Graph critical region

I've seen quicker ways to do it, but I've been using ggplot2 for this.
See examples below.

On Tue, Jun 23, 2009 at 7:57 PM, AbouEl-Makarim

Dear All:

I need some help with graphing the critical regions of hypothesis testing.

Consider the Z-test, assume Z=3.2, and alpha=0.05 (that is Z_(a.pha/2)=1.96.

Then how to graph the rejection region in the following three cases:

Left-tailed test

library(ggplot2)
z <- seq(-4,4, by = .01)
Density <- dnorm(z)
criteria <- factor(rep("retain", length(z)), levels=c("retain", "reject"))
criteria[which(z < qnorm(.05))] <- "reject"
qplot(z,Density, geom=c("path","area"), fill=criteria) +
scale_fill_manual(values=c("grey40", "red"))

Right-tailed test

Same as above except do
criteria[which(z > qnorm(.95))] <- "reject"

Two tailed test

Sorry, haven't figured this one out yet.

Same for the T-test.

t <- seq(-4,4, by = .01)
Density <- dt(t,df=20)
criteria <- factor(rep("retain", length(t)), levels=c("retain", "reject"))
criteria[which(t > qt(.95,df=20))] <- "reject"
qplot(t,Density, geom=c("path","area"), fill=criteria) +
scale_fill_manual(values=c("grey40", "red"))

Hope it helps,
Ista

Thank you so much for your times.

Abou




==========================
AbouEl-Makarim Aboueissa, Ph.D.
Assistant Professor of Statistics
Department of Mathematics & Statistics
University of Southern Maine
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Portland, ME 04104-9300

Tel: (207) 228-8389
Email: aaboueissa at usm.maine.edu
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