# norm.curve

From HH v1.18-1
0th

Percentile

##### plot a normal or a t-curve with both x and z axes.

Plot a normal curve or a t-curve with both x (with mean and se as specified) and z or t (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 or t axis. The existence of any of the arguments se, sd, n forces dual x and (z or t) 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. The shaded area is printed on the plot. When the optional argument df.t is specified, then a t-distribution with df.t degrees of freedom is plotted. norm.observed plots a vertical line with arrowhead markers at the location of the observed xbar.

Keywords
hplot, distribution, aplot
##### Usage
norm.setup(xlim.in=c(-2.5,2.5),
ylim.in = c(0, 0.4)/se,
mean=0,
main.in=main.calc,
se=sd/sqrt(n), sd=1, n=1,
df.t=NULL,
...)

norm.curve(mean=0, se=sd/sqrt(n),
critical.values=mean + se*c(-1, 1)*z.975,
z=do.call("seq",
as.list(c((par()\$usr[1:2]-mean)/se, length=109))),
axis.name=ifelse(is.null(df.t) || df.t == Inf, "z", "t"),
second.axis.label.line=3,
sd=1, n=1,
df.t=NULL,
...)

norm.observed(xbar, col="blue")
##### 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.
df.t
Degrees of freedom for the t distribution. When df.t is NULL, the normal distribution is used.
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. Default value is: if (is.null(df.t)) ## normal ifelse(!(missing(se) && missing(sd) && missing(n)), paste("normal density: se =", round(se,3)), "Standard Normal Density N(0,1)") else
z
z-values (standardized to N(0,1)) used as base of plot.
Valid values for shade are "right", "left", "inside", "outside", "none". Default is "right" for one-sided critical.values and "outside" for two-sided critical values.
col
color of the shaded region and the area of the shaded region.
axis.name
defaults to "z" for the standard normal scale centered on the null hypothesis value of the mean or to "t" for the t distribution with df.t degrees of freedom. For alternative hypotheses, the user
second.axis.label.line
Defaults to 3. Normally not needed. When two curves are drawn, one normal and one t, then the second curve needs a different label for the y-axis. Set this value to 4 to avoid overprinting.
xbar
xbar-value of the observed data.
...
Other arguments which are ignored.
##### Aliases
• norm.setup
• norm.curve
• norm.observed
##### 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.observed(112)

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

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

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='green',
norm.curve(crit=1.645, col='red')

norm.setup(xlim=c(-6, 12), se=2)
norm.curve(crit=2*1.645, se=2, mean=2*(1.645+1.281552),
norm.curve(crit=2*1.645, se=2, mean=0,

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.observed(1.2)
norm.setup(n=2)
norm.curve(n=2)
norm.observed(1.2)
norm.setup(n=4)
norm.curve(n=4)
norm.observed(1.2)
norm.setup(n=10)
norm.curve(n=10)
norm.observed(1.2)
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.observed(1.2)
norm.setup(n=2, ylim=c(0,1.3))
norm.curve(n=2)
norm.observed(1.2)
norm.setup(n=4, ylim=c(0,1.3))
norm.curve(n=4)
norm.observed(1.2)
norm.setup(n=10, ylim=c(0,1.3))
norm.curve(n=10)
norm.observed(1.2)
mtext("all areas under the curve are numerically and visually the same",
side=3, outer=TRUE)

par(mfrow=c(1,1))

## t distribution
mu.H0 <- 16
se.val <- .4
df.val <- 10
crit.val <- mu.H0 - qt(.95, df.val) * se.val
mu.alt <- 15
obs.mean <- 14.8

alt.t <- (mu.alt - crit.val) / se.val
norm.setup(xlim=c(12, 19), se=se.val, df.t=df.val)
norm.curve(crit=crit.val, se=se.val, df.t=df.val, mean=mu.alt,
norm.curve(crit=crit.val, se=se.val, df.t=df.val, mean=mu.H0,
norm.observed(obs.mean)

## normal
norm.setup(xlim=c(12, 19), se=se.val)
norm.curve(crit=crit.val, se=se.val, mean=mu.alt,
norm.curve(crit=crit.val, se=se.val, mean=mu.H0,
norm.observed(obs.mean)

## normal and t
norm.setup(xlim=c(12, 19), se=se.val, main="t(6) and normal")
norm.curve(crit=15.5, se=se.val, mean=16.3,
norm.curve(crit=15.5, se.val, df.t=6, mean=14.7,
norm.curve(crit=15.5, se=se.val, mean=16.3,

norm.setup(xlim=c(12, 19), se=se.val, main="t(6) and normal")
norm.curve(crit=15.5, se=se.val, mean=15.5,
par(old.par)