The number and its uncertainty travel together

NIST Technical Note 1297 distinguishes combined standard uncertainty from expanded uncertainty. The latter multiplies the combined uncertainty by a stated coverage factor, k. A report should identify which kind it uses, explain the components and methods, and give the basis for any claimed level of confidence. A coverage factor of two is not an unconditional guarantee of 95% coverage.

When inputs contribute to a calculated result, their relationships matter too. Correlated inputs cannot always be treated as independent. This 1994 reference is a classic explanation of measurement reporting, not a newly issued standard; NIST marks these legacy pages as no longer updated.

How this changes the way we read concentration

Consider the statement that a concentration is mass divided by volume. The arithmetic can be correct even when the measurements behind it are not equally well characterized. S7’s suggested reading order is: identify the quantity, check the units, then ask what the stated uncertainty describes. A polished result with many decimal places should not end that conversation.

For comparison, imagine two reports displaying the same concentration. Before calling them equivalent, ask whether they use the same quantity definition and explain their uncertainty in comparable terms. If one report gives no uncertainty information, leave that gap visible rather than assigning confidence based on the number’s appearance.

A reading tool, not a preparation guide

This article explains how to question a measurement report. It provides no recipe, reconstitution instructions or dosing calculation. The laboratory artwork is conceptual; it does not represent a calibrated instrument, actual measurement or experimental dataset.