The relationship between purely stochastic sampling error and the number of technical replicates used to estimate concentration at an extreme dilution

Analytical and Bioanalytical Chemistry
Peter L IrwinChin-Yi Chen

Abstract

For any analytical system the population mean (μ) number of entities (e.g., cells or molecules) per tested volume, surface area, or mass also defines the population standard deviation (σ = square root(μ)). For a preponderance of analytical methods, σ is very small relative to μ due to their large limit of detection (>10(2) per volume). However, in theory at least, DNA-based detection methods (real-time, quantitative or qPCR) can detect ≈ 1 DNA molecule per tested volume (i.e., μ ≈ 1) whereupon errors of random sampling can cause sample means (mean) to substantially deviate from μ if the number of samplings (n), or "technical replicates", per observation is too small. In this work the behaviors of two measures of sampling error (each replicated fivefold) are examined under the influence of n. For all data (μ = 1.25, 2.5, 5, 7.5, 10, and 20) a large sample of individual analytical counts (x) were created and randomly assigned into N integral-valued sub-samples each containing between 2 and 50 repeats (n) whereupon N × n = 322 to 361. From these data the average μ-normalized deviation of σ from each sub-sample's standard deviation estimate (s(j), j = 1 to N; N = 7 [n = 50] to 180 [n = 2]) was calculated (Δ). Alternatively, the ave...Continue Reading

References

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Citations

Feb 6, 2013·Analytical and Bioanalytical Chemistry·Peter IrwinYiping He
Nov 20, 2012·Applied and Environmental Microbiology·Darrell P ChandlerPhilip E Long
Jan 1, 2012·Microarrays·Darrell P ChandlerChristopher G Cooney

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