IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v5y2017i3p39-d106203.html
   My bibliography  Save this article

Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation

Author

Listed:
  • Warisa Thangjai

    (Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology NorthBangkok, Bangkok 10800, Thailand)

  • Suparat Niwitpong

    (Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology NorthBangkok, Bangkok 10800, Thailand)

  • Sa-Aat Niwitpong

    (Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology NorthBangkok, Bangkok 10800, Thailand)

Abstract

This paper proposes confidence intervals for a single mean and difference of two means of normal distributions with unknown coefficients of variation (CVs). The generalized confidence interval (GCI) approach and large sample (LS) approach were proposed to construct confidence intervals for the single normal mean with unknown CV. These confidence intervals were compared with existing confidence interval for the single normal mean based on the Student’s t-distribution (small sample size case) and the z-distribution (large sample size case). Furthermore, the confidence intervals for the difference between two normal means with unknown CVs were constructed based on the GCI approach, the method of variance estimates recovery (MOVER) approach and the LS approach and then compared with the Welch–Satterthwaite (WS) approach. The coverage probability and average length of the proposed confidence intervals were evaluated via Monte Carlo simulation. The results indicated that the GCIs for the single normal mean and the difference of two normal means with unknown CVs are better than the other confidence intervals. Finally, three datasets are given to illustrate the proposed confidence intervals.

Suggested Citation

  • Warisa Thangjai & Suparat Niwitpong & Sa-Aat Niwitpong, 2017. "Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation," Mathematics, MDPI, vol. 5(3), pages 1-23, July.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:3:p:39-:d:106203
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/5/3/39/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/5/3/39/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jarvis, M.J. & Tunstall-Pedoe, H. & Feyerabend, C. & Vesey, C. & Saloojee, Y., 1987. "Comparison of tests used to distinguish smokers from nonsmokers," American Journal of Public Health, American Public Health Association, vol. 77(11), pages 1435-1438.
    2. V. Srivastava, 1980. "A note on the estimation of mean in normal population," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 27(1), pages 99-102, December.
    3. Ahmed N Albatineh & B.M. Golam Kibria & Meredith L Wilcox & Bashar Zogheib, 2014. "Confidence interval estimation for the population coefficient of variation using ranked set sampling: a simulation study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 733-751, April.
    4. Kavitha Bhat & K. Aruna Rao, 2007. "On Tests for a Normal Mean with Known Coefficient of Variation," International Statistical Review, International Statistical Institute, vol. 75(2), pages 170-182, August.
    5. Srivastava, V. K. & Singh, R. S., 1990. "Uniformly minimum variance unbiased estimator of efficiency ratio in estimation of normal population mean," Statistics & Probability Letters, Elsevier, vol. 10(3), pages 241-245, 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. Ke-Ting Pan & Giovanni S. Leonardi & Marcella Ucci & Ben Croxford, 2021. "Can Exhaled Carbon Monoxide Be Used as a Marker of Exposure? A Cross-Sectional Study in Young Adults," IJERPH, MDPI, vol. 18(22), pages 1-13, November.
    2. Carla Cruvinel Pontes & Usuf Chikte & Faheema Kimmie-Dhansay & Rajiv T. Erasmus & Andre P. Kengne & Tandi E. Matsha, 2020. "Prevalence of Oral Mucosal Lesions and Relation to Serum Cotinine Levels—Findings from a Cross-Sectional Study in South Africa," IJERPH, MDPI, vol. 17(3), pages 1-10, February.
    3. Magdalena Chełchowska & Tomasz M. Maciejewski & Joanna Mazur & Joanna Gajewska & Anastasiya Zasimovich & Mariusz Ołtarzewski & Jadwiga Ambroszkiewicz, 2019. "Active Tobacco Smoke Exposure in Utero and Concentrations of Hepcidin and Selected Iron Parameters in Newborns," IJERPH, MDPI, vol. 16(11), pages 1-10, June.
    4. Kinga Polanska & Anna Krol & Pawel Kaluzny & Danuta Ligocka & Karolina Mikolajewska & Seif Shaheen & Robert Walton & Wojciech Hanke, 2016. "Estimation of Saliva Cotinine Cut-Off Points for Active and Passive Smoking during Pregnancy—Polish Mother and Child Cohort (REPRO_PL)," IJERPH, MDPI, vol. 13(12), pages 1-15, December.
    5. Maria Paz Garcia-Portilla & Leticia Garcia-Alvarez & Pilar Alejandra Saiz & Eva Diaz-Mesa & Gonzalo Galvan & Fernando Sarramea & Josefa Garcia-Blanco & Edorta Elizagarate & Julio Bobes, 2013. "Effectiveness of a Multi-Component Smoking Cessation Support Programme (McSCSP) for Patients with Severe Mental Disorders: Study Design," IJERPH, MDPI, vol. 11(1), pages 1-17, December.
    6. Sungroul Kim, 2016. "Overview of Cotinine Cutoff Values for Smoking Status Classification," IJERPH, MDPI, vol. 13(12), pages 1-15, December.
    7. Clément de Chaisemartin & Pierre‐Yves Geoffard & Anne‐Laurence le Faou, 2011. "Workplace smoking ban effects on unhappy smokers," Health Economics, John Wiley & Sons, Ltd., vol. 20(9), pages 1043-1055, September.
    8. Hyun-Seung Lee & Ji-Hyun Cho & Young-Jin Lee & Do-Sim Park, 2022. "Effect of Second-Hand Smoke Exposure on Establishing Urinary Cotinine-Based Optimal Cut-Off Values for Smoking Status Classification in Korean Adults," IJERPH, MDPI, vol. 19(13), pages 1-14, June.
    9. Parisa Hasanalipour & Mostafa Razmkhah, 2021. "Testing skew-symmetry based on extreme ranked set sampling," Statistical Papers, Springer, vol. 62(5), pages 2311-2332, October.
    10. Magdalena Chełchowska & Joanna Gajewska & Tomasz M. Maciejewski & Joanna Mazur & Mariusz Ołtarzewski & Jadwiga Ambroszkiewicz, 2020. "Associations between Maternal and Fetal Levels of Total Adiponectin, High Molecular Weight Adiponectin, Selected Somatomedins, and Birth Weight of Infants of Smoking and Non-Smoking Mothers," IJERPH, MDPI, vol. 17(13), pages 1-14, July.
    11. Mandeep S. Jassal & Cassia Lewis-Land & Richard E. Thompson & Arlene Butz, 2020. "Linkage of Maternal Caregiver Smoking Behaviors on Environmental and Clinical Outcomes of Children with Asthma: A Post-Hoc Analysis of a Financial Incentive Trial Targeting Reduction in Pediatric Toba," IJERPH, MDPI, vol. 17(22), pages 1-14, November.
    12. Carrieri, V.; Jones, A.M.;, 2017. "Intergenerational transmission of nicotine within families: have e-cigarettes had an impact?," Health, Econometrics and Data Group (HEDG) Working Papers 17/03, HEDG, c/o Department of Economics, University of York.
    13. Florian Fischer, 2016. "Challenges in Creating Evidence in Environmental Health Risk Assessments: The Example of Second-Hand Smoke," Challenges, MDPI, vol. 7(1), pages 1-9, January.
    14. Sungroul Kim & Benjamin J. Apelberg & Erika Avila-Tang & Lisa Hepp & Dongmin Yun & Jonathan M. Samet & Patrick N. Breysse, 2014. "Utility and Cutoff Value of Hair Nicotine as a Biomarker of Long-Term Tobacco Smoke Exposure, Compared to Salivary Cotinine," IJERPH, MDPI, vol. 11(8), pages 1-15, August.
    15. Yen‐Chung Ho & Hsin‐Chien Lee & Mei‐Feng Lin & Hsiu‐Ju Chang, 2020. "Correlations among life stress, smoking behavior, and depressive symptoms in adolescents: A descriptive study with a mediating model," Nursing & Health Sciences, John Wiley & Sons, vol. 22(4), pages 949-957, December.
    16. Suparat Niwitpong & Sa-aat Niwitpong, 2017. "Confidence intervals for the difference between normal means with known coefficients of variation," Annals of Operations Research, Springer, vol. 256(2), pages 237-251, September.
    17. Magdalena Chełchowska & Jadwiga Ambroszkiewicz & Joanna Gajewska & Joanna Mazur & Leszek Lewandowski & Marzanna Reśko-Zachara & Tomasz M. Maciejewski, 2018. "Influence of Active Exposure to Tobacco Smoke on Nitric Oxide Status of Pregnant Women," IJERPH, MDPI, vol. 15(12), pages 1-14, December.
    18. Hamid Rahmani & Mostafa Razmkhah, 2017. "Perfect ranking test in moving extreme ranked set sampling," Statistical Papers, Springer, vol. 58(3), pages 855-875, September.
    19. Carrieri, Vincenzo & Jones, Andrew M., 2018. "Intergenerational transmission of nicotine within families: Have e-cigarettes influenced passive smoking?," Economics & Human Biology, Elsevier, vol. 31(C), pages 83-93.

    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:gam:jmathe:v:5:y:2017:i:3:p:39-:d:106203. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.