1. What is the Sample Size Formula?

The sample size formula calculates the minimum number of participants needed in a study to achieve statistically significant results. It's based on the population proportion, desired confidence level, and margin of error.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score for desired confidence level (1.96 for 95% CI)
• \( p \) — Estimated proportion (0.5 for maximum variability)
• \( d \) — Margin of error (precision, typically 0.05)

Explanation: The formula accounts for the relationship between confidence level, variability in the population, and desired precision.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure on overly large samples.

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% CI), estimated proportion (0.5 if unknown), and desired margin of error (typically 0.05 or 0.01).

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: What if I don't know the proportion?
A: Use 0.5 (50%) as this gives the maximum sample size and is conservative.

Q3: What's a reasonable margin of error?
A: Typically 5% (0.05) for surveys, though medical studies may use 1-2%.

Q4: Does this work for continuous variables?
A: No, this formula is for proportions. Different formulas exist for means.

Q5: How to adjust for finite populations?
A: For populations under 50,000, use the finite population correction.