norm.curve {HH}R Documentation

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

Description

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.

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       = 0,
                  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=if(se==0) 0 else 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 { ## 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.
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 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. The axis.name.expr allows R users to say expression(z[1]) to get real subscripts.
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 α 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.

Author(s)

Richard M. Heiberger <rmh@temple.edu>

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)

[Package HH version 2.1-25 Index]