Sample Size Calculation for Comparative Study

Sample Size Formula for Two Groups:

\[ n = 2 \left( \frac{Z \cdot \sigma}{\delta} \right)^2 \]

Sample Size per Group (n):

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1. What is Sample Size Calculation for Comparative Study?

Sample size calculation for comparative studies determines the number of participants needed in each group to detect a statistically significant difference between groups. This ensures the study has adequate power to answer the research question.

2. How Does the Calculator Work?

The calculator uses the sample size formula for two independent groups:

\[ n = 2 \left( \frac{Z \cdot \sigma}{\delta} \right)^2 \]

Where:

\( n \) — Sample size per group
\( Z \) — Z-value corresponding to desired power and significance level (unitless)
\( \sigma \) — Standard deviation of the outcome variable (units)
\( \delta \) — Minimum detectable effect size or clinically important difference (units)

Explanation: This formula calculates the required sample size for each group in a two-group comparative study to achieve adequate statistical power.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation is essential for study design. It ensures the study has sufficient power to detect meaningful differences while avoiding unnecessary resource expenditure on overly large samples.

4. Using the Calculator

Tips: Enter the Z-value based on your desired power and alpha level, the estimated standard deviation of your outcome variable, and the minimum effect size you wish to detect. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What Z-value should I use?
A: For 80% power and α=0.05 (two-tailed), use Z=1.96. For 90% power, use Z=2.80. Consult statistical tables for other combinations.

Q2: How do I estimate standard deviation?
A: Use data from pilot studies, previous research, or literature in your field. If unavailable, conduct a small pilot study to estimate variability.

Q3: What is a reasonable effect size?
A: The effect size should represent the minimum clinically important difference. Consider what magnitude of difference would be meaningful in your research context.

Q4: Does this work for all study designs?
A: This formula is for two independent groups with continuous outcomes. Different formulas apply for paired data, categorical outcomes, or more than two groups.

Q5: Should I account for dropout?
A: Yes, increase your calculated sample size by 10-20% to account for potential participant dropout or missing data.