1. What is a Sample Size Calculator?

Definition: This calculator determines the minimum number of participants needed in a study to achieve statistically significant results.

Purpose: It helps researchers design studies with adequate power while minimizing unnecessary data collection costs.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score (determined by confidence level)
• \( p \) — Expected proportion (decimal between 0 and 1)
• \( e \) — Margin of error (decimal between 0 and 1)

Explanation: The formula balances confidence level (Z), variability (p), and desired precision (e) to determine the minimum sample needed.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures study validity, prevents underpowered results, and optimizes research resources.

4. Using the Calculator

Tips:

• Use 1.96 for 95% confidence level (most common)
• Use 0.5 for proportion when uncertain (maximizes sample size)
• Typical margin of error is 0.05 (5%) or 0.03 (3%)

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common values are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI).

Q2: Why use 0.5 for proportion?
A: 0.5 gives the most conservative (largest) sample size when the true proportion is unknown.

Q3: How does margin of error affect sample size?
A: Smaller margins require dramatically larger samples (halving error quadruples sample size).

Q4: When is this formula appropriate?
A: For estimating proportions in large populations (N > 20,000). For smaller populations, use finite population correction.

Q5: Does this account for non-response?
A: No, increase your sample by expected non-response rate (e.g., if 20% won't respond, multiply result by 1.25).