Quaternions and spatial rotation the rotation. As the rotation angles become larger, the slice moves in the negative "z" direction, and the circles become larger until the equator of the sphere is reached, which will correspond to a rotation angle of 180 degrees. Continuing southward, the radii of the circles now become smaller (corresponding to the absolute value of the angle of the rotation considered as a negative number). Finally, as the south pole is reached, the circles shrink once more to the identity rotation, which is also specified as the point at the south pole. Notice that a number of characteristics of such
Degrees of freedom (statistics) if for no other reason than that, all else being equal, the fewer degrees of freedom, the better indices such as χ will be. It has been shown that degrees of freedom can be used by readers of papers that contain SEMs to determine if the authors of those papers are in fact reporting the correct model fit statistics. In the organizational sciences, for example, nearly half of papers published in top journals report degrees of freedom that are inconsistent with the models described in those papers, leaving the reader to wonder which models were actually tested. A common way