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A composite sample is formed by combining material from several collected portions into one mixture, from which material for laboratory measurement is taken. It can represent an aggregate composition when the collection and mixing weights match the intended target. IUPAC describes compositing as preparation of a mixture from several samples; combining them does not by itself prove representativeness.^[ref]

Suppose sampling increments have masses $m_i$ and analyte mass fractions $c_i$. With complete transfer, no chemical change and adequate mixing, conservation of analyte givesEqual increment masses produce an arithmetic mean; unequal masses produce a mass-weighted mean. Weights chosen to represent different parts of the sampling target can differ from the fractions accidentally collected.

An original example shows what is lost. Four equal-mass portions with concentrations $(0,0,0,40)$ milligrams per kilogram give the same composite concentration, 10 milligrams per kilogram, as portions with concentrations $(10,10,10,10)$. A single composite measurement cannot distinguish a localized high value from uniform composition. It addresses the weighted average, not the maximum or the spatial distribution.

The uncertainty of that average depends on dependence between portions. For a random concentration vector with covariance matrix $\Sigma$ and fixed mixing weights,For four equal-weight portions each with standard deviation 2 concentration units and common pairwise correlation coefficient 0.25, this givesand standard deviation about 1.32 units. Assuming independence would instead give 1 unit. This stipulated model concerns collected-material variation; common losses or measurement errors can add other contributions.^[ref]

A practical protocol specifies increment selection, mixing proportions, mixing procedure and reduction to a test portion. Loss of volatile material, segregation of particles or incomplete mixing can make the analysed portion differ from the intended composite. Replicate readings of one final solution test later measurement stages; independent composites are needed to investigate variability introduced during collection and pooling.

A sampling increment is an individual portion collected by one operation of a sampling device. One scoop, one probe withdrawal or one defined cut through a moving stream can produce an increment, provided the collection operation and its extent are specified. IUPAC uses this definition for bulk materials and large units.^[ref]

Several sampling increments may be combined into a composite sample. Their number describes collection operations; repeated instrument readings of the same prepared material do not create more sampling increments. Nor is an increment necessarily representative of the entire lot on its own: its location, time, amount and selection mechanism connect it to the analytical sampling target.

An original mass-balance example combines a0.10kilogram increment containing2milligrams per kilogram of an analyte with a0.30kilogram increment containing10milligrams per kilogram. With complete transfer and no chemical change, the composite mass fraction isThe unweighted average of the two concentrations would be6milligrams per kilogram. Equal weighting of reported increment concentrations is therefore different from physically combining unequal increment masses. Whether either result estimates the intended lot mean also depends on the collection design.

Sparse contamination supplies a second distinction. In a stipulated model where each independent increment has probability0.01of intercepting a contaminated region, $k$ increments all miss it with probability $0.99^k$. Even100such increments have a miss probability of about0.366. This is an illustrative detection model, not a universal sample-count rule; spatial dependence and changing increment size alter it.

A collection record should identify the sampling device, each increment's position or collection interval, its amount and any combining or reduction step. Different increment plans can change analytical sampling uncertainty even when the same analytical instrument is used. The collection stage must be varied to assess that uncertainty, rather than only remeasuring one final extract.