Skip to main content

The Mann-Whitney Test for Interval-Valued Data

Part of the Advances in Intelligent Systems and Computing book series (AISC,volume 642)


The Mann-Whitney test for the two-sample location problem is considered. We adopt this nonparametric test to interval-valued data perceived from the epistemic perspective, where the available observations are just interval-valued perceptions of the unknown true outcomes of the experiment. Unlike typical generalizations of statistical procedures into the interval-valued framework, the proposed test entails very low computational costs. However, the presence of interval-valued data results in set-valued p-value which leads no longer to a definite binary decision (reject or not reject the null hypothesis) but may indicate the abstention from making a final decision if the information is too vague.


  • Interval-valued data
  • Nonparametric test
  • p-value
  • Two-sample test
  • Wilcoxon test

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-66824-6_17
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
USD   269.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-66824-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   349.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.


  1. Couso, I., Dubois, D.: Statistical reasoning with set-valued information: ontic vs. epistemic views. Int. J. Approximate Reasoning 55, 1502–1518 (2014)

    MathSciNet  CrossRef  MATH  Google Scholar 

  2. Filzmoser, P., Viertl, R.: Testing hypotheses with fuzzy data: the fuzzy p-value. Metrika 59, 21–29 (2004)

    MathSciNet  CrossRef  MATH  Google Scholar 

  3. Gibbons, J.D., Chakraborti, S.: Nonparametric Statistical Inference. Marcel Dekker, New York (2003)

    MATH  Google Scholar 

  4. Grzegorzewski, P.: Statistical inference about the median from vague data. Control Cybern. 27, 447–464 (1998)

    MathSciNet  MATH  Google Scholar 

  5. Grzegorzewski, P.: Fuzzy tests - defuzzification and randomization. Fuzzy Sets Syst. 118, 437–446 (2001)

    MathSciNet  CrossRef  MATH  Google Scholar 

  6. Grzegorzewski, P.: Distribution-free tests for vague data. In: Lopez-Diaz, M., Gil, M.A., Grzegorzewski, P., Hryniewicz, O., Lawry, J. (eds.) Soft Methodology and Random Information Systems, pp. 495-502. Springer, Heidelberg (2004)

    Google Scholar 

  7. Kreinovich, V., Servin, C.: How to test hypotheses when exact values are replaced by intervals to protect privacy: case of t-tests, Departamental Technical reports (CS), Paper 892, University of Texas at El Paso (2015)

    Google Scholar 

  8. Mann, H.B., Whitney, D.R.: On a test whether one of two random variables is stochastically larger than the other. Ann. Math. Stat. 18, 50–60 (1947)

    MathSciNet  CrossRef  MATH  Google Scholar 

  9. Moore, R.E.: Automatic error analysis in digital computation, Technical report Space Div. Report LMSD 84821, Lockheed Missiles and Space Co. (1959)

    Google Scholar 

  10. Nguyen, H.T., Kreinovich, V., Wu, B., Xiang, G.: Computing Statistics under Interval and Fuzzy Uncertainty. Springer, Heidelberg (2012)

    CrossRef  MATH  Google Scholar 

  11. Perolat, J., Couso, I., Loquin, K., Strauss, O.: Generalizing the Wilcoxon rank-sum test for interval data. Int. J. Approximate Reasoning 56, 108–121 (2015)

    MathSciNet  CrossRef  MATH  Google Scholar 

  12. Sunaga, T.: Theory of interval algebra and its application to numerical analysis, RAAG Memoirs, Ggujutsu Bunken Fukuy-kai, Tokyo 2(29–46), 547–564 (1958)

    Google Scholar 

  13. Warmus, M.: Calculus of approximations. Bull. de l’Academie Polonaise de Sci. 4, 253–257 (1956)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Przemyslaw Grzegorzewski .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Cite this paper

Grzegorzewski, P., Śpiewak, M. (2018). The Mann-Whitney Test for Interval-Valued Data. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 642. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66823-9

  • Online ISBN: 978-3-319-66824-6

  • eBook Packages: EngineeringEngineering (R0)