norm.curve

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. normal.and.t.dist is a driver function that uses all the others. In R, when RExcel is running (currently only on Windows), it has the side effect of leaving variables in the work space which are intended to be used by the normal.and.t Excel worksheet in the RExcel package for R on Windows. There are no side effects in S-Plus or in R when RExcel is not running.

Keywords
hplot, distribution, aplot
Usage
normal.and.t.dist(std.dev        = 1,
                  n              = NA,
                  deg.freedom    = NA,
                  mu.H0          = 0,
                  xmin           = NA,
                  xmax           = NA,
                  fx.min         = NA,
                  fx.max         = NA,
                  Use.alpha.right= TRUE,
                  alpha.right    = .05,
                  Use.alpha.left = FALSE,
                  alpha.left     = alpha.right,
                  Use.mu.H1      = FALSE,
                  mu.H1          = NA,
                  Use.obs.mean   = FALSE,
                  obs.mean       = NA,
                  hypoth.or.conf = 'Hypoth',
                  col.mean       = 'lime green',
                  col.alpha      = 'blue',
                  col.beta       = 'red',
                  col.conf       = 'pale green',
                  col.conf.arrow = 'dark green',
                  col.mean.label = 'lime green',
                  col.alpha.label= 'blue',
                  col.beta.label = 'red',
                  col.conf.label = 'dark green',
                  cex.crit       = 1.2
                  )

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,
           Use.obs.mean=TRUE,
            ...)

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="blue",
          axis.name=ifelse(is.null(df.t) || df.t==Inf, "z", "t"),
          second.axis.label.line=3,
          sd=1, n=1,
          df.t=NULL,
          axis.name.expr=axis.name,
          Use.obs.mean=TRUE,
          col.label=col,
          hypoth.or.conf="Hypoth",
          col.conf.arrow=par("col"),
          col.conf.label=par("col"),
          col.crit=ifelse(hypoth.or.conf=="Hypoth", 'blue', col.conf.arrow),
          cex.crit=1.2,
          ...)

norm.observed(xbar, t.xbar, t.xbar.H1=NULL,
              col="green",
              p.val=NULL, p.val.x=par()$usr[2]+ left.margin,
              t.or.z=ifelse(is.null(deg.free) || deg.free==Inf, "z", "t"),
              t.or.z.position=par()$usr[1]-left.margin,
              cex.small=par()$cex*.7, col.label=col,
              xbar.negt=NULL, cex.large=par()$cex,
              left.margin=.15*diff(par()$usr[1:2]),
              sided="", deg.free=NULL)

norm.outline(dfunction, left, right, mu.H0, se, deg.free=NULL,
             col.mean="green")
Arguments
xlim.in, ylim.in, xmin, xmax, fx.min, fx.max
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, std.dev, 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, deg.freedom
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.
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.
col.label, col.alpha, col.alpha.label
color of the area of the shaded rejection region and its label.
col.beta, col.beta.label
color of the area of the shaded region For Type II error and its label.
hypoth.or.conf
"Hypoth" or "Conf"
col.conf
Color of plot within confidence limits.
col.conf.arrow
Color of arrow denoting confidence limits.
col.conf.label
Color of label giving confidence level.
col.mean.label
Color of label for observed mean.
col.crit, cex.crit
Color and cex of critical values.
axis.name, axis.name.expr
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, obs.mean
xbar-value of the observed data.
t.xbar
t-value of the observed data under the null hypothesis.
...
Other arguments which are ignored.
Use.obs.mean
Logical. If TRUE, then include "mean" on the plot.
alpha.right, alpha.left
Area in tail of curve.
Use.alpha.right, Use.alpha.left
Logical. If TRUE, then include the specified $\alpha$ on the plot.
t.xbar.H1
t-value under alternate hypothesis.
p.val
under specified hypothesis
p.val.x,t.or.z.position
location on x-axis to put label
t.or.z
label for axis.
cex.small
cex for left margin labels of axis.
xbar.negt
location in data scale of negative t- or z-value corresponding to observed x-value. Used for two-sided p-values.
cex.large
cex for labels in top margin.
left.margin
distance to the left of par()$usr[1].
sided
type of test.
deg.free
degrees of freedom or NULL.
dfunction
"dnorm" or "dt"
left
left end of interval
right
right end of interval
mu.H0, mu.H1
mean under the null hypothesis and alternative hypothesis.
Use.mu.H1
Logical. If TRUE, then include mu.H1 on the plot.
col.mean
Color of outline.
Aliases
  • norm.setup
  • norm.curve
  • norm.observed
  • norm.outline
  • normal.and.t.dist
Examples
normal.and.t.dist()
normal.and.t.dist(xmin=-4)
normal.and.t.dist(std.dev=2)
normal.and.t.dist(std.dev=2, Use.alpha.left=TRUE, deg.free=6)
normal.and.t.dist(std.dev=2, Use.alpha.left=TRUE, deg.free=6, fx.max=.20)


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.outline("dnorm", 112, par()$usr[2], 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)
Documentation reproduced from package HH, version 2.1-12, License: GPL (>= 2)

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