Less is more

There are many things we can do to make our research clearer to readers: make our text well organized and accessible, make clear graphs, consider the psychology of our readers, and use as little math as is necessary to explain our point.  Clarity and elegance trumps formalism and detail.

Intimidated by Equations?
Barbara R. Jasny
Although there is general agreement on the value of a strong tie between theory and data, forging links between theoretical and empirical approaches (and practitioners) is not as straightforward as it should be. New evidence of this disconnect comes from the work of Fawcett and Higginson, who examined the use of mathematical equations in 649 papers dealing with ecology and evolution that were published in 1998. They gathered citation data, excluding instances of self-citation. An increase in the number of equations per page of main text corresponded to a lower rate of citations. Overall, each additional equation in the main text of a paper was associated with a 28% decrease in the citation rate. Burying the equations in an appendix had a salutary effect on citation rate. When the citing papers were divided into theoretical and nontheoretical on the basis of their use of the word "model" in the abstract or title, the authors observed that the negative effect was due to the nontheoretical papers not citing papers with equations. There are caveats to the conclusions—examinations over longer periods of time, analysis of the relative content of the papers, and examination of the effect for online rather than print publication are all warranted. Although the authors conclude that better math education for biologists is the best long-term solution, they suggest that more immediate strategies could include the addition of explanatory text between equations.
The full PNAS article is here.

h/t Marshall Burke


  1. I think anything less than fully disclosing the equations used in analysis (either in text or by way of citation) is intellectual dishonesty. In order to generate reproducible results, a reader should be able to extract from a paper (and all relevant citations) a complete process leading from data collection, through analysis, to conclusions. Connecting mathematical formalism and abstract conceptual models is the duty of all scientists, irrespective of discipline and there is a mutual responsibility on the part of author, reviewer, and reader to ensure clear communication of all components. While the mathematical formalism of certain analyses may be abstruse for some, but without it, we simply wave our hands to join questions, hypotheses and conclusions.

  2. I agree that we shouldn't sacrifice completeness and replicability. But many of these descriptions can be pushed to online supplements or heavily edited down to be more concise. If readers are unwilling to invest the time to read a complete mathematical description, there isn't much value in it being complete. I think there is a balance that needs to be struck, and while searching for that balance, authors should be cognizant of their readers' tendencies.