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Sample Size Formula for Proportion:
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Sample size calculation is a statistical process used to determine the number of observations or replicates needed in a study to detect an effect of a given size with a certain degree of confidence. It ensures that research has adequate power to draw meaningful conclusions.
The calculator uses the sample size formula for proportions:
Where:
Explanation: This formula calculates the minimum sample size needed to estimate a population proportion with a specified margin of error and confidence level.
Details: Proper sample size calculation is crucial for research validity. It helps avoid underpowered studies (too small samples) that may miss true effects, and overpowered studies (too large samples) that waste resources.
Tips: Enter Z-score (typically 1.96 for 95% confidence), estimated proportion (use 0.5 for maximum variability), and desired margin of error. All values must be valid (Z > 0, 0 ≤ p ≤ 1, E > 0).
Q1: What is the most common Z-score used?
A: For 95% confidence level, Z = 1.96 is most commonly used. For 90% confidence, Z = 1.645, and for 99% confidence, Z = 2.576.
Q2: Why use p = 0.5 as default?
A: Using p = 0.5 gives the most conservative (largest) sample size estimate, as it represents maximum variability in the population.
Q3: What is a reasonable margin of error?
A: Typically 3-5% for most surveys. Smaller margins require larger sample sizes but provide more precise estimates.
Q4: Can this formula be used for other types of studies?
A: This formula is specifically for estimating proportions. Different formulas exist for means, correlations, and other statistical parameters.
Q5: What if my population is small?
A: For populations under 10,000, consider using the finite population correction to adjust the sample size downward.