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 confidence intervals, it ensures the estimate has the desired precision and confidence level.

2. How Does the Calculator Work?

The calculator uses the sample size formula for proportions:

Where:

• \( Z \) — Z-score corresponding to the desired confidence level
• \( p \) — Estimated proportion (use 0.5 for maximum sample size)
• \( E \) — Margin of error (desired precision)
• \( n \) — Required sample size

Explanation: The formula calculates the minimum number of samples needed to estimate a population proportion within a specified margin of error at a given confidence level.

3. Importance of Sample Size Determination

Details: Proper sample size ensures study validity, adequate statistical power, and reliable results. Too small samples may miss true effects, while too large samples waste resources.

4. Using the Calculator

Tips: Enter Z-score based on confidence level (1.96 for 95%, 2.58 for 99%), estimated proportion (use 0.5 for conservative estimate), and desired margin of error (typically 0.05 or 0.03).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common Z-scores are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). Choose based on your desired confidence level.

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

Q3: What is a reasonable margin of error?
A: Typically 0.05 (±5%) or 0.03 (±3%) for most surveys. Smaller margins require larger samples.

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 survey responses, prevalence rates, or binary outcomes in research studies.