Manifolds are widely used to model non-linearity arising in
a range of computer vision applications. This paper treats statistics on
manifolds and the loss of accuracy occurring when linearizing the manifold
prior to performing statistical operations. Using recent advances in
manifold computations, we present a comparison between the non-linear
analog of Principal Component Analysis, Principal Geodesic Analysis,
in its linearized form and its exact counterpart that uses true intrinsic
distances. We give examples of datasets for which the linearized version
provides good approximations and for which it does not. Indicators for
the dierences between the two versions are then developed and applied
to two examples of manifold valued data: outlines of vertebrae from a
study of vertebral fractures and spacial coordinates of human skeleton
end-eectors acquired using a stereo camera and tracking software.