1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a study to detect a statistically significant effect. For proportion studies, this formula ensures your results are reliable and representative of the population.

2. How Does the Calculator Work?

The calculator uses the sample size formula for proportions:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score (standard normal deviate)
• \( p \) — Estimated proportion in the population
• \( E \) — Margin of error (precision)

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

3. Importance of Sample Size Determination

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

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% confidence, 2.576 for 99%), estimated proportion (use 0.5 for maximum variability), and desired margin of error (typically 0.05 for ±5%).

5. Frequently Asked Questions (FAQ)

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

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

Q3: What is a reasonable margin of error?
A: Typically 0.05 (±5%) for most surveys, but can range from 0.01 to 0.10 depending on required precision.

Q4: Does this work for finite populations?
A: This formula assumes infinite population. For finite populations, apply a finite population correction factor.

Q5: When should I use this formula?
A: Use for estimating a single proportion, such as prevalence studies, survey research, or quality control sampling.