| norm.curve {Rcmdr.HH} | R Documentation |
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.
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))),
shade, col=par("col"),
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, t.xbar, col="blue")
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 { ## t distribution
if (length(df.t) != 1) stop("df.t must have length 1")
ifelse(!(missing(se) && missing(sd) && missing(n)),
paste("t density: se = ", round(se,3), ", df = ", df.t, sep=""),
paste("t density, df =", df.t))
}
|
z |
z-values (standardized to N(0,1)) used as base of plot. |
shade |
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 must specify either
"z1" or "t1" for the standard normal scale,
or t distibution with df.t degrees of freedom, centered on
the alternate hypothesis value of the mean. |
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. |
t.xbar |
t-value of the observed data under the null hypothesis. |
... |
Other arguments which are ignored. |
Richard M. Heiberger <rmh@temple.edu>
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, (112-100)/5)
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='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',
shade="left", axis.name="z1")
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),
col='green', shade="left", axis.name="z1")
norm.curve(crit=2*1.645, se=2, mean=0,
col='red', 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.observed(1.2, 1.2/(1/sqrt(1)))
norm.setup(n=2)
norm.curve(n=2)
norm.observed(1.2, 1.2/(1/sqrt(2)))
norm.setup(n=4)
norm.curve(n=4)
norm.observed(1.2, 1.2/(1/sqrt(4)))
norm.setup(n=10)
norm.curve(n=10)
norm.observed(1.2, 1.2/(1/sqrt(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.observed(1.2, 1.2/(1/sqrt(1)))
norm.setup(n=2, ylim=c(0,1.3))
norm.curve(n=2)
norm.observed(1.2, 1.2/(1/sqrt(2)))
norm.setup(n=4, ylim=c(0,1.3))
norm.curve(n=4)
norm.observed(1.2, 1.2/(1/sqrt(4)))
norm.setup(n=10, ylim=c(0,1.3))
norm.curve(n=10)
norm.observed(1.2, 1.2/(1/sqrt(10)))
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,
col='green', shade="left", axis.name="t1")
norm.curve(crit=crit.val, se=se.val, df.t=df.val, mean=mu.H0,
col='gray', shade="right")
norm.observed(obs.mean, (obs.mean-mu.H0)/se.val)
## normal
norm.setup(xlim=c(12, 19), se=se.val)
norm.curve(crit=crit.val, se=se.val, mean=mu.alt,
col='green', shade="left", axis.name="z1")
norm.curve(crit=crit.val, se=se.val, mean=mu.H0,
col='gray', shade="right")
norm.observed(obs.mean, (obs.mean-mu.H0)/se.val)
## 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,
col='gray', shade="right")
norm.curve(crit=15.5, se.val, df.t=6, mean=14.7,
col='green', shade="left", axis.name="t1", second.axis.label.line=4)
norm.curve(crit=15.5, se=se.val, mean=16.3,
col='gray', shade="none")
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,
col='gray', shade="right")
norm.curve(crit=15.5, se=se.val, df.t=6, mean=15.5,
col='green', shade="left", axis.name="t1", second.axis.label.line=4)
norm.curve(crit=15.5, se=se.val, mean=15.5,
col='gray', shade="none")
par(old.par)