Sampling Error Calculator
Error margin related to sample size.
Formula first
Overview
Sampling error represents the statistical discrepancy between a sample statistic and the true population parameter resulting from observing only a subset of individuals. This specific formula describes the Law of Large Numbers in a simplified form, showing that the precision of an estimate increases as the sample size grows.
Symbols
Variables
E = Rel. Error Factor, n = Sample Size
Apply it well
When To Use
When to use: This relationship is used during the planning phase of biological experiments to determine how many specimens are needed to achieve a desired level of precision. It is also applied when evaluating the reliability of field survey data or clinical trial results where population-wide testing is impossible.
Why it matters: Reducing sampling error is critical for ensuring that biological conclusions, such as the efficacy of a new vaccine or the biodiversity of an ecosystem, are not just products of random chance. It allows researchers to optimize their budget and time by calculating the point of diminishing returns for sample collection.
Avoid these traps
Common Mistakes
- Using n instead of sqrt(n).
- Treating proportionality as an exact equality.
One free problem
Practice Problem
A marine biologist is measuring the gill surface area of a specific fish species. If the researcher takes a sample size of 64 fish, what is the calculated sampling error using the standard proportionality constant of 1?
Solve for:
Hint: The error is the reciprocal of the square root of the sample size.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Sampling error
- Wikipedia: Law of Large Numbers
- Biostatistics: A Foundation for Analysis in the Health Sciences by Daniel and Cross
- Statistics by Freedman, Pisani, and Purves
- Wikipedia: Standard error
- Moore, McCabe, and Craig Introduction to the Practice of Statistics
- OCR A-Level Biology A — Biodiversity