Editing Directional statistics (section)

{{Short description|Subdiscipline of statistics}}
'''Directional statistics''' (also '''circular statistics''' or '''spherical statistics''') is the subdiscipline of [[statistics]] that deals with [[Direction (geometry)|directions]] ([[unit vector]]s in [[Euclidean space]], '''R'''<sup>''n''</sup>), [[Cartesian Coordinate System|axes]] ([[Line (geometry)|lines]] through the origin in '''R'''<sup>''n''</sup>) or [[Rotation (mathematics)|rotations]] in '''R'''<sup>''n''</sup>. More generally, directional statistics deals with observations on compact [[Riemannian manifold]]s including the [[Stiefel manifold]].

[[File:Fb5 cover.jpg|thumb|250px|right|The overall shape of a [[protein]] can be parameterized as a sequence of points on the unit  [[sphere]]. Shown are two views of the spherical [[histogram]] of such points for a large collection of protein structures. The statistical treatment of such data is in the realm of directional statistics.<ref name="compbiol.plosjournals.org">{{cite journal|title=Hamelryck, T., Kent, J., Krogh, A. (2006) Sampling realistic protein conformations using local structural bias. PLoS Comput. Biol., 2(9): e131|journal=PLOS Computational Biology|volume=2|issue=9|pages=e131|doi=10.1371/journal.pcbi.0020131|pmid=17002495|pmc=1570370|year = 2006|last1 = Hamelryck|first1 = Thomas|last2=Kent|first2=John T.|last3=Krogh|first3=Anders|bibcode=2006PLSCB...2..131H |doi-access=free }}</ref>]]

The fact that 0 [[degree (angle)|degrees]] and 360 degrees are identical [[angle]]s, so that for example 180 degrees is not a sensible [[average|mean]] of 2 degrees and 358 degrees, provides one illustration that special statistical methods are required for the analysis of some types of data (in this case, angular data). Other examples of data that may be regarded as directional include statistics involving temporal periods (e.g. time of day, week, month, year, etc.), compass directions, [[dihedral angle]]s in molecules, orientations, rotations and so on.