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Sample Size Formula:
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Sample size calculation determines the number of participants needed in a study to achieve statistically significant results. For proportion estimation, it ensures the sample accurately represents the population proportion within a specified margin of error.
The calculator uses the sample size formula for proportion estimation:
Where:
Explanation: This formula calculates the minimum sample size needed to estimate a population proportion with specified confidence and precision.
Details: Proper sample size ensures study results are statistically valid, prevents underpowered studies, and helps allocate resources efficiently while maintaining research credibility.
Tips: Enter Z-score (1.96 for 95% CI, 2.576 for 99% CI), estimated proportion (0.5 for conservative estimate), and desired margin of error (typically 0.05 or 0.03).
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: Why use p=0.5 as default?
A: p=0.5 provides the most conservative (largest) sample size estimate, ensuring adequate power regardless of the actual population proportion.
Q3: What is a reasonable margin of error?
A: Typically 0.05 (5%) for general research, 0.03 (3%) for more precise studies, and 0.01 (1%) for high-precision requirements.
Q4: Does this work for small populations?
A: For populations under 10,000, apply the finite population correction: nadjusted = n / (1 + (n-1)/N) where N is population size.
Q5: When is this formula appropriate?
A: For simple random sampling when estimating a single proportion. Different formulas are needed for means, comparisons, or complex sampling designs.