1. What is the Sample Size Formula?

The sample size formula for proportions calculates the minimum number of participants needed in a study to achieve statistical significance. It ensures that research results are reliable and representative of the population being studied.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for proportions:

Where:

• \( n \) — Required sample size (count)
• \( Z \) — Z-score corresponding to confidence level (unitless)
• \( p \) — Estimated proportion (decimal)
• \( e \) — Margin of error (decimal)

Explanation: The formula balances confidence level (Z), expected proportion (p), and acceptable error margin (e) to determine the minimum sample size needed for statistical reliability.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation is crucial for research validity. Too small a sample may not detect true effects, while too large wastes resources. It ensures studies have adequate statistical power.

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% confidence), proportion estimate (0.5 for maximum variability), and margin of error (typically 0.05). All values must be valid (Z > 0, 0 ≤ p ≤ 1, 0 < e ≤ 1).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Use 1.96 for 95% confidence level, 1.645 for 90%, and 2.576 for 99% confidence level.

Q2: Why use p = 0.5 as default?
A: p = 0.5 gives the maximum sample size, ensuring adequate power when the true proportion is unknown.

Q3: What is a good margin of error?
A: Typically 0.05 (5%) for most studies, but can be adjusted based on research requirements and precision needed.

Q4: Does this work for finite populations?
A: This formula is for infinite populations. For finite populations, additional correction factors may be needed.

Q5: When should I use this formula?
A: Use for studies measuring proportions or percentages, such as survey research, prevalence studies, and opinion polls.