IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v223y2024icp588-600.html

Testing for proportions when data are classified into a large number of groups

Author

Listed:
  • Alba-Fernández, M.V.
  • Jiménez-Gamero, M.D.
  • Jiménez-Jiménez, F.

Abstract

When dealing with categorical data, a common concern is to check if the observed relative frequencies agree with a certain fixed vector of ideal proportions. Suppose that the population is divided into subpopulations or groups. In such a case, the ideal proportions could vary among groups and one may be interested in simultaneously testing if the observed proportions agree with those ideal proportions in all groups. A novel procedure is proposed for carrying out such a testing problem. The test statistic is shown to be asymptotically normal, avoiding the use of complicated resampling methods to get p-values. The asymptotic behavior of the test under alternatives is also studied. Here, by asymptotic, we mean when the number of groups increases; the sample sizes of the data from each group can either stay bounded or grow with the number of groups. The finite sample performance of the new test is empirically evaluated through an extensive simulation study. The usefulness of the proposal is illustrated with some data sets.

Suggested Citation

  • Alba-Fernández, M.V. & Jiménez-Gamero, M.D. & Jiménez-Jiménez, F., 2024. "Testing for proportions when data are classified into a large number of groups," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 588-600.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:588-600
    DOI: 10.1016/j.matcom.2024.04.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424001459
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.04.019?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Frédéric Ouimet, 2021. "General Formulas for the Central and Non-Central Moments of the Multinomial Distribution," Stats, MDPI, vol. 4(1), pages 1-10, January.
    2. Solomon Harrar & Arne Bathke, 2012. "A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 135-165, February.
    3. Thomas Dohmen & Armin Falk & David Huffman & Uwe Sunde & Jürgen Schupp & Gert G. Wagner, 2011. "Individual Risk Attitudes: Measurement, Determinants, And Behavioral Consequences," Journal of the European Economic Association, European Economic Association, vol. 9(3), pages 522-550, June.
    4. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    5. Park, Junyong & Park, DoHwan, 2012. "Testing the equality of a large number of normal population means," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1131-1149.
    6. Junyong Park, 2019. "Testing homogeneity of proportions from sparse binomial data with a large number of groups," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 505-535, June.
    7. M. D. Jiménez-Gamero & M. Cousido-Rocha & M. V. Alba-Fernández & F. Jiménez-Jiménez, 2022. "Testing the equality of a large number of populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 1-21, March.
    8. Jiménez-Gamero, M. Dolores & Franco-Pereira, Alba M., 2021. "Testing the equality of a large number of means of functional data," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    9. D. Zhan & J. D. Hart, 2014. "Testing equality of a large number of densities," Biometrika, Biometrika Trust, vol. 101(2), pages 449-464.
    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. M. D. Jiménez-Gamero, 2024. "Testing normality of a large number of populations," Statistical Papers, Springer, vol. 65(1), pages 435-465, February.
    2. Jiménez-Gamero, M.D. & Sillero-Denamiel, M.R., 2025. "The k-sample problem using Gini covariance for large k," Journal of Multivariate Analysis, Elsevier, vol. 210(C).
    3. Jiménez-Gamero, M. Dolores & Franco-Pereira, Alba M., 2021. "Testing the equality of a large number of means of functional data," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    4. M. Dolores Jiménez-Gamero & Marina Valdora & Daniela Rodríguez, 2025. "Testing homoscedasticity of a large number of populations," Statistical Papers, Springer, vol. 66(2), pages 1-32, February.
    5. Herrmann, Tabea & Hübler, Olaf & Menkhoff, Lukas & Schmidt, Ulrich, 2016. "Allais for the poor," Kiel Working Papers 2036, Kiel Institute for the World Economy.
    6. Wojciech Hardy & Michal Krawczyk & Joanna Tyrowicz, 2015. ""Thou shalt not leech" Are digital pirates conditional cooperators?," Working Papers 2015-26, Faculty of Economic Sciences, University of Warsaw.
    7. Goldzahl, Léontine, 2017. "Contributions of risk preference, time orientation and perceptions to breast cancer screening regularity," Social Science & Medicine, Elsevier, vol. 185(C), pages 147-157.
    8. Kirchler, Michael & Lindner, Florian & Weitzel, Utz, 2020. "Delegated investment decisions and rankings," Journal of Banking & Finance, Elsevier, vol. 120(C).
    9. Ranganathan, Kavitha & Lejarraga, Tomás, 2021. "Elicitation of risk preferences through satisficing," Journal of Behavioral and Experimental Finance, Elsevier, vol. 32(C).
    10. Fossen, Frank M. & Glocker, Daniela, 2017. "Stated and revealed heterogeneous risk preferences in educational choice," European Economic Review, Elsevier, vol. 97(C), pages 1-25.
    11. Goytom Abraha Kahsay & Daniel Osberghaus, 2018. "Storm Damage and Risk Preferences: Panel Evidence from Germany," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 71(1), pages 301-318, September.
    12. Belzil, Christian & Sidibé, Modibo, 2016. "Internal and External Validity of Experimental Risk and Time Preferences," IZA Discussion Papers 10348, IZA Network @ LISER.
    13. Jean Spinks & Son Nghiem & Joshua Byrnes, 2021. "Risky business, healthy lives: how risk perception, risk preferences and information influence consumer’s risky health choices," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 22(5), pages 811-831, July.
    14. Zubanov, Nick & Cadsby, Bram & Song, Fei, 2017. "The," IZA Discussion Papers 10542, IZA Network @ LISER.
    15. Alserda, Gosse A.G. & Dellaert, Benedict G.C. & Swinkels, Laurens & van der Lecq, Fieke S.G., 2019. "Individual pension risk preference elicitation and collective asset allocation with heterogeneity," Journal of Banking & Finance, Elsevier, vol. 101(C), pages 206-225.
    16. Volland, Benjamin, 2017. "The role of risk and trust attitudes in explaining residential energy demand: Evidence from the United Kingdom," Ecological Economics, Elsevier, vol. 132(C), pages 14-30.
    17. Dohmen, Thomas & Non, Arjan & Stolp, Tom, 2021. "Reference points and the tradeoff between risk and incentives," Journal of Economic Behavior & Organization, Elsevier, vol. 192(C), pages 813-831.
    18. Tianzhuo Liu & Huifang Jiao, 2018. "Insights into the Effects of Cognitive Factors and Risk Attitudes on Fire Risk Mitigation Behavior," Computational Economics, Springer;Society for Computational Economics, vol. 52(4), pages 1213-1232, December.
    19. Riedel, Nadine & Schildberg-Hörisch, Hannah, 2013. "Asymmetric obligations," Journal of Economic Psychology, Elsevier, vol. 35(C), pages 67-80.
    20. Marc A. Ragin & Benjamin L. Collier & Johannes G. Jaspersen, 2021. "The effect of information disclosure on demand for high‐load insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(1), pages 161-193, March.

    More about this item

    Keywords

    ;
    ;
    ;

    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:eee:matcom:v:223:y:2024:i:c:p:588-600. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.