Computational Statistics

, Volume 24, Issue 2, pp 233–246 | Cite as

Visualizing hypothesis tests in multivariate linear models: the heplots package for R

  • John FoxEmail author
  • Michael Friendly
  • Georges Monette
Original Paper


Hypothesis-error (or “HE”) plots, introduced by Friendly (J Stat Softw 17(6):1–42, 2006a; J Comput Graph Stat 16:421–444, 2006b), permit the visualization of hypothesis tests in multivariate linear models by representing hypothesis and error matrices of sums of squares and cross-products as ellipses. This paper describes the implementation of these methods in the heplots package for R, as well as their extension, for example from two to three dimensions and by scaling hypothesis ellipses and ellipsoids in a natural manner relative to error.


Multivariate linear model MANOVA Linear hypotheses Data ellipses Statistical graphics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Dempster AP (1969) Elements of continuous multivariate analysis. Addison-Wesley, Reading, MAzbMATHGoogle Scholar
  2. Friendly M, Kwan E (2003) Effect ordering for data displays. Computational Statistics and Data Analysis 43: 509–539zbMATHCrossRefMathSciNetGoogle Scholar
  3. Friendly M (2006a) Data ellipses, HE plots and reduced-rank displays for multivariate linar models: SAS software and examples. J Stat Softw 17(6): 1–42Google Scholar
  4. Friendly M (2006b) HE plots for multivariate general linear models. J Comput Graph Stat 16: 421–444MathSciNetGoogle Scholar
  5. Hand D, Daly F, Lunn AD, McConway KJ, Ostrowski E (1994) A Handbook of Small Data Sets. Chapman and Hall, LondonGoogle Scholar
  6. Johnson RA, Wichern DW (1992) Applied multivariate statistical analysis, 3rd edn. Prentice Hall, Englewood CliffszbMATHGoogle Scholar
  7. Monette G (1990) Geometry of multiple regression and interactive 3-D graphics. In: Fox J, Long JS (eds) Modern methods of data analysis. Sage, Beverly Hills, pp 209–256Google Scholar
  8. Timm NH (1975) Multivariate analysis with applications in education and psychology. Wadsworth (Brooks/Cole), BelmontGoogle Scholar
  9. Tubb A, Parker A, Nickless G (1980) The analysis of Romano-British pottery by atomoic absorbtion spectrophotometry. Archaeometry 22: 153–171CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of SociologyMcMaster UniversityHamiltonCanada
  2. 2.Department of PsychologyYork UniversityTorontoCanada
  3. 3.Department of Mathematics and StatisticsYork UniversityTorontoCanada

Personalised recommendations