title: Variance decomposition: a tool enabling strategic improvement of the precision of analytical recovery and concentration estimates associated with microorganism enumeration methods.
abstract: Concentrations of particular types of microorganisms are commonly measured in various waters, yet the accuracy and precision of reported microorganism concentration values are often questioned due to the imperfect analytical recovery of quantitative microbiological methods and the considerable variation among fully replicated measurements. The random error in analytical recovery estimates and unbiased concentration estimates may be attributable to several sources, and knowing the relative contribution from each source can facilitate strategic design of experiments to yield more precise data or provide an acceptable level of information with fewer data. Herein, variance decomposition using the law of total variance is applied to previously published probabilistic models to explore the relative contributions of various sources of random error and to develop tools to aid experimental design. This work focuses upon enumeration-based methods with imperfect analytical recovery (such as enumeration of Cryptosporidium oocysts), but the results also yield insights about plating methods and microbial methods in general. Using two hypothetical analytical recovery profiles, the variance decomposition method is used to explore 1) the design of an experiment to quantify variation in analytical recovery (including the size and precision of seeding suspensions and the number of samples), and 2) the design of an experiment to estimate a single microorganism concentration (including sample volume, effects of improving analytical recovery, and replication). In one illustrative example, a strategically designed analytical recovery experiment with 6 seeded samples would provide as much information as an alternative experiment with 15 seeded samples. Several examples of diminishing returns are illustrated to show that efforts to reduce error in analytical recovery and concentration estimates can have negligible effect if they are directed at trivial error sources.
authors.affiliation: Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada. Electronic address: pj2schmi@alumni.uwaterloo.ca.
authors.forename: P J
authors.initials: PJ
authors.lastname: Schmidt
authors.affiliation: Department of Civil and Environmental Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: M B
authors.initials: MB
authors.lastname: Emelko
authors.affiliation: Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: M E
authors.initials: ME
authors.lastname: Thompson
mesh_terms: D003458:Cryptosporidium / Q000502:physiology; D004784:Environmental Monitoring / Q000379:methods*; D015233:Models, Statistical; D014871:Water Microbiology
keywords: Cryptosporidium; Experimental design; Law of total variance; Probabilistic modelling