IDEAS home Printed from https://ideas.repec.org/a/bpj/sagmbi/v13y2014i6p12n1.html
   My bibliography  Save this article

When is Menzerath-Altmann law mathematically trivial? A new approach

Author

Listed:
  • Ferrer-i-Cancho Ramon
  • Baixeries Jaume

    (Complexity and Quantitative Linguistics Lab, LARCA Research Group, Departament de Ciències de la Computació, Universitat Politècnica de Catalunya, Campus Nord, Edifici Omega, Jordi Girona Salgado 1-3, 08034 Barcelona (Catalonia), Spain)

  • Hernández-Fernández Antoni
  • Dębowski Łukasz

    (Institute of Computer Science, Polish Academy of Sciences, ul. Jana Kazimierza 5, 01-248 Warszawa, Poland)

  • Mačutek Ján

    (Department of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovakia)

Abstract

Menzerath’s law, the tendency of Z (the mean size of the parts) to decrease as X (the number of parts) increases, is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z=Y/X, which would imply that Z scales with X as Z∼1/X. That scaling is a very particular case of Menzerath-Altmann law that has been rejected by means of a correlation test between X and Y in genomes, being X the number of chromosomes of a species, Y its genome size in bases and Z the mean chromosome size. Here we review the statistical foundations of that test and consider three non-parametric tests based upon different correlation metrics and one parametric test to evaluate if Z∼1/X in genomes. The most powerful test is a new non-parametric one based upon the correlation ratio, which is able to reject Z∼1/X in nine out of 11 taxonomic groups and detect a borderline group. Rather than a fact, Z∼1/X is a baseline that real genomes do not meet. The view of Menzerath-Altmann law as inevitable is seriously flawed.

Suggested Citation

  • Ferrer-i-Cancho Ramon & Baixeries Jaume & Hernández-Fernández Antoni & Dębowski Łukasz & Mačutek Ján, 2014. "When is Menzerath-Altmann law mathematically trivial? A new approach," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(6), pages 1-12, December.
    • Handle: RePEc:bpj:sagmbi:v:13:y:2014:i:6:p:12:n:1
    DOI: 10.1515/sagmb-2013-0034
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/sagmb-2013-0034
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/sagmb-2013-0034?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    2. Michael Dunn & Simon J. Greenhill & Stephen C. Levinson & Russell D. Gray, 2011. "Evolved structure of language shows lineage-specific trends in word-order universals," Nature, Nature, vol. 473(7345), pages 79-82, May.
    3. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Averi Chakrabarti & Karen A Grépin & Stéphane Helleringer, 2019. "The impact of supplementary immunization activities on routine vaccination coverage: An instrumental variable analysis in five low-income countries," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-11, February.
    2. Harold Alderman & John Hoddinott & Bill Kinsey, 2006. "Long term consequences of early childhood malnutrition," Oxford Economic Papers, Oxford University Press, vol. 58(3), pages 450-474, July.
    3. Huh, Yesol & Kim, You Suk, 2023. "Cheapest-to-deliver pricing, optimal MBS securitization, and welfare implications," Journal of Financial Economics, Elsevier, vol. 150(1), pages 68-93.
    4. Fan Li & Prashant Loyalka & Hongmei Yi & Yaojiang Shi & Natalie Johnson & Scott Rozelle, 2016. "Ability Tracking and Social Capital in China’s Rural Secondary School System," LICOS Discussion Papers 37916, LICOS - Centre for Institutions and Economic Performance, KU Leuven.
    5. Ji Yan & Sally Brocksen, 2013. "Adolescent risk perception, substance use, and educational attainment," Journal of Risk Research, Taylor & Francis Journals, vol. 16(8), pages 1037-1055, September.
    6. Sènakpon Fidèle A. Dedehouanou & Luca Tiberti & Hilaire G. Houeninvo & Djohodo Inès Monwanou, 2019. "Working while studying: Employment premium or penalty for youth in Benin?," Working Papers PMMA 2019-03, PEP-PMMA.
    7. Mengyuan Zhou, 2022. "Does the Source of Inheritance Matter in Bequest Attitudes? Evidence from Japan," Journal of Family and Economic Issues, Springer, vol. 43(4), pages 867-887, December.
    8. Sandra Müllbacher & Wolfgang Nagl, 2017. "Labour supply in Austria: an assessment of recent developments and the effects of a tax reform," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 44(3), pages 465-486, August.
    9. Campbell, Randall C. & Nagel, Gregory L., 2016. "Private information and limitations of Heckman's estimator in banking and corporate finance research," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 186-195.
    10. Giuliani, Elisa & Martinelli, Arianna & Rabellotti, Roberta, 2016. "Is Co-Invention Expediting Technological Catch Up? A Study of Collaboration between Emerging Country Firms and EU Inventors," World Development, Elsevier, vol. 77(C), pages 192-205.
    11. Maurice Mutisya & Moses W. Ngware & Caroline W. Kabiru & Ngianga-bakwin Kandala, 2016. "The effect of education on household food security in two informal urban settlements in Kenya: a longitudinal analysis," Food Security: The Science, Sociology and Economics of Food Production and Access to Food, Springer;The International Society for Plant Pathology, vol. 8(4), pages 743-756, August.
    12. Ilona Babenko & Benjamin Bennett & John M Bizjak & Jeffrey L Coles & Jason J Sandvik, 2023. "Clawback Provisions and Firm Risk," The Review of Corporate Finance Studies, Society for Financial Studies, vol. 12(2), pages 191-239.
    13. Şahan, Duygu & Tuna, Okan, 2018. "Environmental innovation of transportation sector in OECD countries," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Kersten, Wolfgang & Blecker, Thorsten & Ringle, Christian M. (ed.), The Road to a Digitalized Supply Chain Management: Smart and Digital Solutions for Supply Chain Management. Proceedings of the Hamburg International C, volume 25, pages 157-170, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    14. Mehzabin Tuli, Farzana & Mitra, Suman & Crews, Mariah B., 2021. "Factors influencing the usage of shared E-scooters in Chicago," Transportation Research Part A: Policy and Practice, Elsevier, vol. 154(C), pages 164-185.
    15. Ruomeng Cui & Dennis J. Zhang & Achal Bassamboo, 2019. "Learning from Inventory Availability Information: Evidence from Field Experiments on Amazon," Management Science, INFORMS, vol. 65(3), pages 1216-1235, March.
    16. Peppel-Srebrny, Jemima, 2021. "Not all government budget deficits are created equal: Evidence from advanced economies' sovereign bond markets," Journal of International Money and Finance, Elsevier, vol. 118(C).
    17. Blackburn, McKinley L. & Vermilyea, Todd, 2012. "The prevalence and impact of misstated incomes on mortgage loan applications," Journal of Housing Economics, Elsevier, vol. 21(2), pages 151-168.
    18. Shvartsman, Elena & Beckmann, Michael, 2015. "Stressed by your job: What is the role of personnel policy?," Working papers 2015/15, Faculty of Business and Economics - University of Basel.
    19. Luiz Paulo Fávero & Joseph F. Hair & Rafael de Freitas Souza & Matheus Albergaria & Talles V. Brugni, 2021. "Zero-Inflated Generalized Linear Mixed Models: A Better Way to Understand Data Relationships," Mathematics, MDPI, vol. 9(10), pages 1-28, May.
    20. Tiantian Gu & Anand Venkateswaran, 2018. "Firm-supplier relations and managerial compensation," Review of Quantitative Finance and Accounting, Springer, vol. 51(3), pages 621-649, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:sagmbi:v:13:y:2014:i:6:p:12:n:1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.