Official account, TSH test and T4/T3 tests: pituitary regulation and interpretation of distinct hormone measurements.

SEER module, intestinal subdivisions and different transport/processing roles.

SEER module, alimentary tract and accessory organs.

SEER module, lymphatic fluid return, vessels and lymphoid organs.

Official account of chamber sequence, valve locations and coronary supply.

Official institutional statement, WHO/RHR/18.15, 16 October 2018. Overview: hymenal appearance does not establish a history of vaginal intercourse.

SEER module, cellular and connective-tissue organization; tendon and fascia.

SEER module, renal position, nephron and urine drainage.

SEER module, lung organization and visceral/parietal pleura.

Official definition and listed reproductive organs.

SEER institutional teaching modules: introductory organization, tissue structure and organ systems.

Analytical sampling uncertainty is the contribution to measurement uncertainty arising when collected material is used to infer a property of a specified sampling target. The target might be a bulk lot or a defined location and time interval. Its composition need not equal that of one convenient portion. Sampling and physical preparation therefore belong in the measurement model when the measurand concerns the larger target.^[ref]

A duplicated experiment can separate two random components. Within each target, collect two independent samples by the stated protocol, prepare them separately, and analyse each twice. For a simple model,where $i=1,2$ labels collection and $j=1,2$ labels analysis; all random terms are centered and independent except for the shared $S_i$ within a sample. The within-sample difference has variance $2{\sigma }_a^2$. The difference between the two sample means has variance $2{\sigma }_s^2+{\sigma }_a^2$. Repeating this design across targets supports estimation of both components; different target means cancel in each within-target difference.^[ref]

For original stipulated difference standard deviations2and5milligrams per kilogram, respectively,in squared concentration units. One analysis on one sample has combined standard deviation $\sqrt{13.5}\approx 3.67$milligrams per kilogram. Averaging two analyses of that same sample gives $\sqrt{11.5+2/2}\approx 3.54$; averaging one analysis from each of two independent samples gives $\sqrt{(11.5+2)/2}\approx 2.60$. More laboratory replication and more independent collection address different contributions.

A collaborative wheat-and-coffee trial varied the sampler as well as the collected material. Its contrasting reproducibility and repeatability findings show why the uncertainty depends on which collection conditions are allowed to vary.^[ref]

Duplicate sampling with one sampler and protocol does not establish absence of a shared sampling bias. Reference comparisons, alternative protocols or inter-organisational trials can test additional effects. Common preparation losses or measurement calibration errors also require covariance terms beyond the independent model.

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.

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.

Matrix-matched calibration estimates the response–amount relationship using standards whose sample matrix reproduces relevant measurement conditions of the unknown samples. Matching is intended to control an analytical matrix effect, rather than merely to make a standard look similar. A calibration is a relationship under given conditions; transferring it requires those conditions to remain appropriate.^[ref]

For an original local model, let the sample response be $y=b_M+s_{M}c$. Standards in a matching matrix estimate $b_M$ and $s_M$, giving $\hat{c}=(y-b_M)/s_M$. Choose $b_M=3$, $s_M=1.2$ and true $c=10$, hence $y=15$. The matched calibration gives10. A neat-reference model with $b_0=1$, $s_0=2.5$ instead gives $(15-1)/2.5=5.6$.

A partial match can still fail. If the actual sample slope is $1.5$ while its offset remains3, the same true $c=10$ now gives $y=18$. Applying the nominal matrix-matched slope $1.2$ gives $(18-3)/1.2=12.5$, a25% overestimate. The name of the calibration method is not evidence that all samples share one slope.

Where standards enter the workflow matters. Standards prepared before extraction can incorporate preparation loss into their response–amount relationship. Standards added after preparation primarily characterize the final-extract response. Applying an additional recovery correction to a calibration that already incorporates the same loss can double-count it.

A suitable analyte-free matrix may be unavailable. A surrogate sample matrix can then be evaluated, but similarity must be tested rather than assumed. An analytical blank constrains particular background contributions, and an internal standard can compensate only for response changes it follows appropriately. Assess matching across the intended sample types, analyte levels and preparation conditions.

A blank indication is the measured response obtained when the quantity of interest is assumed absent or not contributing. In analytical chemistry, an analytical blank supplies the material used for that comparison. The indication is an output of the measurement system; it is neither the material itself nor necessarily a zero reading.^[ref]

For an invented example, a blank produces5 detector-response units. A sample produces15 units. Under an additive background model, the response attributable to the sample above this blank is10 units. Converting that response into an analyte concentration requires the appropriate instrument calibration. Five detector units do not mean5 micromolar simply because both numbers describe the same measurement sequence.

A blank value is obtained when an applicable conversion model expresses the blank response as a measured quantity value.^[ref] Keeping that conversion explicit prevents confusing an instrument indication with a reported concentration. Repeated blank indications also provide information about background variability used in a limit of detection. A stable offset and a noisy background can have the same mean while supporting different detection performance; blank correction of the mean alone does not make their standard deviations equal.

Blank correction removes the modeled effect of a blank indication from a measured response. The analytical blank supplies evidence about a background contribution; the measurement model specifies how to correct for it. The quantities combined must be of the same kind.^[ref]

For an additive example, a sample response of12 units and mean blank response of2 units give a corrected response of10 units. The correction retains measurement uncertainty. If sample response $X$ is independent of the mean of $n$ independent blank measurements, thenWith sample variance4, single-blank variance9 and $n=9$, the corrected variance is5, not zero. Dependence requires the corresponding covariance term in the propagation.

A different measurement model can require division. Invented transmittance indications0.4 for the sample and0.5 for the blank give corrected transmittance $0.4/0.5=0.8$. The associated absorbance is $-{\log }_{10}(0.8)\approx 0.09691$. Subtracting0.5 from0.4 would represent a different operation.^[ref] These examples show why specifying the blank material alone does not specify a valid blank correction.