IDEAS home Printed from https://ideas.repec.org/a/ibn/masjnl/v9y2015i13p1.html
   My bibliography  Save this article

The Modification and Evaluation of the Alexander-Govern Test in Terms of Power

Author

Listed:
  • Tobi Kingsley Ochuko
  • Suhaida Abdullah
  • Zakiyah Binti Zain
  • Sharipah Soaad Syed Yahaya

Abstract

This study centres on the comparison of independent group tests in terms of power, by using parametric method, such as the Alexander-Govern test. The Alexander-Govern (AG) test uses mean as its central tendency measure. It is a better alternative compared to the Welch test, the James test and the ANOVA, because it produces high power and gives good control of Type I error rates for a normal data under variance heterogeneity. But this test is not robust for a non-normal data. When trimmed mean was applied on the test as its central tendency measure under non-normality, the test was only robust for two group condition, but as the number of groups increased more than two groups, the test was no more robust. As a result, a highly robust estimator known as the MOM estimator was applied on the test, as its central tendency measure. This test is not affected by the number of groups, but could not control Type I error rates under skewed heavy tailed distribution. In this study, the Winsorized MOM estimator was applied in the AG test, as its central tendency measure. A simulation of 5,000 data sets were generated and analysed on the test, using the SAS package. The result of the analysis, shows that with the pairing of unbalanced sample size of (15-15-20-30) with equal variance of (1-1-1-1) and the pairing of unbalanced sample size of (15-15-20-30) with unequal variance of (1-1-1-36) with effect size index (f = 0.8), the AGWMOM test only produced a high power value of 0.9562 and 0.8336 compared to the AG test, the AGMOM test and the ANOVA respectively and the test is considered to be sufficient.

Suggested Citation

  • Tobi Kingsley Ochuko & Suhaida Abdullah & Zakiyah Binti Zain & Sharipah Soaad Syed Yahaya, 2015. "The Modification and Evaluation of the Alexander-Govern Test in Terms of Power," Modern Applied Science, Canadian Center of Science and Education, vol. 9(13), pages 1-1, December.
    • Handle: RePEc:ibn:masjnl:v:9:y:2015:i:13:p:1
    as

    Download full text from publisher

    File URL: https://ccsenet.org/journal/index.php/mas/article/download/54030/28825
    Download Restriction: no
    File URL: https://ccsenet.org/journal/index.php/mas/article/view/54030
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Krishnamoorthy, K. & Lu, Fei & Mathew, Thomas, 2007. "A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5731-5742, August.
    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. Julia Volaufova, 2009. "Heteroscedastic ANOVA: old p values, new views," Statistical Papers, Springer, vol. 50(4), pages 943-962, August.
    2. Lili Yue & Jianhong Shi & Jingxuan Luo & Jinguan Lin, 2023. "A Parametric Bootstrap Approach for a One-Way Error Component Regression Model with Measurement Errors," Mathematics, MDPI, vol. 11(19), pages 1-13, October.
    3. Li, Xinmin & Wang, Juan & Liang, Hua, 2011. "Comparison of several means: A fiducial based approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1993-2002, May.
    4. Tobi Kingsley Ochuko & Suhaida Abdullah & Zakiyah Binti Zain & Sharipah Syed Soaad Yahaya, 2015. "Modifying and Evaluating the Alexander-Govern Test Using Real Data," Modern Applied Science, Canadian Center of Science and Education, vol. 9(12), pages 1-1, November.
    5. Li, Xinmin, 2009. "A generalized p-value approach for comparing the means of several log-normal populations," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1404-1408, June.
    6. H. V. Kulkarni & S. M. Patil, 2021. "Uniformly implementable small sample integrated likelihood ratio test for one-way and two-way ANOVA under heteroscedasticity and normality," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 273-305, June.
    7. A. Malekzadeh & M. Kharrati-Kopaei & S. Sadooghi-Alvandi, 2014. "Comparing exponential location parameters with several controls under heteroscedasticity," Computational Statistics, Springer, vol. 29(5), pages 1083-1094, October.
    8. Xu, Li-Wen & Yang, Fang-Qin & Abula, Aji’erguli & Qin, Shuang, 2013. "A parametric bootstrap approach for two-way ANOVA in presence of possible interactions with unequal variances," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 172-180.
    9. Tobi Kingsley Ochuko & Suhaida Abdullah & Zakiyah Binti Zain & Sharipah Soaad Syed Yahaya, 2015. "Winsorized Modified One Step M-estimator in Alexander-Govern Test," Modern Applied Science, Canadian Center of Science and Education, vol. 9(11), pages 1-51, October.
    10. Weizhong Tian & Yaoting Yang & Tingting Tong, 2022. "Confidence Intervals Based on the Difference of Medians for Independent Log-Normal Distributions," Mathematics, MDPI, vol. 10(16), pages 1-14, August.
    11. Malekzadeh, Ahad & Esmaeli-Ayan, Asghar, 2021. "An exact method for testing equality of several groups in panel data models," Statistics & Probability Letters, Elsevier, vol. 177(C).
    12. Jin-Ting Zhang & Xuefeng Liu, 2013. "A modified Bartlett test for heteroscedastic one-way MANOVA," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 135-152, January.
    13. Marianthi Hatziioannou & Efkarpia Kougiagka & Ioannis Karapanagiotidis & Dimitris Klaoudatos, 2022. "Proximate Composition, Predictive Analysis and Allometric Relationships, of the Edible Water Frog ( Pelophylax epeiroticus ) in Lake Pamvotida (Northwest Greece)," Sustainability, MDPI, vol. 14(6), pages 1-15, March.
    14. 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.
    15. Ali Jafari & Mohammad Kazemi, 2013. "A parametric bootstrap approach for the equality of coefficients of variation," Computational Statistics, Springer, vol. 28(6), pages 2621-2639, December.
    16. Sadooghi-Alvandi, S.M. & Malekzadeh, A., 2014. "Simultaneous confidence intervals for ratios of means of several lognormal distributions: A parametric bootstrap approach," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 133-140.
    17. Roth, Lucas & Lowitzsch, Jens & Yildiz, Özgür, 2023. "Which (co-)ownership types in renewables are associated with the willingness to adopt energy-efficient technologies and energy-conscious behaviour? Data from German households," Energy Policy, Elsevier, vol. 180(C).
    18. Hod Orkibi & Efrat Dafner, 2016. "Exposure to Risk Factors and the Subjective Wellbeing of Adolescents: the Mediating Role of Time Perspective," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 9(3), pages 663-682, September.
    19. repec:sip:wpaper:12-026 is not listed on IDEAS
    20. Xiong, Shifeng, 2011. "An asymptotics look at the generalized inference," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 336-348, February.
    21. Zhang, Guoyi & Christensen, Ronald & Pesko, John, 2021. "Parametric boostrap and objective Bayesian testing for heteroscedastic one-way ANOVA," Statistics & Probability Letters, Elsevier, vol. 174(C).

    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

    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:ibn:masjnl:v:9:y:2015:i:13:p: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: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    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.