Sample Size Calculation For Experimental Study

Sample Size Formula:

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

Z_α/2 (Critical Value):

(1.96 for 95%)

Z_β (Power Value):

(0.84 for 80%)

Standard Deviation (σ):

units

Effect Size (δ):

units

Sample Size Required (n):

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1. What Is Sample Size Calculation?

Sample size calculation is a crucial step in experimental 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 two-sample comparisons:

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

Where:

\( n \) — Sample size required per group
\( Z_{\alpha/2} \) — Critical value for significance level (typically 1.96 for 95% confidence)
\( Z_{\beta} \) — Critical value for power (typically 0.84 for 80% power)
\( \sigma \) — Standard deviation of the outcome variable
\( \delta \) — Minimum detectable effect size

Explanation: This formula ensures adequate statistical power to detect meaningful differences between groups while controlling for Type I and Type II errors.

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation prevents underpowered studies (missing true effects) and overpowered studies (wasting resources), ensuring research validity and efficiency.

4. Using The Calculator

Tips: Enter standard deviation and effect size in consistent units. Use standard values for Z_α/2 (1.96) and Z_β (0.84) unless specific requirements dictate otherwise.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between one-tailed and two-tailed tests?
A: Two-tailed tests detect differences in either direction, while one-tailed tests detect differences in one specific direction. Most studies use two-tailed tests.

Q2: How do I determine the standard deviation?
A: Use pilot study data, previous literature, or clinical expertise. If unknown, conduct a small pilot study first.

Q3: What is an appropriate effect size?
A: Effect size should represent the minimum clinically important difference. Consult clinical guidelines or expert opinion.

Q4: Can this calculator be used for other study designs?
A: This formula is for two-group comparisons. Different formulas exist for paired studies, survival analysis, and other designs.

Q5: What if I expect dropouts?
A: Increase the calculated sample size by the expected dropout rate (e.g., if 10% dropout expected, multiply by 1.1).