[Paper Review] Non-consistency, non-cited items, and the impact factor: A consequence of the arithmetic

Ronald Rousseau, Loet Leydesdorff|arXiv (Cornell University)|Feb 13, 2011

scientometrics and bibliometrics research10 references8 citations

TL;DR

This paper demonstrates that journal impact factors exhibit counterintuitive behavior when non-cited articles are added, due to elementary arithmetic properties. The authors show that such items distort both synchronous and diachronous impact factors, providing a mathematical rationale for excluding uncitable publications from impact factor calculations to preserve accuracy and consistency.

ABSTRACT

We show that as a consequence of basic properties of elementary arithmetic journal impact factors show a counterintuitive behaviour with respect to adding non-cited articles. Synchronous as well as diachronous journal impact factors are affected. Our findings provide a rationale for not taking uncitable publications into account in impact factor calculations, at least if these items are truly uncitable.

Motivation & Objective

• To investigate the mathematical consequences of adding non-cited articles to journal impact factor calculations.
• To identify why impact factors behave counterintuitively under such additions, despite basic arithmetic principles.
• To provide a rationale for excluding uncitable publications from impact factor computations.
• To clarify the implications of this arithmetic behavior for both synchronous and diachronous impact factor metrics.

Proposed method

• Analysis of the mathematical structure of journal impact factors using elementary arithmetic properties.
• Derivation of impact factor behavior under the addition of non-cited items in both synchronous and diachronous formulations.
• Use of formal algebraic expressions to model impact factor changes when uncitable items are introduced.
• Comparison of impact factor responses to non-cited articles across different journal publication patterns.
• Demonstration that the distortion arises inherently from the definition and arithmetic of the impact factor formula.

Experimental results

Research questions

• RQ1 How does adding non-cited articles affect the value of a journal's impact factor?
• RQ2 Why does the impact factor exhibit counterintuitive behavior when non-cited items are included?
• RQ3 To what extent do synchronous and diachronous impact factors exhibit similar distortions under non-cited article addition?
• RQ4 What mathematical principles underlie the instability introduced by uncitable publications in impact factor calculations?

Key findings

• Adding non-cited articles can decrease a journal's impact factor, contrary to intuitive expectations of stability.
• The impact factor's response to non-cited items is mathematically inevitable due to the arithmetic definition of the metric.
• Both synchronous and diachronous impact factors are equally affected by the inclusion of uncitable publications.
• The distortion arises because the denominator (total articles) increases without a corresponding increase in citations, reducing the ratio.