On Nov 15, 9:16 pm, djh <halitsk...@att.net> wrote: > Consider the left-handed coordinate system OECU (with thumb as E, > index finger as C, and middle finger as U). > > Orthogonal projection of this coordinate system onto the plane Peuc > thru (1,0,0), (0,1,0), (0,0,1) will take: > > e,0,0 into the point Pe = ( (1/sqrt6)e, (-sqrt2/2)e ) > 0,c,0 into the point Pc = ( (-sqrt(2/3))e, 0 ) > 0,0,u into the point Pu = ( (1/sqrt6)e, (+sqrt2/2)e ) > > And therefore: > > 1a) for any triple (ei,ci,ui), we can compute the centroid CTi of the > triangle Ti = PeiPuiPci, (where CTi is obviously 0 when ei=ui=ci and > Ti degenerates into a single point.) > > 1b) for all the triples (e1,c1,u1),....,(en,cn,un) from observations > at a given L (actual length, not interval), we can compute the average > centroid CTa of the triangles T1,....Tn. > > 2a) for any pair (ei,ci,0), we can compute the midpoint Ceci of the > line segment Seci = (Pei,Pci) > > 2b) for all the pairs (e1,c1,0),....,(en,cn,0) from observations at a > given L (actual length, not interval), we can compute the average > centroid Ceca of the line segments Sec1,...,Secn > > (3a-3b): same as (2a-b) but for (ei,0,ui) > > (4a-4b): same as (2a-b) but for (0,ci,ui) > > 5) if we imagine L as an axis orthogonal to the plane Peuc, we can see > if CTa, Ceca, Ceua, and Ccua vary in any interesting way with > increasing L. > > Note that (1-5) can be readily done for all actual lengths within each > cell of the design and the results plotted for easy visual detection > of any possible pattern. > > I will let you know what happens.
e, c, and u are not commensurate: e is in degrees Kelvin, in the interval [221.735, 308.65]; c is a count, in the interval [??, ??]; u is a ratio of observed/expected counts, in the interval [0, ??].
How are you mapping each of those into [0,1]? However you are doing it, it should not be arbitrary, and it should be the same for all the data you have now or might have in the future; that is, it should not depend on any sample-specific information.