Skip to main content
SpringerLink
Log in

A Simple Graphical Way of Evaluating Coverage and Directional Non-coverages

  • Conference paper
  • First Online:
Computational Science and Its Applications – ICCSA 2017 (ICCSA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10405))

Included in the following conference series:

  • 1802 Accesses

Abstract

Evaluation of the coverage probability and, more recently, of the intervalar location of confidence intervals, is a useful procedure if exact and asymptotic methods for constructing confidence intervals are used for some populacional parameter. In this paper, a simple graphical procedure is presented to execute this kind of evaluation in confidence methods for linear combinations of k independent binomial proportions. Our proposal is based on the representation of the mesial and distal non-coverage probabilities on a plane. We carry out a simulation study to show how this graphical representation can be interpreted and used as a basis for the evaluation of intervalar location of confidence interval methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Anbar, D.: On estimating the difference between two proportions, with special reference to clinical trials. Biometrics 39, 257–262 (1983)

    Article  Google Scholar 

  2. Mee, R.: Confidence bounds for the difference between two proportions. Biometrics 40, 1175–1176 (1984)

    MathSciNet  Google Scholar 

  3. Newcombe, R.: Interval estimation for the difference between independent proportions: comparison of eleven methods. Stat. Med. 17, 873–890 (1998)

    Article  Google Scholar 

  4. Agresti, A., Caffo, B.: Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures. Am. Stat. 54, 280–288 (2000)

    MathSciNet  MATH  Google Scholar 

  5. Brown, L., Li, X.: Confidence intervals for two sample binomial distribution. J. Stat. Plan. Infer. 130, 359–375 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fagerland, M., Lydersen, S., Laake, P.: Recommended confidence intervals for two independent binomial proportions. Stat. Methods Med. Res., 1–31 (2011)

    Google Scholar 

  7. Decrouez, G., Robison, A.: Confidence intervals for the weighted sum of two independent binomial proportions. Aust. N. Z. Stat. 54, 281–299 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Martín Andrés, A., Álvarez Hernández, M.: Optimal method for realizing two-sided inferences about a linear combination of two proportions. Commun. Stat. Simul. Comput. 42, 327–343 (2013). doi:10.1080/03610918.2011.650263

    Article  MathSciNet  MATH  Google Scholar 

  9. Tebbs, J., Roths, S.: New large-sample confidence intervals for a linear combination of binomial proportions. J. Stat. Plan. Infer. 138, 1884–1893 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Price, R., Bonett, D.: An improved confidence interval for a linear function of binomial proportions. Comput. Stat. Data Anal. 45, 449–456 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Martín Andrés, A., Álvarez Hernández, M., Herranz Tejedor, I.: Inferences about a linear combination of proportions. Stat. Methods Med. Res. 20, 369–387 (2012). doi:10.1177/0962280209347953. Erratum in Stat. Methods Med. Res. 21(4), 427–428 (2012). doi:10.1177/0962280211423597

  12. Martín Andrés, A., Herranz Tejedor, I., Álvarez Hernández, M.: The optimal method to make inferences about a linear combination of proportions. J. Stat. Comput. Simul. 82, 123–135 (2012). doi:10.1080/00949655.2010.530601

    Article  MathSciNet  MATH  Google Scholar 

  13. Escudeiro, S., Freitas, A., Afreixo, A.: Approximate confidence intervals for a linear combination of binomial proportions: a new variant. Commun. Stat. Simul. Comput. (2016). doi:10.1080/03610918.2016.1241408

  14. Agresti, A., Coull, B.: Approximate is better than exact for interval estimation of binomial proportions. Am. Stat. 52, 119–126 (1998)

    MathSciNet  Google Scholar 

  15. Newcombe, R.: Measures of location for confidence intervals for proportions. Commun. Stat. Theory Methods 40, 1743–1767 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Newcombe, R.: Confidence Intervals for Proportions and Related Measures of Effect Size. CRC Press, Boca Raton (2013)

    MATH  Google Scholar 

  17. Laud, P., Daneb, A.: Confidence intervals for the difference between independent binomial proportions: comparison using a graphical approach and moving averages. Pharmaceut. Statist. 13, 294–308 (2014)

    Article  Google Scholar 

  18. R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing (2016)

    Google Scholar 

Download references

Acknowledgments

This work was partially supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT – Fundação para a Ciência e a Tecnologia), within project UID/MAT/04106/2013.

Author information

Authors and Affiliations

  1. University of Aveiro, Aveiro, Portugal

    Adelaide Freitas & Vera Afreixo

  2. Polytechnic of Coimbra (ESAC), Coimbra, Portugal

    Sara Escudeiro

Authors
  1. Adelaide Freitas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sara Escudeiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vera Afreixo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adelaide Freitas .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Trieste, Trieste, Italy

    Giuseppe Borruso

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  9. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  10. University of Trieste, Trieste, Italy

    Alfredo Cuzzocrea

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Freitas, A., Escudeiro, S., Afreixo, V. (2017). A Simple Graphical Way of Evaluating Coverage and Directional Non-coverages. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10405. Springer, Cham. https://doi.org/10.1007/978-3-319-62395-5_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-62395-5_41

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62394-8

  • Online ISBN: 978-3-319-62395-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation