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Required sample size for surveys and A/B tests by confidence level and margin of error
The Sample Size Calculator determines how many observations you need to achieve a desired confidence level and margin of error. It supports both population proportion surveys and mean estimation, with options for finite population correction when the total population is small. Market researchers, academics planning studies, and data scientists designing A/B tests use this before starting data collection.
Frequently Asked Questions
Sobre Esta Calculadora
Sample size determination is one of the most important steps in planning any study or survey. Collecting too few samples makes your conclusions unreliable; collecting too many wastes time and resources. The required sample size depends on three factors: the desired confidence level, the acceptable margin of error, and an estimate of the population variance.
For proportion surveys, p = 0.5 gives the most conservative (largest) sample size because it maximizes the variance p(1−p). If you have prior information suggesting the proportion is closer to 0.1 or 0.9, you can use a smaller sample size. For mean estimation, you need an estimate of the standard deviation, often from a pilot study or previous research.
The finite population correction factor (√((N−n)/(N−1))) reduces the required sample size when sampling more than 5-10% of the total population N. This is important for surveys of small towns, niche customer segments, or employee populations.
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Exemplo Resolvido
Sample size needed for a survey with ±3% margin of error at 95% confidence
Entradas:
- Confidence level: 95% (z* = 1.96)
- Margin of error (E): 3% = 0.03
- Expected proportion (p): 0.5 (maximum variance, most conservative)
Passo a Passo:
- Formula: n = (z*² × p × (1−p)) / E²
- z*² = 1.96² = 3.8416
- p × (1−p) = 0.5 × 0.5 = 0.25
- E² = 0.03² = 0.0009
- n = (3.8416 × 0.25) / 0.0009 = 0.9604 / 0.0009 = 1,067