Sample Size Calculation Formula For RCT

Sample Size Formula For RCT Comparing Means:

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

Z Alpha (Z_α):

(e.g., 1.96 for α=0.05)

Z Beta (Z_β):

(e.g., 0.84 for 80% power)

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 RCT?

Sample size calculation for randomized controlled trials (RCT) is a critical step in study design that determines the number of participants needed in each group to detect a statistically significant effect with adequate power.

2. How Does The Calculator Work?

The calculator uses the standard sample size formula for comparing means:

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

Where:

\( n \) — Sample size per group
\( Z_{\alpha} \) — Z-value for significance level (α)
\( Z_{\beta} \) — Z-value for power (1-β)
\( \sigma \) — Standard deviation
\( \delta \) — Effect size (clinically important difference)

Explanation: This formula ensures adequate statistical power to detect a specified effect size while controlling for Type I and Type II errors.

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation is essential for ensuring study validity, optimizing resource allocation, meeting ethical requirements, and providing credible results for peer review and publication.

4. Using The Calculator

Tips: Enter Z-values for your chosen significance level and power, provide the estimated standard deviation from pilot studies or literature, and specify the minimum clinically important effect size you wish to detect.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Z_α and Z_β?
A: For α=0.05 (two-tailed), Z_α=1.96; for 80% power, Z_β=0.84; for 90% power, Z_β=1.28.

Q2: How do I estimate standard deviation?
A: Use data from pilot studies, previous similar research, or published literature. If unavailable, consider a conservative estimate based on clinical expertise.

Q3: What if I have unequal group sizes?
A: This formula assumes equal allocation. For unequal allocation, use adjustment factors or specialized software.

Q4: Should I account for dropout?
A: Yes, increase the calculated sample size by dividing by (1 - expected dropout rate) to maintain power.

Q5: When should I use different formulas?
A: For proportions, survival analysis, or cluster randomized trials, different sample size formulas are required.