[S] Again: CIs for Median (via boxplot())

marcel.baumgartner@rdls.nestle.com
Wed, 28 Oct 1998 08:09:06 +0100


In August, Ming Yin summarized the way confidence
interval for the median are computed, using boxplot:

CI <- boxplot(x,plot=F)
CI$conf

He notes that the formula is:

median +/- 1.58*((Hinge Spread)/sqrt(n))

What is "Hinge Spread" ?

I tried the IQR and get values which are close (S-PLUS4.5, Release 2),
but not quite the same:

> set.seed(48583)
> x.CI <- boxplot(x, plot = F)
> x.CI$conf
[,1]
[1,] 0.43084893
[2,] -0.03551373
> x.IQR <- diff(quantile(x, c(0.25, 0.75)))
> median(x) - (1.58 * x.IQR)/sqrt(length(x))
75%
-0.03141699
> median(x) + (1.58 * x.IQR)/sqrt(length(x))
75%
0.4267522

Can someone give me a definition of "Hinge Spread" ? Are there
"better" ways available to compute CIs for medians ?
I'll summarize on the list.

Greetings

Marcel

Marcel Baumgartner Direct: ++41 21 785 8917
Nestlé Research Center Central: ++41 21 785 81 11
Vers-chez-les-Blanc FAX: ++41 21 785 85 54
PO Box 44
CH-1000 Lausanne 26 Marcel.Baumgartner@rdls.nestle.com

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