1. What is the Sample Size Formula?

The sample size formula calculates the number of participants needed in a study to achieve statistical significance. It's based on the Z-score, expected proportion, and desired margin of error, providing researchers with the minimum sample size required for reliable results.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( Z \) — Z-score (dimensionless)
• \( p \) — Proportion (dimensionless)
• \( e \) — Margin of error (dimensionless)

Explanation: The formula calculates the minimum sample size needed to achieve a certain level of confidence and precision in statistical estimates.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation is crucial for study design, ensuring statistical power, minimizing type I and type II errors, and providing reliable and valid research results.

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), proportion (estimated probability), and margin of error (desired precision level). All values must be valid (Z > 0, 0 ≤ p ≤ 1, 0 < e ≤ 1).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical Z-score value?
A: Common Z-scores are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence).

Q2: How to estimate the proportion (p)?
A: Use previous studies, pilot data, or 0.5 (most conservative estimate) if no prior information is available.

Q3: What margin of error is appropriate?
A: Typically 0.05 (5%) or 0.03 (3%) for most studies, but depends on the required precision.

Q4: Are there limitations to this formula?
A: This formula assumes simple random sampling and may need adjustment for complex sampling designs or small populations.

Q5: When should I use finite population correction?
A: When the sample size exceeds 5% of the total population, finite population correction should be applied.