Sampling & Sample Size

03 · Field Statistics, Practically

This section addresses three questions that determine an audit's cost and credibility: how many samples the study requires, what can be done when resources cannot support that number, and how large loads are reduced to a sortable size without introducing bias.

How many samples?

Sample size depends on two practical questions: how variable the material is from sample to sample, and how precise the final estimate needs to be. Population size plays almost no role — a large city and a small town require similar sample counts for the same precision. The calculator below answers both directions of the question; the underlying statistics (based on ASTM D5231) are available beneath it for readers who want them.

Sample-size calculator

How variable is the material of interest between samples? Roughly what share of the stream is it expected to be?

Planning a study

How many sorting samples would the target precision require?

Target precision

Working with what you have

What precision can a fixed number of samples support?

Sorting samples you can afford

Guide-level estimates at 90% confidence, following the ASTM D5231 approach. "Precision" is relative to the component's own share. Each sorting sample is 91–136 kg, sorted in full.

Optional detail · the statistics behind the calculator

Number of sorting samples

n = ( t · s / (e · x̄) )² equivalently n = ( t · CV / e )²

t = Student's t for your confidence level · s = between-sample std. dev. of the component share · x̄ = mean component share · CV = s/x̄ · e = relative precision you want to claim. Size for the governing component — the one whose CV/importance combination demands the most samples.

Precision improves with the square root of sample count

Relative precision (90% confidence) vs. number of sorting samples, for two component variabilities

FIG 03-1 · Precision scales with √n — doubling the sample count improves precision by approximately 30%, which is why the curve flattens. ASTM D5231's worked example: ±10% at 90% confidence on corrugated cardboard requires ~52 sorting samples. In practice, many studies fix a defensible n (20–30 per stratum-season is common) and report the precision that n delivers, component by component.

Practical working minimums

Sorting sample size: 91–136 kg (200–300 lb) per sorting sample, drawn from a ~450 kg (1,000 lb) grab of the selected load (ASTM D5231). Facility audits: the full generation period if it's sortable; otherwise cone & quarter down to sorting-sample size. Curbside: ~100 households per stratum per event, spread across collection days (5–7 day week, loads selected without bias — random selection). Low-prevalence categories (household hazardous waste, electronics) remain highly variable at these sample sizes and are best reported as indicative.

Working within limited resources

A full statistically designed audit is expensive and time-intensive, and for many organizations the resources are simply not available. A smaller study remains a legitimate and useful undertaking provided the scope of its claims is matched to the scope of its sampling. The tiers below describe what different levels of effort can support; the essential discipline is the same at every tier — a documented method, consistent categories, and results reported with their limitations stated.

Tier	Typical effort	What it involves	Can support	Cannot support
1 · Visual assessment	Hours	Walkthrough of bins and containers; fullness estimates; photographs; top visible contaminants noted per stream	Program design conversations; identifying obvious issues (bin placement, signage, service levels); scoping a future sort	Composition percentages; any quantitative claim
2 · Indicative sort	1 day	One or two sorting samples per stream, sorted to tier-2 categories by a small trained crew	Order-of-magnitude composition; identifying the two or three largest divertible components; a defensible starting point for targets	Precision claims; stratum- or department-level comparisons; trend claims from a single event
3 · Reduced study	2–5 days	Roughly 5–15 sorting samples, one season, trimmed category list focused on the decision at hand	Composition with stated (wide) precision; capture or contamination estimates for the governing question; year-over-year comparison when repeated consistently	Fine category detail; seasonal generalization; claims about low-prevalence materials
4 · Full statistical audit	1–4 weeks per event	Sample counts set by the calculator above; stratified; one to four seasonal events	Published composition studies; regulatory and contractual benchmarks; program evaluation with confidence statements	—

Stretching a limited budget

Several design choices reduce cost substantially while preserving usefulness. Trimming the category list to tier 2 — or to a short custom list built around the decision at hand — reduces sort time more than any other single choice. Sampling only the stream that bears on the question (for example, garbage only, when the question is diversion potential) halves or thirds the field effort. Trained volunteer labour — student groups, green teams, service clubs — can staff a sort under one experienced supervisor, and partnerships with local colleges and universities can supply both labour and analytical support. Published composition profiles for comparable sectors or communities can serve as context where local sorting is not feasible, provided they are cited as external benchmarks rather than presented as local measurements.

Compositing — combining material from several days or sources into a single sorted sample — improves how representative a single sample is of the average, and is a reasonable economy measure. Its cost is statistical: variability between samples can no longer be estimated, so composited results are reported as indicative values without precision statements.

Finally, consistency substitutes for scale in one important respect: a small audit repeated with an identical method, categories, and season is well suited to tracking change over time, even where its absolute precision in any single year is limited. For many organizations, an annual indicative sort held rigorously constant is more decision-useful than a single large study never repeated.

Reporting under resource constraints

A constrained audit is reported with the same structure as a full one — the difference lies in the language of the claims. Results are described as indicative or screening-level; percentages are rounded rather than reported to decimal places; precision statements are omitted unless the sample count supports them; and the limitations section states what was not sampled. A small study honestly bounded is a credible document; the difficulties arise only when small-study numbers are presented with large-study certainty.

Sub-sampling large loads: coning & quartering

When a load is too large to sort in full, it is reduced without introducing selection bias: mix, cone, flatten, quarter, retain opposite quarters, and repeat until the retained sample reaches sorting-sample size (91–136 kg). Each reduction step is recorded on the sample tracking log.

FIG 03-2 · Coning & quartering. Retained quarters (amber) are re-mixed and quartered again until the sub-sample reaches sorting-sample size; discarded quarters return to disposal.

Sources & further reading

ASTM International — D5231-92(2016): Standard Test Method for Determination of the Composition of Unprocessed Municipal Solid Waste (sorting-sample mass, t-statistic sample sizing, unbiased load selection, 5–7 day sorting week)