On Wednesday 26 February 2003 04:23 pm, Volker Franz wrote: > Hi John, > > >>>>> "JF" == John Fox <[EMAIL PROTECTED]> writes: > > JF> Dear Volker, If the data ellipse (or, in this case, circle) is > JF> scaled so that its shadows (projections) on the axes each > JF> includes 68% of the data (that is of the marginal distribution > JF> of each variable), then the ellipse will include less than 68% > JF> of the data (i.e., of the joint distribution of the two > JF> variables). Conversely, to include 68% of the data in the > JF> ellipse, the shadows of the ellipse have to be larger. > JF> Did I understand your point correctly? > > I am not sure. I will try to rephrase my initial request: > > Let X by a one--dimensional random variable (standard normal > distribution; mean=0; std=1). The 68% confidence intervall of X will > approximately be: [-1,1]. Now, if I combine X with a stochastically > independent second random variable Y, the marginal distribution of X > should not change. Therefore, the projections of the error ellipse on > the X--axis should still be: [-1,1].
Why so ? Let Y be an independent copy of X (i.e., Y ~ N(0,1) too, independent of X). Then P(Y is in [-Inf , Inf]) = 1. Now, think of the 2-D confidence region [-1, 1] x [-Inf, Inf]. This will have (by independence of X and Y) probability 0.68. Now, how can you expect an ellipse that will have the same X-range, that is a strict subset of this region, to still have joint probability 0.68 ? Hope that helps, Deepayan ______________________________________________ [EMAIL PROTECTED] mailing list http://www.stat.math.ethz.ch/mailman/listinfo/r-devel
