NormalAndTplot: Specify plots to illustrate Normal and t Hypothesis Tests or Confidence Intervals.

Description

Specify plots to illustrate Normal and t Hypothesis Tests or Confidence Intervals.

Usage

NormalAndTplot(mean0, ...)
## S3 method for class 'default':
NormalAndTplot(mean0=0,
             mean1=NA,
             xbar=NA,
             sd=1, df=Inf, n=1,
             xlim=c(-3, 3), ylim, alpha.right=.05, alpha.left=0,
             float=TRUE, ntcolors="original",
             digits=4, digits.axis=digits, digits.float=digits,
             distribution.name=c("normal","z","t"),
             type=c("hypothesis", "confidence"),
             zaxis=FALSE, z1axis=FALSE,
             cex.z=.5, cex.prob=.6, cex.top.axis=1,
             main, xlab, ylab,
             prob.labels=(type=="hypothesis"),
             xhalf.multiplier=1,
             cex.main=1,
             key.axis.padding=4.5, ...)
## S3 method for class 'htest':
NormalAndTplot(mean0, type="hypothesis", xlim=NULL, ...,
             xbar, sd, df, n, alpha.left, alpha.right, distribution.name, sub
             ## these input arguments sfter ... will be ignored
             )

Arguments

mean0

Null hypothesis $mu_0$. When graphing a confidence interval, mean0 will be used for xbar should xbar itself have the value NA.

mean1

Alternative hypothesis $mu_1$.

xbar

Observed $\bar(x)$.

Standard deviation $\sigma$ for normal-, or $s$ for $t$-distribution.

Degrees of freedom for $t$-distribution.

Number of observations.

main, xlab, ylab, xlim, ylim, sub

Standard xyplot arguments. Default values are constructed if these arguments are missing.

...

Additional xyplot arguments.

alpha.left, alpha.right

For type="hypothesis", the sum of these two numbers is the probability of the Type I Error $\alpha$. When both of these numbers are positive, there is a two-sided test. Note that it is not required that they be equal. If one of the numbers

float

Logical. If TRUE, then the probabilities $\alpha$, $\beta$, power, and $p$-values or the confidence value are displayed on the graph. If FALSE, these values are not displayed.

ntcolors

Vector of colors used in the graph. The default value is "original", which implies the ten colors

c(col.alpha = "blue", col.notalpha = "lightblue",
    col.beta = "red", col.power = "pink", col.pvalue = "green",
    col.pvaluetransluce

digits.axis, digits.float, digits

digits.axis is the number of significant digits for the top axis. digits.float is the number of significant digits for the floating probability values on the graph. digits is a convenience argument to s

distribution.name

Name of distribution.

type

"hypothesis" for a Hypothesis Test graph, or "confidence" for a Confidence Interval graph.

z1axis, zaxis

Logical. Should the $z_1$-axis centered on $mu_1$ or the $z_0$-axis centered on $mu_0$ be displayed?

cex.z, cex.prob, cex.top.axis, cex.main

cex.z is the cex value for the $z$ and $z_1$ axes on the plot. cex.prob is the cex value for the floating probabilities on the graph. cex.top.axis is the cex value

key.axis.padding

tuning constant to create additional room above the graph for a larger cex.main to fit.

prob.labels

logical. If TRUE label the floating probability values with their name, such as $alpha$. If FALSE, then don't label them. The default is TRUE for type="hypothesis" and FALSE

xhalf.multiplier

Numerical tuning constant to control the width of the floating
    probability values.  Empirically, we need a smaller value for the
    shiny
    app then we need for direct writing onto a graphic device.

`Value`

"trellis" object.

`Details`

This graphs produced by this single function cover most of the first semester
introductory Statistics course.

`Examples`

Run this codeNormalAndTplot(mean0=0, mean1=2,  xbar=1.8,  xlim=c(-3, 5))
   NormalAndTplot(mean0=0, mean1=2,  xbar=1.8,  xlim=c(-3, 5), distribution.name="t", df=4)
   NormalAndTplot(mean0=100, sd=12, mean1=113,  xbar=105,  xlim=c(92, 120), n=20)
   NormalAndTplot(mean0=100, sd=12, mean1=113,  xbar=105,  xlim=c(92, 120), n=20, z1axis=TRUE)
   NormalAndTplot(mean0=100, sd=12,  xbar=105,  xlim=c(92, 108), n=20, ntcolors="stoplight")
   NormalAndTplot(xbar=95, sd=10, xlim=c(65, 125), type="confidence",
                  alpha.left=.025, alpha.right=.025)

shiny::runApp(file.path(system.file(package="HH"), "shiny"))

## mean1 and xbar
  NormalAndTplot(mean0=0, mean1=2,  xbar=1.8,  xlim=c(-3, 5))
  NormalAndTplot(mean0=0, mean1=-2, xbar=-1.8, xlim=c(-5, 3),
                 alpha.left=.05,  alpha.right=0)
  NormalAndTplot(mean0=0, mean1=2,  xbar=2.1,  xlim=c(-3, 5),
                 alpha.left=.025, alpha.right=.025)
  NormalAndTplot(mean0=0, mean1=-2, xbar=-2.1, xlim=c(-5, 3),
                 alpha.left=.025, alpha.right=.025)

## mean1
  NormalAndTplot(mean0=0, mean1=2,  xbar=NA, xlim=c(-3, 5))
  NormalAndTplot(mean0=0, mean1=-2, xbar=NA, xlim=c(-5, 3),
                 alpha.left=.05,  alpha.right=0)
  NormalAndTplot(mean0=0, mean1=2,  xbar=NA, xlim=c(-3, 5),
                 alpha.left=.025, alpha.right=.025)
  NormalAndTplot(mean0=0, mean1=-2, xbar=NA, xlim=c(-5, 3),
                 alpha.left=.025, alpha.right=.025)

## xbar
  NormalAndTplot(mean0=0, mean1=NA, xbar=1.8,  xlim=c(-3, 5))
  NormalAndTplot(mean0=0, mean1=NA, xbar=-1.8, xlim=c(-5, 3),
                 alpha.left=.05,  alpha.right=0)
  NormalAndTplot(mean0=0, mean1=NA, xbar=2.1,  xlim=c(-3, 5),
                 alpha.left=.025, alpha.right=.025)
  NormalAndTplot(mean0=0, mean1=NA, xbar=-2.1, xlim=c(-5, 3),
                 alpha.left=.025, alpha.right=.025)

## t distribution
## mean1 and xbar
  NormalAndTplot(mean0=0, mean1=2,  xbar=1.8,  xlim=c(-3, 5),
                 distribution.name="t", df=4)
  NormalAndTplot(mean0=0, mean1=-2, xbar=-1.8, xlim=c(-5, 3),
                 alpha.left=.05,  alpha.right=0, distribution.name="t", df=4)
  NormalAndTplot(mean0=0, mean1=2,  xbar=2.1,  xlim=c(-3, 5),
                 alpha.left=.025, alpha.right=.025, distribution.name="t", df=4)
  NormalAndTplot(mean0=0, mean1=-2, xbar=-2.1, xlim=c(-5, 3),
                 alpha.left=.025, alpha.right=.025, distribution.name="t", df=4)

## mean1
  NormalAndTplot(mean0=0, mean1=2,  xbar=NA, xlim=c(-3, 5),
                 distribution.name="t", df=4)
  NormalAndTplot(mean0=0, mean1=-2, xbar=NA, xlim=c(-5, 3),
                 alpha.left=.05,  alpha.right=0, distribution.name="t", df=4)
  NormalAndTplot(mean0=0, mean1=2,  xbar=NA, xlim=c(-3, 5),
                 alpha.left=.025, alpha.right=.025, distribution.name="t", df=4)
  NormalAndTplot(mean0=0, mean1=-2, xbar=NA, xlim=c(-5, 3),
                 alpha.left=.025, alpha.right=.025, distribution.name="t", df=4)

## xbar
  NormalAndTplot(mean0=0, mean1=NA, xbar=1.8,  xlim=c(-3, 5),
                 distribution.name="t", df=4)
  NormalAndTplot(mean0=0, mean1=NA, xbar=-1.8, xlim=c(-5, 3),
                 alpha.left=.05,  alpha.right=0, distribution.name="t", df=4)
  NormalAndTplot(mean0=0, mean1=NA, xbar=2.1,  xlim=c(-3, 5),
                 alpha.left=.025, alpha.right=.025, distribution.name="t", df=4)
  NormalAndTplot(mean0=0, mean1=NA, xbar=-2.1, xlim=c(-5, 3),
                 alpha.left=.025, alpha.right=.025, distribution.name="t", df=4)

## confidence intervals

  NormalAndTplot(mean0=0, xlim=c(-3, 4), type="confidence")
  NormalAndTplot(xbar=01, xlim=c(-3, 4), type="confidence")
  NormalAndTplot(mean0=0, xlim=c(-4, 3), type="confidence",
                 alpha.left=.05,  alpha.right=0)
  NormalAndTplot(mean0=0, xlim=c(-3, 3), type="confidence",
                 alpha.left=.025, alpha.right=.025)
  NormalAndTplot(mean0=95, sd=10, xlim=c(65, 125), type="confidence",
                 alpha.left=.025, alpha.right=.025)
  NormalAndTplot(mean0=95, sd=10, xlim=c(65, 125), type="confidence",
                 alpha.left=.025, alpha.right=.025,
                 distribution="t", df=10)
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