## Introduction

New thermochemical determinations, such as enthalpies of formation, bond dissociation energies, or reaction free energies, can contribute constructively to the existing body of knowledge only if their fidelity level is also conveyed. The latter is normally achieved by providing associated uncertainties, which, to be valid, need to be properly quantified and unambiguous, that is, must follow a common convention.

### Expression of uncertainties in thermochemistry

The standard for expressing uncertainties in thermochemistry is to provide earnest estimates of the 95% confidence intervals (*u*_{95%}). The convention was introduced in the 1930s by Rossini,[1] who proposed that the quoted uncertainty should correspond to twice the standard deviation *σ*, once the components due to random errors have been augmented by realistic estimates of all suspected systematic errors. The convention was immediately adopted for all thermochemical work at the US National Bureau of Standards, influencing similar research at other laboratories, and by mid-1950s it became a *de facto* worldwide standard,[2] subsequently formalized by IUPAC recommendations,[3] and matter-of-factly followed by virtually all major thermodynamic tabulations, such as CODATA,[4] JANAF,[5] or Gurvich et al.[6]

### Accuracy versus precision and trueness

The role of uncertainty is to convey a quantitative indication of accuracy. Colloquially, accuracy and precision are incorrectly treated as synonyms; compounding the confusion is the fact that scholarly literature that emphatically distinguishes these two terms, often treats accuracy as synonymous with trueness.

According to International Organization for Standardization (ISO) standards,[7] precision reflects the degree of consistency between repeated measurements and provides an account of the spread of the distribution of a series of measurements, whereas trueness reflects the bias between the mean of the measured values and the (unknown) true value, caused by errors that do not average out by repetition (Fig. 1). The spread is caused primarily by random errors, the bias primarily by systematic errors. Accuracy reflects the *combined effect* of the achieved precision and the perceived trueness.

Notably—by virtue of combining the account of random errors with best estimates of all conceivable systematic errors—the *u*_{95%} uncertainty as used in thermochemistry intends to quantify the expected accuracy, rather than just precision or just trueness. If *u*_{95%} uncertainties are properly quantified, than the true value should lie inside the quoted error bounds at least 19 times out of 20.

### Type A and Type B uncertainties

The Guide to the Expression of Uncertainty in Measurement[8] (GUM, formerly ISO GUM) classifies the components of the uncertainty based on the *method* of their evaluation, rather than on their *nature* (random vs. systematic). Type A components are those that are evaluated by statistical analysis of a series of observations, Type B are those evaluated by other means, typically by estimation based on knowledge and experience of the evaluator. By formalizing Type B methods, ISO GUM provided for the first time a well-defined procedure for quantifying uncertainty components that arise from systematic errors. Irrespective of whether they are Type A or B, once the individual uncertainty components are evaluated, ISO GUM treats them as equally valid and makes no further distinctions in their use.

In ordinary cases, the uncertainty components are *unsigned* and essentially *uncorrelated* (correlation coefficients *ρ*_{ij} ≈ 0), and the final uncertainty is obtained by adding the components in quadrature (square root of the sum of squares). If the *sign* of a significant component of the bias is known, then the appropriate correction to the measured value must also be worked out. If the uncertainty components are *correlated*, their summation becomes more involved: in the limiting case of a perfect correlation between two components (*ρ*_{ij} = 1), their combined uncertainty corresponds to their simple sum.