Title: nth-order effect
Long Title: IUPAC Gold Book - <em>n</em><sup>th</sup>-order effect
DOI: 10.1351/goldbook.10078
Status: current

Definition
Effect of a factor where the term is a factor raised to the power \(n\).

Example
The yield of a synthesis is modelled in terms of the temperature \(T\) and concentration of a reactant \(c\): \[\hat Y = {\hat \beta}_{0} + {\hat \beta}_{1}T + {\hat \beta}_{2}c + {\hat \beta}_{11}T^{2} + {\hat \beta}_{22}c^{2} + {\hat \beta}_{12}Tc\] The coefficients \({\hat \beta}_{11}\) and \({\hat \beta}_{22}\) are the second-order effects of \(T\) and \(c\) respectively.

Related Terms
- Effect of a factor: https://goldbook.iupac.org/terms/view/10068
- interaction effect: https://goldbook.iupac.org/terms/view/10075
- main effect: https://goldbook.iupac.org/terms/view/10076

Source
- PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 416 (https://doi.org/10.1515/pac-2015-0605)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/10078/html
- json: https://goldbook.iupac.org/terms/view/10078/json
- xml: https://goldbook.iupac.org/terms/view/10078/xml

Citation: Citation: '<em>n</em><sup>th</sup>-order effect' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.10078
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Accessed: 2026-05-09T21:58:59+00:00