Sample Size Calculator
Determine optimal sample sizes for research studies with power analysis, cost considerations, and sensitivity analysis for statistical precision.
Sample Size Calculator
80%90%95%99%
Desired precision
Population variability
Sample Size Results
Required Sample Size
97
For 95% confidence level
Estimation Requirements
Parameter: Population mean
Confidence Level: 95%
Margin of Error: ±2
Critical Value: 1.960
Sample Size Needed: 97
Key Assumptions
• Population follows normal distribution (or large sample)
• Standard deviation estimate is accurate
• Random sampling from target population
• No systematic bias or measurement error
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What is Sample Size Calculator?
Sample size calculation determines the minimum number of observations needed to achieve your research objectives with specified precision and confidence. It helps balance statistical power, practical constraints, and cost considerations to ensure reliable and meaningful results.
Key Concepts
- Confidence Level: The probability that repeated sampling would yield similar results
- Margin of Error: The maximum difference between sample estimate and true population parameter
- Statistical Power: The probability of detecting a true effect (1 - β)
- Effect Size: The magnitude of difference you want to be able to detect
- Standard Deviation: Measure of variability in your population
Types of Sample Size Calculations
- Estimation: For confidence intervals and precision requirements
- Hypothesis Testing: For detecting differences with specified power
- Equivalence Testing: For showing two treatments are similar
- Non-inferiority Testing: For showing one treatment isn't worse
Factors Affecting Sample Size
- Precision Requirements: Smaller margin of error → larger sample
- Confidence Level: Higher confidence → larger sample
- Population Variability: More variability → larger sample
- Effect Size: Smaller effects → larger sample to detect
- Statistical Power: Higher power → larger sample
Real-World Applications
- Clinical Trials: Determine patient enrollment for drug efficacy studies
- Market Research: Size surveys for customer satisfaction and preferences
- Quality Control: Sample size for process monitoring and improvement
- Academic Research: Plan experiments and observational studies
- Public Health: Size epidemiological studies and health surveys
- A/B Testing: Determine test duration and user requirements
Practical Considerations
- Budget Constraints: Balance statistical needs with available resources
- Time Limitations: Consider data collection timeframes
- Non-response Rates: Increase calculated size by 10-30%
- Dropout Rates: Account for participant attrition in longitudinal studies
- Feasibility: Ensure sample size is practically achievable
Common Mistakes to Avoid
- Using unrealistic estimates for parameters (especially standard deviation)
- Not accounting for multiple comparisons or subgroup analyses
- Ignoring clustering or stratification in the design
- Setting effect sizes that are too small to be practically meaningful
- Not planning for non-response and missing data
FAQ - Sample Size Calculator
You can use pilot studies, literature values, similar previous studies, or conservative estimates. For proportions, use p=0.5 if unknown (gives the largest sample size). For means, use the full range divided by 4-6 as a rough estimate.