HH (version 1.5)

norm.curve: plot a normal curve with both x and z axes.

Description

Plot a normal curve with both x (with mean and se as specified) and z (mean=0, se=1) axes. Shade a region for rejection region, acceptance region, confidence interval. The density axis is marked in units appropriate for the z axis. The existence of any of the arguments se, sd, n forces dual x and z scales. When none of these arguments are used, the main title defaults to "Standard Normal Density N(0,1)" and only the z scale is printed. A second density curve, appropriate for an alternative hypothesis is displayed when the argument axis.name="z1" is specified.

Usage

norm.setup(xlim.in=c(-2.5,2.5),
           ylim.in = c(0, 0.4)/se,
           mean=0,
           main.in=ifelse(
             !(missing(se) && missing(sd) && missing(n)),
             paste("normal density:  se =", round(se,3)),
             "Standard Normal Density N(0,1)"),
           se=sd/sqrt(n), sd=1, n=1, ...)

norm.curve(mean=0, se=sd/sqrt(n),
         critical.values=mean + se*c(-1.96, 1.96),
         z=do.call("seq",
                   as.list(c((par()$usr[1:2]-mean)/se, length=109))),
         shade, col=par("col"), axis.name="z", sd=1, n=1, ...)

Arguments

xlim.in, ylim.in

xlim, ylim. Defaults to correct values for standard Normal(0,1). User must set values for other mean and standard error.

mean

Mean of the normal distribution in xbar-scale, used in calls to dnorm.

se

standard error of the normal distribution in xbar-scale, used in calls to dnorm.

sd, n

standard deviation and sample size of the normal distribution in x-scale. These may be used as an alternate way of specifying the standard error se.

critical.values

Critical values in xbar-scale. A scalar value implies a one-sided test. A vector of two values implies a two-sided test.

main.in

Main title.

z

z-values (standardized to N(0,1)) used as base of plot.

shade

Valid values for shade are "right", "left", "inside", "outside". Default is "right" for one-sided critical.values and "outside" for two-sided critical values.

col

color of the shaded region.

axis.name

"z" for the standard normal scale centered on the null hypothesis value of the mean. "z1" for the standard normal scale centered on the alternate hypothesis value of the mean.

...

Other arguments which are ignored.

Examples

old.par <- par(oma=c(4,0,2,5), mar=c(7,7,4,2)+.1)

norm.setup()
norm.curve()

norm.setup(xlim=c(75,125), mean=100, se=5)
norm.curve(100, 5, 100+5*(1.645))

norm.setup(xlim=c(75,125), mean=100, se=5)
norm.curve(100, 5, 100+5*(-1.645), shade="left")

norm.setup(xlim=c(75,125), mean=100, se=5)
norm.curve(mean=100, se=5, col=2)

norm.setup(xlim=c(75,125), mean=100, se=5)
norm.curve(100, 5, 100+5*c(-1.96, 1.96))

norm.setup(xlim=c(-3, 6))
norm.curve(crit=1.645, mean=1.645+1.281552, col=3,
           shade="left", axis.name="z1")
norm.curve(crit=1.645, col=2)

norm.setup(xlim=c(-6, 12), se=2)
norm.curve(crit=2*1.645, se=2, mean=2*(1.645+1.281552),
           col=3, shade="left", axis.name="z1")
norm.curve(crit=2*1.645, se=2, mean=0,
           col=2, shade="right")


par(mfrow=c(2,1))
norm.setup()
norm.curve()
mtext("norm.setup(); norm.curve()", side=1,  line=5)
norm.setup(n=1)
norm.curve(n=1)
mtext("norm.setup(n=1); norm.curve(n=1)", side=1,  line=5)
par(mfrow=c(1,1))


par(mfrow=c(2,2))

## naively scaled,
## areas under the curve are numerically the same but visually different
norm.setup(n=1)
norm.curve(n=1)
norm.setup(n=2)
norm.curve(n=2)
norm.setup(n=4)
norm.curve(n=4)
norm.setup(n=10)
norm.curve(n=10)
mtext("areas under the curve are numerically the same but visually different",
      side=3, outer=TRUE)

## scaled so all areas under the curve are numerically and visually the same
norm.setup(n=1, ylim=c(0,1.3))
norm.curve(n=1)
norm.setup(n=2, ylim=c(0,1.3))
norm.curve(n=2)
norm.setup(n=4, ylim=c(0,1.3))
norm.curve(n=4)
norm.setup(n=10, ylim=c(0,1.3))
norm.curve(n=10)
mtext("all areas under the curve are numerically and visually the same",
      side=3, outer=TRUE)

par(mfrow=c(1,1))


par(old.par)