Skip to main content

Understanding Group Comfort Through Directional Statistics

  • Conference paper
  • First Online:
Book cover Social Robotics (ICSR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9388))

Included in the following conference series:

  • 6370 Accesses

Abstract

This paper has the dual aims of introducing and using directional statistics to investigate the comfort levels of pairs of people approached by a robot from different directions. Data from pairs seated in three maximally-different seating configurations are analysed. These data are in the form of circular distributions of ranked comfort levels. Statistical tests for uniformity of circular distributions and for determining if differences exist between pairs of circular distributions are introduced and used to analyse the directional properties of the data. It is shown that directional statistics can be used to compare comfort level ranks that capture all tested robot approach directions; something that cannot be achieved with linear statistics.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Mardia, K.V., Jupp, P.E.: Directional Statistics. John Wiley & Sons (2009)

    Google Scholar 

  2. Mardia, K.V.: Statistics of Directional Data. Academic Press (1972)

    Google Scholar 

  3. Dautenhahn, K., Walters, M., Woods, S., Koay, K.L., Nehaniv, C.L., Sisbot, A., Alami, R., Siméon, T.: How may I serve you? a robot companion approaching a seated person in a helping context. In: 1st ACM SIGCHI/SIGART Conf. Human-Robot Interact., pp. 172–179. ACM (2006)

    Google Scholar 

  4. Walters, M.L., Dautenhahn, K., Woods, S.N., Koay, K.L., Te Boekhorst, R., Lee, D.: Exploratory studies on social spaces between humans and a mechanical-looking robot. Connection Science 18(4), 429–439 (2006)

    Article  Google Scholar 

  5. Walters, M.L., Dautenhahn, K., Woods, S.N., Koay, K.L.: Robotic etiquette: results from user studies involving a fetch and carry task. In: 2nd ACM/IEEE Int. Conf. Human-Robot Interact., pp. 317–324. IEEE (2007)

    Google Scholar 

  6. Karreman, D., Utama, L., Joosse, M., Lohse, M., van Dijk, B., Evers, V.: Robot etiquette: how to approach a pair of people? In: ACM/IEEE Int. Conf. Human-Robot Interact., pp. 196–197. ACM (2014)

    Google Scholar 

  7. Ball, A., Silvera-Tawil, D., Rye, D., Velonaki, M.: Group comfortability when a robot approaches. In: Beetz, M., Johnston, B., Williams, M.-A. (eds.) ICSR 2014. LNCS, vol. 8755, pp. 44–53. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  8. Hinkelmann, K., Kempthorne, O.: Design and Analysis of Experiments. Introduction to Experimental Design, vol. 1. John Wiley & Sons (1994)

    Google Scholar 

  9. Rao, B.: Nonparametric Functional Estimation. Academic Press (1983)

    Google Scholar 

  10. Siegel, S.: Non-Parametric Statistics. McGraw-Hill (1956)

    Google Scholar 

  11. Jupp, P.: Modifications of the Rayleigh and Bingham tests for uniformity of directions. J. Multivariate Anal. 77(1), 1–20 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Stuart, A., Ord, J.: Kendall’s Advanced Theory of Statistics, vol. 1. Halsted Press (1994)

    Google Scholar 

  13. Watson, G.S.: Goodness-of-fit tests on a circle II. Biometrika, 57–63 (1962)

    Google Scholar 

  14. Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures. CRC Press (2003)

    Google Scholar 

  15. Brown, B.: Grouping corrections for circular goodness-of-fit tests. J. Royal Stat. Soc. Ser. B (Methodological), 275–283 (1994)

    Google Scholar 

  16. Maag, U.R.: A \(k\)-sample analogue of Watson’s \(U^2\) statistic. Biometrika 53(3–4), 579–583 (1966)

    MathSciNet  MATH  Google Scholar 

  17. Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Royal Stat. Soc. Ser. B (Methodological), 289–300 (1995)

    Google Scholar 

  18. Kendon, A.: Spacing and orientation in co-present interaction. In: Esposito, A., Campbell, N., Vogel, C., Hussain, A., Nijholt, A. (eds.) Second COST 2102. LNCS, vol. 5967, pp. 1–15. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Ball, A., Rye, D., Silvera-Tawil, D., Velonaki, M.: Group vs. individual comfort when a robot approaches. In: Proc. 24th Int. Symp. Robot and Human Interactive Communication (RO-MAN 2015) (2015) (in press)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Adrian Ball .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Ball, A., Rye, D., Silvera-Tawil, D., Velonaki, M. (2015). Understanding Group Comfort Through Directional Statistics. In: Tapus, A., André, E., Martin, JC., Ferland, F., Ammi, M. (eds) Social Robotics. ICSR 2015. Lecture Notes in Computer Science(), vol 9388. Springer, Cham. https://doi.org/10.1007/978-3-319-25554-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25554-5_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25553-8

  • Online ISBN: 978-3-319-25554-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics