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HH (version 2.2-17)

norm.curve: 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. It's primary function is drawing a plot. It returns an invisible list containing the values it calculated and displayed on the graph. norm.curve draws the curves and filled areas as requested by the normal.and.t.dist function. Any out of bounds errors (for example, with normal.and.t.dist(deg.free=1)) are suppressed with par(err=-1) by this function and restored to the previous value when the norm.curve function completes.

Usage

normal.and.t.dist(mu.H0          = 0,
                  mu.H1          = NA,
                  obs.mean       = 0,
                  std.dev        = 1,
                  n              = NA,
                  deg.freedom    = NA,
                  alpha.left     = alpha.right,
                  alpha.right    = .05,
                  Use.mu.H1      = FALSE,
                  Use.obs.mean   = FALSE,
                  Use.alpha.left = FALSE,
                  Use.alpha.right= TRUE,
                  hypoth.or.conf = 'Hypoth',
                  xmin           = NA,
                  xmax           = NA,
                  gxbar.min      = NA,
                  gxbar.max      = NA,
                  cex.crit       = 1.2,
                  polygon.density= -1,
                  polygon.lwd    = 4,
                  col.mean       = 'limegreen',
                  col.mean.label = 'limegreen',
                  col.alpha      = 'blue',
                  col.alpha.label= 'blue',
                  col.beta       = 'red',
                  col.beta.label = 'red',
                  col.conf       = 'palegreen',
                  col.conf.arrow = 'darkgreen',
                  col.conf.label = 'darkgreen'
                  )

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,
          polygon.density=-1,
          polygon.lwd=4,
          col.border=ifelse(is.na(polygon.density), FALSE, col),
          ...)

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

Value

beta.left, beta.middle, beta.right, crit.val, crit.val.H1, crit.val.H1.left, crit.val.left, crit.val.left.z, crit.val.z, obs.mean.H0.p.val, obs.mean.H0.side, obs.mean.H0.z, obs.mean.H1.z, obs.mean.x.neg, obs.mean.x.pos, obs.mean.z.pos, standard, standard.error, standard.normalAn invisible list containing the calculated values of probabilities and critical values in the data scale, the null hypothesis z- or t-scale, and the alternative hypothesis z- or t-scale, as specified.

Examples

Run this code
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, gxbar.max=.20)
normal.and.t.dist(std.dev=2, Use.alpha.left=TRUE, deg.free=6,
                  gxbar.max=.20, polygon.density=10)
normal.and.t.dist(std.dev=2, Use.alpha.left=FALSE, deg.free=6,
                  gxbar.max=.20, polygon.density=10,
                  mu.H1=2, Use.mu.H1=TRUE,
                  obs.mean=2.5, Use.obs.mean=TRUE, xmin=-7)
normal.and.t.dist(std.dev=2, hypoth.or.conf="Conf")
normal.and.t.dist(std.dev=2, hypoth.or.conf="Conf", deg.free=8)

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)

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