From: Robert A. Knop Jr. (robert.a.knop@vanderbilt.edu)
Date: Fri Apr 11 2003 - 03:42:27 PDT
Saul indicated that he does not like having multiple lots with filled
and drawn contours of confidence intervals overlayed on the same plots.
Does everybody else think these are as confusing as Saul does?
I've been thinking about this, and I don't believe at the moment that we
can get away from showing several of these in several different contexts
without losing the ability to communiate some of what we want to
communicate. In general, when we want to inviate a comparison of two
confidence intervals, unless the difference is gross, a lot of the
information gets lost in a side-by-side or a top-to-bottom plot that you
can see when the two are overlayed.
With single data points, you can just compare the numbers and the error
bars; with data sets with one dimensional error bars, you can easily
plot two sets with different symbols to see consistency. However, with
two dimensional confidence intervals, your only options for comparison
are to plot side by side or to overlay; if the point is comparison, I
think it's much clearer and easier to overlay.
A couple of examples. First, consider Figure 4 from the 2003-Apr-04
draft. First consider the left plot. The point of that is that using
only the new high-z data, we get consistent confidence intervals from
what we got using the old high-z data. This is an important point of
the paper; a new set which gives consistent results. If these are
plotted side by side or top to bottom, the nature of the consistency
becomes less clear. They look about the same, and people will probably
take that away, but it's very hard to see what really is the degree of
overlap without overlaying the two. Consider the right side: this shows
how much the confidence intervals improve by adding the new data to the
old data. Again, this comparison is less obvious if you can't directly
compare the two on the same axis.
I would agree that this isn't necessary for Figure 5, where the old data
is sort of gratuitous, and any side by side or top to bottom figure is
going to get the gross point across. Similarly, for the w plot
(currently figure 9), showing the old data isn't necessary, and does
just confuse the issue.
A second example: the prior. Saul's top-to-bottom figure shows how much
the use of the prior affects the uncertainties on the confidence
intervals. It does not as easily show the bias we like to talk about.
Again, in Figure 8 from the 2003-Apr-04 draft, by overlaying I find it
much easier to see just how much something has shifted compared to
something else.
What do other people think on this matter? So far I've only really
heard from Saul on the matter. Am I completely out on a limb here, and
in fact are those overlayed plots too confusing? Or does anybody else
agree that when we're trying to invite a comparison between two things,
overlaying is what makes the most sense?
-Rob
-- --Prof. Robert Knop Department of Physics & Astronomy, Vanderbilt University robert.a.knop@vanderbilt.edu
This archive was generated by hypermail 2.1.4 : Fri Apr 11 2003 - 03:42:53 PDT