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Sample Size Formula:
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The sample size computation formula for proportions calculates the minimum number of participants needed in a study to achieve statistical significance. This formula is essential for designing research studies, surveys, and clinical trials to ensure results are reliable and valid.
The calculator uses the sample size formula for proportions:
Where:
Explanation: The formula determines the minimum sample size needed to estimate a population proportion with a specified level of confidence and precision.
Details: Proper sample size calculation ensures studies have adequate power to detect effects, prevents wasting resources on underpowered studies, and provides credible results that can be generalized to the population.
Tips: Enter the Z-score corresponding to your desired confidence level (e.g., 1.96 for 95% confidence), the estimated proportion (between 0 and 1), and the margin of error (between 0 and 1). All values must be valid and within specified ranges.
Q1: What Z-score should I use?
A: Common Z-scores are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence). Choose based on your desired confidence level.
Q2: What if I don't know the proportion (p)?
A: Use 0.5 as it gives the maximum sample size and is conservative when the true proportion is unknown.
Q3: How do I choose the margin of error?
A: Margin of error represents the precision you want. Smaller margins (e.g., 0.05) give more precise results but require larger samples.
Q4: When is this formula appropriate?
A: This formula is used for estimating population proportions in survey research, prevalence studies, and when the outcome is binary.
Q5: Are there adjustments for finite populations?
A: Yes, for small populations, use the finite population correction: \( n_{adj} = \frac{n}{1 + \frac{(n-1)}{N}} \) where N is population size.