated standard deviation, and the minimum effect size you want to detect. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is statistical power?
A: Power (1-β) is the probability of correctly rejecting a false null hypothesis, typically set at 80% or 90% in research studies.

Q2: How do I determine the effect size?
A: Effect size should be based on clinical relevance, previous research, or pilot studies. It represents the minimum difference considered meaningful.

Q3: What if I don't know the standard deviation?
A: Use estimates from previous studies, pilot data, or literature reviews. Conservative estimates are preferable to avoid underpowered studies.

Q4: Can this be used for other study designs?
A: This formula is for comparing two independent means. Different formulas exist for proportions, correlations, and other statistical tests.

Q5: Should I adjust for multiple comparisons?
A: Yes, if conducting multiple tests, consider adjusting the alpha level (e.g., Bonferroni correction) which will increase the required sample size.