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Sample Size Formula:
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Sample size calculation is a statistical process used to determine the number of participants or observations needed in a study to detect a significant effect with a specified level of confidence and precision.
The calculator uses the standard 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 ensures that research studies have sufficient statistical power to detect meaningful effects, prevents wasted resources on underpowered studies, and provides reliable and valid results.
Tips: Enter Z-score (1.96 for 95% confidence), proportion estimate (use 0.5 for maximum variability), and margin of error (typically 0.05 for ±5%). All values must be valid (Z > 0, 0 ≤ p ≤ 1, 0 < e ≤ 1).
Q1: What is the most common Z-score used?
A: 1.96 is most commonly used, which corresponds to a 95% confidence level in statistical analysis.
Q2: Why use p = 0.5 as default?
A: Using p = 0.5 provides the most conservative estimate and maximum sample size, ensuring adequate power regardless of the actual population proportion.
Q3: What is a typical margin of error?
A: For most surveys and studies, margins of error between 3% (0.03) and 5% (0.05) are commonly used, balancing precision with practicality.
Q4: When should I adjust the proportion value?
A: Adjust the proportion when you have prior knowledge or estimates about the expected proportion in your population from previous studies or pilot data.
Q5: Does this work for all types of studies?
A: This formula is specifically for estimating proportions. Different formulas are needed for means, correlations, or other statistical parameters.