Professional statistical sample size calculator with real-time results and advanced features
Use 50% for maximum variance if unknown
Finite population correction applied if provided
Required Sample Size
385
Sample size is the number of observations or participants included in a statistical study. It's one of the most critical decisions in research design, directly affecting the reliability, validity, and generalizability of your findings.
The right sample size ensures your study has sufficient statistical power to detect meaningful effects while avoiding unnecessary costs and ethical concerns. Too small, and you risk missing important findings; too large, and you waste resources.
The probability that your confidence interval contains the true population parameter. Higher confidence levels require larger sample sizes but provide greater certainty.
The maximum amount by which your sample estimate might differ from the true population value. Smaller margins of error require larger sample sizes for the same confidence level.
The expected percentage of the population with the characteristic of interest. Use 50% (0.5) when unknown, as this maximizes required sample size and provides conservative estimates.
Where:
• n = required sample size
• z = z-score for confidence level
• p = expected population proportion
• e = margin of error (as decimal)
Additional variable:
• N = population size
Applied when population is finite and relatively small
| Confidence Level | Z-Score | Usage |
|---|---|---|
| 90% | 1.645 | Exploratory research |
| 95% | 1.96 | Standard research |
| 99% | 2.58 | Critical decisions |
| 99.9% | 3.29 | High-stakes research |
For continuous variables:
• σ = population standard deviation
• e = desired margin of error
Use when studying means rather than proportions
The probability of detecting an effect if it truly exists. Typically set at 80% or 90%. Higher power requires larger sample sizes but reduces the risk of missing important findings.
The magnitude of the difference you want to detect. Smaller effect sizes require larger sample sizes to achieve adequate statistical power.
Typical Requirements: Large samples (300-1000+) for population estimates with acceptable margins of error.
Example:
National poll: n=1000, 95% confidence, ±3% margin
Considerations:
Requirements: Power analysis based on expected treatment effect, typically requiring 80-90% power.
Example:
Drug trial: detect 10% improvement, 90% power
Special Factors:
Focus: Detecting small but meaningful differences in conversion rates or user behavior metrics.
Example:
Detect 2% conversion lift with 95% confidence
Considerations:
Balance: Cost-effectiveness with statistical rigor, often using quota sampling and demographic stratification.
Example:
Brand awareness study: n=500-1000
Factors:
Precision: Small margins of error for defect rates, often requiring large samples for rare events.
Example:
Defect rate <1%, ±0.5% precision
Applications:
Rigor: High statistical standards with power analysis and effect size reporting increasingly required by journals.
Standards:
80% power, medium effect size (d=0.5)
Requirements:
Allows you to stop data collection early if results are conclusive, potentially saving time and resources while maintaining statistical validity.
Applications:
Incorporates prior knowledge and beliefs to determine sample size, updating estimates as data is collected.
Advantages:
ML models require different considerations, focusing on training/validation splits and model complexity.
Guidelines:
With massive datasets, statistical significance is easy to achieve, but practical significance becomes more important.
Considerations:
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