IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v30y2003i3p335-341.html
   My bibliography  Save this article

A note on the Zhang omnibus test for normality based on the Q statistic

Author

Listed:
  • Sueli Mingoti
  • Otaviano Neves

Abstract

A discussion about the estimators proposed by Zhang (1999) for the true standard deviation C of a normal distribution is presented. Those estimators, called by Zhang q 1 and q 2 , are functions of the expected values of the order statistics from a standard normal distribution and they were the basis of the Q statistic used in the derivation of a new test for normality proposed by Zhang. Although the type I error and the power of the test was discussed by Zhang, no study was performed to test the reliability of q 1 and q 2 as estimators of C . In this paper, it is shown that q 1 is a very poor estimator for C especially when C is large. On the other hand, the estimator q 2 has a performance very similar to the well-known sample standard deviation S. When some correlation is introduced among the sample units it can be seen that the estimator q 1 is much more affected than the estimators q 2 and S.

Suggested Citation

  • Sueli Mingoti & Otaviano Neves, 2003. "A note on the Zhang omnibus test for normality based on the Q statistic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 335-341.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:3:p:335-341
    DOI: 10.1080/0266476022000030101
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/0266476022000030101
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/0266476022000030101?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. Paul Zhang, 1999. "Omnibus test of normality using the Q statistic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 519-528.
    2. Nien Fan Zhang, 1998. "Estimating process capability indexes for autocorrelated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(4), pages 559-574.
    3. J. P. Royston, 1982. "An Extension of Shapiro and Wilk's W Test for Normality to Large Samples," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 115-124, June.
    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. Minguez, Ana & Javier Sese, F., 2022. "Why do you want a relationship, anyway? Consent to receive marketing communications and donors’ willingness to engage with nonprofits," Journal of Business Research, Elsevier, vol. 148(C), pages 356-367.
    2. Sueli Mingoti & Julia De Carvalho & Joab De Oliveira Lima, 2008. "On the estimation of serial correlation in Markov-dependent production processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 763-771.
    3. Murigi, Michael & Muchai, Dianah Ngui & Ogada, Maurice Juma, 2024. "Drivers of Participation in Smallholders Banana Contract Farming in Kenya," African Journal of Economic Review, African Journal of Economic Review, vol. 12(2), June.
    4. Lawrence L. Giventer, 1992. "Kolmogorov-Smirnov One and Two Variable Tests," Stata Technical Bulletin, StataCorp LP, vol. 1(2).
    5. Lauren Bin Dong & David E. A. Giles, 2004. "An Empirical Likelihood Ratio Test for Normality," Econometrics Working Papers 0401, Department of Economics, University of Victoria.
    6. Michele Scagliarini, 2010. "Inference on Cpk for autocorrelated data in the presence of random measurement errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(1), pages 147-158.
    7. Richard Goldstein, 1992. "Test for General Specification Error in Linear Regression," Stata Technical Bulletin, StataCorp LP, vol. 1(2).
    8. Tomasz Górecki & Lajos Horváth & Piotr Kokoszka, 2020. "Tests of Normality of Functional Data," International Statistical Review, International Statistical Institute, vol. 88(3), pages 677-697, December.
    9. Steven Dubnoff, 1992. "Questions and Answers about Stat/Transfer," Stata Technical Bulletin, StataCorp LP, vol. 1(2).
    10. Kyei, Collins Baffour & Cantah, William Godfred & Junior Owusu, Peterson, 2023. "Effect of commodity prices on financial soundness; insight from adaptive market hypothesis in the Ghanaian setting," Resources Policy, Elsevier, vol. 86(PA).
    11. Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "An Exhaustive Power Comparison of Normality Tests," Mathematics, MDPI, vol. 9(7), pages 1-20, April.
    12. Manuelita Ureta, 1992. "Data Calculator," Stata Technical Bulletin, StataCorp LP, vol. 1(2).
    13. Phil Lignier & Diane Jarvis & Daniel Grainger & Taha Chaiechi, 2024. "Spatial Heterogeneity and Subjective Wellbeing: Exploring the Role of Social Capital in Metropolitan Areas Using Multilevel Modelling," Journal of Happiness Studies, Springer, vol. 25(5), pages 1-23, June.
    14. Lawrence C. Hamilton, 1992. "How Robust is Robust Regression?," Stata Technical Bulletin, StataCorp LP, vol. 1(2).
    15. Amir Abolhassani & Gale Boyd & Majid Jaridi & Bhaskaran Gopalakrishnan & James Harner, 2023. "“Is Energy That Different from Labor?” Similarity in Determinants of Intensity for Auto Assembly Plants," Energies, MDPI, vol. 16(4), pages 1-35, February.
    16. Marta Benková & Dagmar Bednárová & Gabriela Bogdanovská, 2024. "Process Capability Evaluation Using Capability Indices as a Part of Statistical Process Control," Mathematics, MDPI, vol. 12(11), pages 1-29, May.
    17. Francesco Danuso, 1992. "Triangle Graphic for Soil Texture," Stata Technical Bulletin, StataCorp LP, vol. 1(2).
    18. Ted Anagnoson, 1992. "Why is the Cubic Spline So-Called?," Stata Technical Bulletin, StataCorp LP, vol. 1(2).
    19. Richard E. Deleon & J. Theodore Anagnoson, 1992. "Importing Stata's Graphs Into MS-Word or Wordperfect," Stata Technical Bulletin, StataCorp LP, vol. 1(2).
    20. Guglielmo Maria Caporale & Luis Alberiko Gil-Alana & Pedro Jose Piqueras Martinez, 2024. "Dynamic Factor Models and Fractional Integration—With an Application to US Real Economic Activity," Econometrics, MDPI, vol. 12(4), pages 1-14, December.

    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:taf:japsta:v:30:y:2003:i:3:p:335-341. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.