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Sample Size Formula:
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The single proportion sample size calculation determines the number of participants needed in a study to estimate a population proportion with a specified level of confidence and margin of error. This is essential for designing surveys, clinical trials, and research studies.
The calculator uses the sample size formula for a single proportion:
Where:
Explanation: The formula calculates the minimum number of observations needed to estimate a population proportion within a specified margin of error at a given confidence level.
Details: Proper sample size calculation ensures that research studies have sufficient statistical power to detect meaningful effects while avoiding unnecessary resource expenditure on overly large samples.
Tips: Enter the Z-score corresponding to your desired confidence level (1.96 for 95% CI), the estimated proportion (use 0.5 for maximum variability if unknown), and your desired margin of error (typically 0.05 or 0.03).
Q1: What Z-score should I use for different confidence levels?
A: Common Z-scores are 1.645 for 90% confidence, 1.96 for 95% confidence, and 2.576 for 99% confidence.
Q2: What if I don't know the estimated proportion?
A: Use p = 0.5 as this provides the most conservative (largest) sample size estimate, ensuring adequate power regardless of the true proportion.
Q3: How does margin of error affect sample size?
A: Smaller margins of error require larger sample sizes. Halving the margin of error quadruples the required sample size.
Q4: When is this formula appropriate?
A: This formula is appropriate when sampling from a large population and when the sample proportion is expected to be not too close to 0 or 1.
Q5: What about finite population correction?
A: For populations smaller than 20,000, a finite population correction may be applied to reduce the required sample size.