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Sample Size Formula:
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Sample size calculation is a crucial step in research design that determines the number of participants needed to detect a statistically significant effect. It ensures studies have adequate power while optimizing resources and minimizing ethical concerns.
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 specified confidence and precision.
Details: Proper sample size calculation prevents underpowered studies (missing true effects) and overpowered studies (wasting resources). It ensures research validity and reliability while meeting statistical requirements.
Tips: Enter proportion as decimal (0-1), Z-score based on confidence level (1.96 for 95% CI), and margin of error as decimal (0.05 for ±5%). All values must be valid and within specified ranges.
Q1: What Are Common Z-score Values?
A: 1.645 for 90% confidence, 1.96 for 95% confidence, and 2.576 for 99% confidence level.
Q2: How To Choose The Proportion Value?
A: Use 0.5 for maximum variability when unsure, or use pilot study data. Conservative approach uses p=0.5 for largest sample size.
Q3: What Is A Reasonable Margin Of Error?
A: Typically 0.05 (±5%) for general research, 0.03 (±3%) for precise estimates, and 0.01 (±1%) for high-precision requirements.
Q4: When Is This Formula Appropriate?
A: For estimating sample size when measuring proportions or percentages in survey research and observational studies with large populations.
Q5: What About Finite Population Correction?
A: For small populations, apply finite population correction: \( n_{adj} = \frac{n}{1 + \frac{(n-1)}{N}} \) where N is population size.