A problem has been
submitted to me last evening, so it became my little headache for the weekend!
I am not shure of my solutions...
It is about comparaison
of two clouds of points, like I use to do with samples comparisons but with a
supplemental dimension. The datas are two lists of points with x and y
coordinates.
In this graph the clouds
seems to be completely overlapped, the points in bold are the
barycenters.
I have drawn the
barycenter line because my first idea was to reduce the dimensions by
orthogonal projection. I have took the coordinates of each points orthogonaly
projecter on the barycenter line and compute the distances from a common
reference (the pont projected with the min (x)). There must be a bug in my
script or in the graph because the projections are clearly not orthogonal... I
need time to work on that problem.
The result is two lists
of distances that I can test by a classical Student...
This density graph show
the relative distributions of the two mesures populations, computed from the
two clouds. The dark lines are the means and the ligts are the mean+/-2sd.The
Student pval is in the title of the graph.
This method do not take
account of the 2D dispersion of the clouds so I have also used the distances to
the barycenters instead of the orthogonal projections (this methode is way more
simple but this idea has took time to come...).
This method produces very
different values and the variabilities of the clouds seems to be preserved.
This density graph show
the relative distributions of the distances from the barycenters.
The script, the data
sources and the figures are
here.
