1. What is Sample Size Calculation?

The sample size calculation determines the number of participants needed in a study to detect an effect of a given size with a certain degree of confidence. It's crucial for study design and statistical power.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for proportions:

Where:

• \( Z \) — Z-score corresponding to desired confidence level
• \( p \) — Expected proportion (decimal)
• \( E \) — Margin of error (decimal)

Explanation: The formula calculates the minimum number of participants needed to estimate a population proportion with specified precision.

3. Importance of Sample Size

Details: Proper sample size ensures study validity, adequate power to detect effects, and prevents wasting resources on underpowered studies.

4. Using the Calculator

Tips: Common Z-scores: 1.96 (95% CI), 2.576 (99% CI). For unknown proportion, use 0.5 for maximum sample size. Margin typically 0.05 (5%) or less.

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Use 1.96 for 95% confidence level, 2.576 for 99% confidence level.

Q2: What if I don't know the expected proportion?
A: Use 0.5 (50%) as this gives the most conservative (largest) sample size.

Q3: How does margin of error affect sample size?
A: Smaller margins require larger samples. Halving the margin quadruples the required sample size.

Q4: Is this formula for continuous or categorical data?
A: This specific formula is for categorical data (proportions). Different formulas exist for continuous data.

Q5: What about population size?
A: This formula assumes large populations. For small populations, finite population correction is needed.