IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i5p1131-1149.html
   My bibliography  Save this article

Testing the equality of a large number of normal population means

Author

Listed:
  • Park, Junyong
  • Park, DoHwan

Abstract

It is challenging to consider the problem of testing the equality of normal population means when the number of populations is large compared to the sample sizes. In ANOVA with the assumption of homogeneous variance, the F-test is known as an exact test. When variances are heterogeneous, due to the complication, there are various tests with only approximate forms–either approximate chi-square or approximate F-test. Two types of tests are proposed with their asymptotic normality as the number of population increases. p-values from those tests are adjusted based on higher order asymptotics such as Edgeworth expansion so that the proposed tests can be considered even for moderate values of k. Numerical studies including simulations and real data examples are presented with comparison to existing tests.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:5:p:1131-1149
    DOI: 10.1016/j.csda.2011.08.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003161
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.08.017?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. Joachim Hartung & Dogan Argaç & Kepher Makambi, 2002. "Small sample properties of tests on homogeneity in one—way Anova and Meta—analysis," Statistical Papers, Springer, vol. 43(2), pages 197-235, April.
    2. Tian, Lili, 2006. "Testing equality of inverse Gaussian means under heterogeneity, based on generalized test variable," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1156-1162, November.
    3. Saha, Krishna K. & Bilisoly, Roger, 2009. "Testing the homogeneity of the means of several groups of count data in the presence of unequal dispersions," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3305-3313, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).

    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. Mario Hasler, 2016. "Heteroscedasticity: multiple degrees of freedom vs. sandwich estimation," Statistical Papers, Springer, vol. 57(1), pages 55-68, March.
    2. Hu, Wei & Yang, Zhaojun & Chen, Chuanhai & Wu, Yue & Xie, Qunya, 2021. "A Weibull-based recurrent regression model for repairable systems considering double effects of operation and maintenance: A case study of machine tools," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    3. Chiu, Sung Nok & Wang, Ling, 2009. "Homogeneity tests for several Poisson populations," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4266-4278, October.
    4. Sadooghi-Alvandi, Soltan Mohammad & Malekzadeh, Ahad, 2013. "A note on testing homogeneity of the scale parameters of several inverse Gaussian distributions," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1844-1848.
    5. Chang, Ming & You, Xuqun & Wen, Muqing, 2012. "Testing the homogeneity of inverse Gaussian scale-like parameters," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1755-1760.
    6. Shi, Jian-Hong & Lv, Jiang-Long, 2012. "A new generalized p-value for testing equality of inverse Gaussian means under heterogeneity," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 96-102.
    7. Cuizhen Niu & Xu Guo & Wangli Xu & Lixing Zhu, 2014. "Testing equality of shape parameters in several inverse Gaussian populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 795-809, August.
    8. Liu, Xuhua & Xu, Xingzhong, 2010. "A new generalized p-value approach for testing the homogeneity of variances," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1486-1491, October.
    9. Li, Xinmin & Tian, Lili & Wang, Juan & Muindi, Josephia R., 2012. "Comparison of quantiles for several normal populations," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2129-2138.
    10. Mohammad Reza Kazemi & Ali Akbar Jafari, 2019. "Inference about the shape parameters of several inverse Gaussian distributions: testing equality and confidence interval for a common value," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 529-545, July.
    11. Ye, Ren-Dao & Ma, Tie-Feng & Wang, Song-Gui, 2010. "Inferences on the common mean of several inverse Gaussian populations," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 906-915, April.
    12. Samadrita Bera & Nabakumar Jana, 2022. "On estimating common mean of several inverse Gaussian distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 115-139, January.
    13. Xu Guo & Hecheng Wu & Gaorong Li & Qiuyue Li, 2017. "Inference for the common mean of several Birnbaum–Saunders populations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 941-954, April.
    14. Liu, Xuhua & Li, Na & Hu, Yuqin, 2015. "Combining inferences on the common mean of several inverse Gaussian distributions based on confidence distribution," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 136-142.
    15. Zhongxue Chen & Hon Ng & Saralees Nadarajah, 2014. "A note on Cochran test for homogeneity in one-way ANOVA and meta-analysis," Statistical Papers, Springer, vol. 55(2), pages 301-310, May.

    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:csdana:v:56:y:2012:i:5:p:1131-1149. 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.elsevier.com/locate/csda .

    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.