PROPOSIA

Sample Size Calculator

Sample sizes and margins of error using Cochran's formula with finite population correction — plus a methodology paragraph ready to paste.

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Sample Size Calculator

Design statistically robust studies with confidence. Calculate sample sizes, estimate margins of error, and generate professional methodology narratives for your grant proposals.

5%
1% (Precise)20% (Rough)
50%

Use 50% if you are unsure (Industry Standard).

Proposal Snippet Generator
"This study establishes a sample size of 385 participants to ensure statistical validity. Based on a confidence level of 95% and an estimated population proportion of 50%, this sample size yields a margin of error of ±5.0%. This configuration ensures that the study results are representative of an infinite population within the specified reliability thresholds."

Required Sample Size

385

To achieve a margin of error of 5% with 95% confidence, you need 385 respondents.

Visual Analysis

Diminishing Returns Curve
Study Architect Analysis

📋 Study Interpretation

You need 385 participants to achieve a 95% confidence level with a margin of error of ±5.0%.

🔍 Statistical Context

  • Assumption: Population proportion estimated at 50%.
  • Definition: The calculated sample size ensures that the true population parameter falls within the margin of error 95% of the time.

📉 Trade-off Analysis

Sample size grows exponentially with precision requirements.

  • Cost Saving Option: Increasing the margin of error to 6.0% reduces the required sample to 267 (saving 118 respondents).

Methodology & Technical Reference

Primary Formula (Infinite Population)

This calculator uses Cochran's Formula to determine the sample size needed to estimate a population proportion with a specific margin of error and confidence level.

n₀ = (Z² × p × (1-p)) / e²
  • Z: Z-score (e.g., 1.96 for 95% confidence).
  • p: Population proportion (assumed 0.5 for max variance).
  • e: Margin of Error (e.g., 0.05 for ±5%).

Finite Population Correction

When the population size (N) is known and small relative to the sample, a Finite Population Correction (FPC) is applied to reduce the required sample size.

n = n₀ / (1 + (n₀ - 1) / N)
Note on Power Analysis: This tool calculates sample sizes for descriptive statistics (Confidence Intervals). It is distinct from Power Analysis, which is used to calculate sample sizes for hypothesis testing.