# [Rd] [Package car/data.ellipse]: confidence intervals off by factor sqrt(2)??? (PR#2584)

John Fox jfox@mcmaster.ca
Wed Feb 26 22:31:03 2003

```Dear Volker,

If the data ellipse (or, in this case, circle) is scaled so that its
shadows (projections) on the axes each includes 68% of the data (that is of
the marginal distribution of each variable), then the ellipse will include
less than 68% of the data (i.e., of the joint distribution of the two
variables). Conversely, to include 68% of the data in the ellipse, the
shadows of the ellipse have to be larger.

Did I understand your point correctly?

John

At 09:40 PM 2/26/2003 +0100, volker.franz@tuebingen.mpg.de wrote:
>Full_Name: Volker Franz
>Version: Version 1.6.2  (2003-01-10)
>OS: Debian
>Submission from: (NULL) (192.124.28.104)
>
>
>Hi there,
>
>it seems to me that data.ellipse of package "car" (Version 1.0-1)
>produces confidence interval's which are too big. To see this, do:
>
>library(car)
>plot(c(-2,2),c(-2,2),pch=0)
>data.ellipse(rnorm(10000),rnorm(10000),levels=0.68,plot.points=F)
>abline(v=+1)
>abline(v=-1)
>abline(h=+1)
>abline(h=-1)
>
>To my knowledge, this should result in a circle with radius
>1. However, the circle is larger. It seems that the problem is due to
>an erroneous specification of the degrees of freedom and can be fixed
>with the following patch:
>
>======================================================================
>--- Ellipse.R   Wed Feb 26 17:49:43 2003
>+++ Ellipse.orig        Thu Sep 19 18:20:41 2002
>@@ -34,7 +34,7 @@
>          stop("x and y must be vectors of the same length")
>      if (plot.points & !add) plot(x, y, xlab=xlab, ylab=ylab, col=col,
> pch=pch,
>las=las, ...)
>      if (plot.points & add) points(x, y, col=col, pch=pch, ...)
>-    dfn<-1
>+    dfn<-2
>      dfd<-length(x)-1
>      if (robust) {
>          require(MASS)
>======================================================================
>
>Or --- am I totally on the wrong track here?
>
>Best
>Volker
>
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>R-devel@stat.math.ethz.ch mailing list
>http://www.stat.math.ethz.ch/mailman/listinfo/r-devel

____________________________
John Fox
Department of Sociology
McMaster University
email: jfox@mcmaster.ca
web: http://www.socsci.mcmaster.ca/jfox

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