Discussion

I am not competent to discuss the psychiatric, geronto-logical, or neurological meaning of any of these findings. (Indeed, I look forward very much to receiving my copy of this volume just so that I can learn some of the neu-robiology of the callosum as it may relate to these sturdy statistical contrasts.) It may be useful, nevertheless, if I pursue some of the morphometric issues here. Why is it that the new methods are so much more powerful than the traditional approach to cause-and-effect analysis via sectioning the area of the arch? There are three general reasons, I would argue, that this new toolkit of methods ought to replace the old in studies of the callosum: the richness of this parametric treatment of shape, the reliance on omnibus statistical tests rather than ad hoc Bon-ferroni corrections of localized analyses, and the power of the associated visualizations.

Studying Shape Differences per se The standard sectoral approach studies only the area inside the cal-losal form. Such approaches incorporate no representation of shapes of individual callosa by any parameter vector that can be diagrammed, regionalized, or tested by formal statistical procedure. They are thus ineffective at detecting changes that alter shape without much altering area. In the second example here, just such an effect was found: Group difference in the region of the isthmus is mainly of position, much less of relative area. In the first example, the change at isthmus incorporates some areal shrinkage but also some displacement. The areal approach is clearly much less likely to find such changes than, say, the relative enlargement of splenium. The splenium sector, shown at the right in Figure 4.6, occupies a fraction of the total callosal area that differs in a ratio of 17% between the sexes. This difference is significant at p @ 0.03 by conventional t-test (before the Bonferroni correction). By contrast, the difference of position of the border at the upper right in the right panel of Figure 4.7, a different descriptor of the same shape difference, is significant at about p @ 0.003 by t-test in the normal direction. Put most tersely, there is

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