Calculate material percentage uncertainty from observed particle counts — material_percentage

Calculates the absolute confidence-interval half-width for an observed material-class percentage from the total number of particles characterized. The calculation is the single-property proportion equation described by Cowger et al. (2024), rearranged to solve for error after observation.

Usage

material_percentage_uncertainty(count, percentage, confidence = 0.95)

Arguments

count: positive whole-number total particle count. May be a scalar or a numeric vector.
percentage: observed material-class percentage in the closed interval 0–100. May be a scalar or a numeric vector.
confidence: confidence level in the open interval 0–1. Defaults to 0.95. May be a scalar or a numeric vector.

Value

A numeric vector containing absolute uncertainty half-widths in percentage points. Inputs must either have length one or share one common length.

Details

For proportion p = percentage / 100, total observed count n, and two-tailed normal critical value z, the returned half-width is 100 * abs(z) * sqrt(p * (1 - p) / n). This is a material-composition uncertainty under representative random particle sampling. It does not include laboratory, spectral-identification, concentration, finite- population, or multiple-property uncertainty. In particular, the published Wald-style equation returns zero at exactly 0 and 100 percent.

References

Cowger W, Markley LAT, Moore S, Gray AB, Upadhyay K, Koelmans AA (2024). "How many microplastics do you need to (sub)sample?" Ecotoxicology and Environmental Safety, 275, 116243. doi:10.1016/j.ecoenv.2024.116243 .

Author

Win Cowger

Examples

material_percentage_uncertainty(100, c(20, 50, 80))
#> [1] 7.839856 9.799820 7.839856
material_percentage_uncertainty(100, 50, confidence = 0.90)
#> [1] 8.224268