Skip to main content

Second-order Statistical Analysis of Directions

  • Conference paper
Animal Migration, Navigation, and Homing

Part of the book series: Proceedings in Life Sciences ((LIFE SCIENCES))


If circular samples of equal size are reduced to their respective mean vectors, a sample of mean vectors is formed. This sample is referred to as a second-order sample. Kolmogorov’s test of goodness of fit may be used as a test for concentration. Since second-order samples are essentially bivariate, Hotelling’s T2 test (in case of normality) or a nonparametric competitor may be applied. Here a linear-circular correlation technique is recommended. Also studied is the comparison of two independent second-order samples.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others


  • Arendse, M.C., Vrins, J.C.M.: Magnetic orientation and its relation to photic orientation in Tenebvio Molitor L. Netherl. J. Zool. 25, 407–437 (1975)

    Article  Google Scholar 

  • Batschelet, E.: Statistical Methods for the Analysis of Problems in Animal Orientation and Certain Biological Rhythms. Washington, D.C.: Am. Inst. Biol. Sci., 1965

    Google Scholar 

  • Batschelet, E.: Recent statistical methods for orientation data. In: Animal Orientation and Navigation. Galler, al. (eds.). NASA-Symposium. Washington, D.C.: U.S. Government Printing Office, 1972

    Google Scholar 

  • Conover, W.J.: Practical Nonparametric Statistics. New York and London: Wiley, 1971

    Google Scholar 

  • Ercolini, A., Scapini, F.: Fototassia negativa e orientamento astronomico solare in due specie di stafilinidi ripari. Redia 59, 135–153 (1976)

    Google Scholar 

  • Fiore, L., Ioalé, P.: A method for studying orientation in pigeons by operant conditioning. Rev. Comp. Animal 7, 275–278 (1973)

    Google Scholar 

  • Greenwood, J.A., Durand, D.: The distribution of length and components of the sum of n random unit vectors. Ann. Math. Stat, 26, 233–246 (1955)

    Article  Google Scholar 

  • Halberg, F., Tong, Y.L., Johnson, E.A.: Circadian system phase — An aspect of temporal morphology. In: Cellular Aspects of Biorhythms. Symposium on Rhythmic Research in Wiesbaden. Berlin — Heidelberg — New York: Springer, 1965

    Google Scholar 

  • Hald, A.: Statistical Theory with Engineering Applications. New York: Wiley, 1952

    Google Scholar 

  • Heiligenberg, W.: Electrolocation and jamming avoidance in a Hypopygus (Rhamphichthyidae, Gymnotoidei), an electric fish with pulse-type discharges. J. Comp. Physiol. 91, 223–240 (1974)

    Article  Google Scholar 

  • Herrnkind, W.F., McLean, R.: Field studies of homing, mass emigration, and orientation in the spiny lobster, Panulirus Argus. Ann. New York Acad. Sci. 188, 359–377 (1971)

    Article  CAS  Google Scholar 

  • Hotelling, H.: The generalization of Student’s ratio. Ann. Math. Stat. 2, 360–378 (1931)

    Article  Google Scholar 

  • Mardia, K.V.: A nonparametric test for the bivariate two-sample location problem. J. R. Stat. Soc, Ser. B. 29, 320–342 (1967)

    Google Scholar 

  • Mardia, K.V.: Statistics of Directional Data. London — New York: Academic Press, 1972

    Google Scholar 

  • Mardia, K.V.: Linear-circular correlation coefficients and rhythmometry. Biometrika 63, 403–405 (1976)

    Article  Google Scholar 

  • Wallraff, H.G.: Über die Flugrichtungen verfrachteter Brieftauben in Abhängigkeit vom Heimatort und vom Ort der Freilassung. Z. Tierpsychol. 27, 303–351 (1970)

    Google Scholar 

  • Zar, J.H.: Biostatistical Analysis. Englewood Cliffs, N.J.: Prentice-Hall, 1974

    Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Batschelet, E. (1978). Second-order Statistical Analysis of Directions. In: Schmidt-Koenig, K., Keeton, W.T. (eds) Animal Migration, Navigation, and Homing. Proceedings in Life Sciences. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-11148-2

  • Online ISBN: 978-3-662-11147-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics