Measurement Uncertainty in Hemp Testing: What the Plus-or-Minus Value Means

A laboratory result can be carefully measured and still not be an exact, perfectly known value. Measurement uncertainty expresses that limited knowledge in a structured way.

On a hemp test report, a result might appear as:

0.28% total THC ± 0.03%

The number before the plus-or-minus sign is the reported measured value. The second number describes an uncertainty interval under stated assumptions. To interpret it correctly, the report should also identify the units, type of uncertainty, coverage factor or probability, method, and sample.

What measurement uncertainty is

NIST defines measurement uncertainty as a non-negative parameter characterizing the dispersion of quantity values attributed to the measurand, based on the information used.

The measurand is the quantity intended to be measured—for example, total delta-9 THC mass fraction in a prepared hemp sample under a specified method.

Uncertainty does not say that “anything could be true.” It describes the range or dispersion supported by the measurement model and available information.

What it is not

Measurement uncertainty is not automatically:

• a laboratory mistake;
• evidence of misconduct;
• the same as batch-to-batch variation;
• the same as variation between gummies or flowers;
• a legal tolerance;
• a product specification;
• a rounding allowance; or
• proof that every value inside an interval is equally likely.

Error and uncertainty are also different. Measurement error is the difference between a measured result and the value of the measurand, but the exact true value is generally unknown. Uncertainty can be evaluated even when the exact error cannot.

Why a result needs more than one number

Analytical measurements depend on multiple inputs and steps:

• sample selection;
• sample mass;
• grinding or homogenization;
• moisture determination;
• extraction and dilution;
• reference standards;
• calibration;
• instrument response;
• repeatability;
• method corrections; and
• calculation and rounding.

An uncertainty evaluation combines relevant components according to a measurement model. Some components can be estimated from repeated observations. Others come from calibration certificates, reference-material values, resolution, prior validation data, or other technical information.

The final uncertainty belongs to the stated measurement result. It does not automatically cover variability that was never included, such as differences among untested units across a production batch.

Type A and Type B evaluations

Metrology guidance commonly groups uncertainty evaluations into two categories.

Type A evaluation uses statistical analysis of repeated observations. A laboratory might examine the spread among repeated preparations or measurements performed under defined conditions.

Type B evaluation uses other information. Examples can include:

• calibration-certificate uncertainty;
• certified reference-material values;
• balance or volumetric-equipment specifications;
• instrument resolution;
• validated recovery information; and
• prior technical knowledge about an input quantity.

The letters do not mean that Type A is more important or Type B is less scientific. They describe how a component was evaluated. Both can contribute to the combined standard uncertainty.

A report reader usually does not need to reproduce the laboratory’s full uncertainty budget. The laboratory should be able to identify the measurement model, important components, calculation procedure, and reporting format when required by its method or accreditation system.

Standard and expanded uncertainty

Standard uncertainty is expressed like a standard deviation. When multiple components contribute, they can be combined into a combined standard uncertainty.

Expanded uncertainty multiplies the combined standard uncertainty by a coverage factor, commonly written k:

U = k × uc

The measurement may then be reported as:

y ± U

NIST explains that, when the underlying assumptions support it, a coverage factor near 2 is commonly associated with an interval of approximately 95% coverage. That relationship is not automatic. The report must state or support the coverage factor and probability.

Do not assume every plus-or-minus value uses k = 2 or 95% coverage.

Reading an interval

If a report states:

• result: 0.28% total THC;
• expanded uncertainty: 0.03%;
• coverage factor: k = 2; and
• coverage probability: approximately 95%;

the displayed interval is 0.25% to 0.31% under the stated measurement model.

This arithmetic is straightforward:

0.28% - 0.03% = 0.25%

0.28% + 0.03% = 0.31%

It does not mean the sample repeatedly moves between those values. It describes knowledge about the measured quantity.

Uncertainty and USDA production compliance

USDA’s Domestic Hemp Production Program requires laboratories performing the specified crop-compliance testing to estimate and report measurement uncertainty with total THC results. USDA’s acceptable-hemp-THC framework uses the reported value and uncertainty under the applicable production rules.

That scope matters. USDA production testing concerns composite samples from a producer’s crop lot, total THC, dry-weight reporting, and pre- or post-harvest compliance. It does not create a universal decision rule for every retail oil, gummy, capsule, or concentrate.

When reading a finished-product COA, identify the law, program, specification, or customer requirement that controls the decision. Do not transplant the USDA crop rule onto another matrix.

Uncertainty near a threshold

Uncertainty becomes especially visible when a measured value is close to a specification or legal limit.

Three separate elements must be identified:

1. Measured result: the laboratory’s value.
2. Uncertainty statement: the evaluated interval and coverage information.
3. Decision rule: how the relevant authority compares the result and uncertainty with the limit.

Different programs can use different decision rules. Some compare the reported value directly. Some account for an uncertainty interval. Some define an “acceptable” range in statute or regulation.

The laboratory result alone does not reveal which rule applies.

Uncertainty is not the same as sampling variation

A laboratory can estimate measurement uncertainty for the portion it analyzed. That does not prove the submitted portion represents every part of the lot.

Consider a jar of gummies. An uncertainty statement for a homogenized laboratory sample can account for the analytical procedure. It may not include unit-to-unit differences unless the sampling and study design evaluated them.

Likewise, one composite crop sample is intended to represent a defined lot under a sampling protocol. The inference depends on how the lot was defined and how specimens were selected—not only on the instrument’s uncertainty.

Sampling Matters addresses that separate layer.

Uncertainty and interlaboratory differences

Two laboratories can report different values without either number being fabricated. Differences can arise from sampling, preparation, moisture correction, calibration, analytical method, integration, reference standards, reporting limits, and calculations.

NIST’s Cannabis Laboratory Quality Assurance Program compared results from participating laboratories with carefully characterized materials. Its reports show why measurement comparability requires more than matching instrument names.

An uncertainty statement helps interpret one result. It does not, by itself, explain every difference between laboratories.

What to look for on a report

Find:

• the measured value and unit;
• the named analyte or calculated total;
• the matrix;
• whether uncertainty is standard or expanded;
• the uncertainty value;
• coverage factor k;
• coverage probability, if stated;
• the method;
• sample and batch identifiers;
• dry-weight or as-received basis;
• rounding rule; and
• the decision rule or governing requirement, where relevant.

If a report only prints ± without explaining what follows, ask the laboratory or report issuer for the uncertainty statement.

Keep units aligned

A result and its uncertainty must use compatible units. If the result is 0.28% and expanded uncertainty is 0.03 percentage points, the interval is 0.25% to 0.31%.

That is different from a relative uncertainty of 3%. Three percent of 0.28% is 0.0084 percentage points.

Also distinguish percent from percentage points. Moving from 0.28% to 0.31% is an increase of 0.03 percentage points, not 0.03% of the original value.

Propagating uncertainty through a conversion

Converting a laboratory concentration to a container amount can introduce additional inputs. For an oil, a simplified calculation might use:

concentration × bottle volume = calculated container amount

If concentration has uncertainty and bottle volume also has uncertainty, the container result inherits both. If the laboratory reports milligrams per gram but the label uses milliliters, density becomes another measured input.

For a gummy, converting milligrams per gram to milligrams per piece uses unit mass. A single average unit weight may not describe the spread among all pieces.

Copying the concentration’s plus-or-minus value unchanged onto a container total is therefore usually wrong. The uncertainty must be propagated through the actual measurement model. When the required input uncertainties are missing, label the arithmetic as a nominal calculation rather than inventing a confidence interval.

Rounding can change a threshold comparison

The measured value and uncertainty should be rounded consistently with the reporting procedure. Excess decimal places can create an appearance of precision that the measurement does not support.

For example, a raw calculation of 0.29746% with an expanded uncertainty of 0.02137 percentage points might be reported with fewer digits under the laboratory’s rounding policy. The legal decision should use the required reported or unrounded values according to the governing rule—not whichever display produces the preferred outcome.

Ask whether the specification defines:

• the number of decimal places;
• rounding before or after comparison;
• use of an uncertainty interval;
• treatment of values below reporting limits; and
• a guard band or other decision rule.

These are policy choices layered on top of the measurement. They are not determined by the plus-or-minus symbol alone.

Relative uncertainty

Uncertainty can be expressed in the same unit as the result or as a relative value. If a result is 10 mg/g with expanded uncertainty of 1 mg/g, the relative expanded uncertainty is 10%.

At low concentrations, the relative uncertainty can be large even when the absolute uncertainty looks small. Near a detection or quantification limit, methods may not support the same relative precision achieved near the center of the calibration range.

This connects measurement uncertainty with LOD and LOQ but does not make the terms interchangeable. Detection limits address capability near background; uncertainty describes dispersion associated with a reported measurement result.

“ND” Is Not Always Zero explains that boundary.

How to summarize responsibly

A complete plain-language statement could read:

The laboratory reported total THC of 0.28% by dry weight for the identified sample, with expanded uncertainty of 0.03 percentage points at the stated coverage factor. The applicable decision rule determines how that interval is used.

Do not shorten that to “the true result is definitely between 0.25% and 0.31%” unless the report’s uncertainty model and coverage statement support that wording.

Checklist

• What quantity was measured?
• Which sample and batch were tested?
• What are the units and basis?
• Is the value standard or expanded uncertainty?
• Is k shown?
• Is a coverage probability stated?
• Does the uncertainty include sampling or only analytical components?
• Which decision rule applies?
• Is the result being converted to another unit or container total?

Measurement uncertainty is not a flaw that should be hidden. It is information about how much confidence the measurement process can support.

Primary sources

• NIST, Measurement Uncertainty
• NIST, Basic Definitions of Uncertainty
• NIST, Expanded Uncertainty and Coverage Factors
• USDA AMS, Hemp Laboratory Testing Guidelines
• NIST, CannaQAP Exercise 2