Sample Calculator: Finite Population Survey
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Número total de usuarios en tu población
Usar 50% si no tienes estimación previa
TL; DR
A finite population is one whose number of individuals is known and measurable. Cochran's formula includes a correction factor that adjusts sample size according to the proportion it represents of the total population, ensuring statistical precision without wasting resources.
When to use this calculator?
Use this calculator when you have a defined and quantifiable population universe:
• Known population: company employees, registered users, closed community members
• Less than 100,000 individuals - for larger populations, the infinite formula is mathematically equivalent
• Surveys or questionnaires requiring academic rigor or publication
• When your sample represents more than 5% of the population (industry 5% rule)
The finite correction factor reduces required sample size compared to infinite formula, optimizing resources.
Mathematical Foundation: Cochran's Formula
The finite population formula includes a correction factor in the denominator:
n = (N × Z² × p × q) / ((N - 1) × E² + Z² × p × q)
N = Total population size | Z = Z-score of confidence level
p = Expected proportion (0.5 = maximum variability) | q = 1 - p | E = Margin of error
Asymptotic behavior: As N increases, the function converges to infinite population value. For N > 100,000, difference is < 1%, validating simplified formula use.
The 5% rule: If n < 5% of N, finite correction unnecessary. Between 5-10%, recommended. >10%, essential.
Standard Statistical Parameters
95% Confidence Level (Z=1.96): Industry and academic standard. Means if you repeat 100 studies, in 95 the results will fall within confidence interval. Ideal for publications and critical decisions.
Confidence alternatives: 99% (Z=2.576) for mission-critical studies, 90% (Z=1.645) for agile business decisions, 80% (Z=1.282) for rapid prototypes.
±5% Margin of Error: Optimal balance between precision and resources. Reducing to ±3% can double/triple sample. Increasing to ±7% may be acceptable for non-critical business decisions.
Inversely proportional relationship: Lower margin of error or higher confidence = significantly larger sample. Calculator should show this trade-off.
50% Proportion: Conservative approach maximizing size (maximum variability). With historical data (e.g., '30% prefers A'), use that value to reduce sample without compromising validity.
Critical LatAm Considerations
Most critical success factor: Cultural and linguistic adaptation. Meticulous design with localized language and cultural sensitivity are indispensable for data reliability in Latin American market.
Mandatory Mobile-First: 96.1% mobile penetration in Brazil, similar across region. Design surveys optimized for small screens from the start, not as post-adaptation.
Deep Localization (not translation): Adapt idioms, tone (tú/usted/vos) and expressions by country. Significant variations between Mexico, Argentina, Chile, Colombia. What works in one may confuse in another.
Cultural Sensitivity in Questions: Avoid direct income questions (taboo in many LatAm contexts). Use validated proxies: 'devices at home', 'education level', 'housing type', 'number of rooms'.
Intra-Regional Diversity: Consider significant cultural variations by country when recruiting. Adapt selection criteria and screeners to specific market.
No-show rate: In LatAm, consider adding 10-15% extra sample to compensate for typical absenteeism, especially in in-person studies.