IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v26y2017i3d10.1007_s11749-017-0530-x.html
   My bibliography  Save this article

New two-sample tests for skewed populations and their connection to theoretical power of Bootstrap-t test

Author

Listed:
  • Haiyan Wang

    (Kansas State University)

  • Bo Tong

    (AbbVie Inc.)

  • Huaiyu Zhang

    (Kansas State University)

  • Xukun Li

    (Kansas State University)

Abstract

Various tests are available to compare the means of two populations. Tests for skewed data, however, are not well studied even though they are often needed in pharmaceutical study and agricultural economics. In particular, there is no available result to give power and sample size calculation for a two-sample Bootstrap-t test in skewed populations. In this paper, we propose easy-to-compute new tests and study their theoretical properties. The proposed work starts with derivation of a second-order Edgeworth expansion for the pooled two-sample t-statistic. Then new test rejection regions are formed based on Cornish–Fisher expansion of quantiles. The new tests account for first-order and second-order population skewnesses that were ignored in two-sample t test. We report the theoretical type I error accuracy and power of the newly proposed tests and the large sample t test. We also provide the detailed conditions under which the proposed tests give better power than the two-sample large sample test. Our new tests, $$\hbox {TCF}_1$$ TCF 1 and TCF, are asymptotically equivalent to Bootstrap-t test up to $$O(N^{-1})$$ O ( N - 1 ) and $$O(N^{-3/2})$$ O ( N - 3 / 2 ) , respectively. Compared with commonly used two-sample parametric and nonparametric tests, the new tests are computationally efficient, give better power for skewed data with moderate sample size, and provide sample size calculation to achieve desired power at a given significance level. Empirical studies confirmed our theoretical results.

Suggested Citation

  • Haiyan Wang & Bo Tong & Huaiyu Zhang & Xukun Li, 2017. "New two-sample tests for skewed populations and their connection to theoretical power of Bootstrap-t test," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 661-683, September.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0530-x
    DOI: 10.1007/s11749-017-0530-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-017-0530-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-017-0530-x?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. Phillip Dinh & Xiao-Hua Zhou, 2006. "Nonparametric Statistical Methods for Cost-Effectiveness Analyses," Biometrics, The International Biometric Society, vol. 62(2), pages 576-588, June.
    2. An, Lihua & Ahmed, S. Ejaz, 2008. "Improving the performance of kurtosis estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2669-2681, January.
    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. Caterina Conigliani & Andrea Tancredi, 2009. "A Bayesian model averaging approach for cost‐effectiveness analyses," Health Economics, John Wiley & Sons, Ltd., vol. 18(7), pages 807-821, July.
    2. N. O. A. S. Jourdain & D. J. Cole & M. S. Ridout & J. Marcus Rowcliffe, 2020. "Statistical Development of Animal Density Estimation Using Random Encounter Modelling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(2), pages 148-167, June.
    3. Burch, Brent D., 2011. "Assessing the performance of normal-based and REML-based confidence intervals for the intraclass correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1018-1028, February.
    4. Caterina Conigliani, 2008. "A bayesian model averaging approach with non-informative priors for cost-effectiveness analyses in health economics," Departmental Working Papers of Economics - University 'Roma Tre' 0094, Department of Economics - University Roma Tre.
    5. Zou, Guang Yong & Taleban, Julia & Huo, Cindy Y., 2009. "Confidence interval estimation for lognormal data with application to health economics," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3755-3764, September.
    6. Brent D. Burch, 2017. "Distribution-dependent and distribution-free confidence intervals for the variance," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 629-648, November.
    7. Peter H. Westfall, 2014. "Kurtosis as Peakedness, 1905-2014. R.I.P," The American Statistician, Taylor & Francis Journals, vol. 68(3), pages 191-195, April.

    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:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0530-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.