# NormalAndTplot

From HH v3.1-19
0th

Percentile

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

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

Keywords
hplot
##### Usage
NormalAndTplot(mean0, ...)
## S3 method for class 'default':
NormalAndTplot(mean0=0,
mean1=NA,
xbar=NA,
df=Inf, n=1,
sd=1,
xlim=c(-3, 3)*sd/sqrt(n) + range(c(mean0, mean1, xbar), na.rm=TRUE),
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","binomial"),
type=c("hypothesis", "confidence"),
zaxis=FALSE, z1axis=FALSE,
cex.z=.5, cex.prob=.6, cex.top.axis=1,
main=NA, xlab, ylab,
prob.labels=(type=="hypothesis"),
xhalf.multiplier=1,
yhalf.multiplier=1,
cex.main=1,
number.vars=1,
sub=NULL,
NTmethod="default",
power=FALSE,
beta=FALSE,
...)
## S3 method for class 'htest':
NormalAndTplot(mean0, type="hypothesis", xlim=NULL, mean1=NA, ...,
xbar, sd, df, n, alpha.left, alpha.right, ## ignored
distribution.name, sub ## these input arguments 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 $\bar{x}$.
sd
Standard deviation in the data scale $\sigma$ for normal-, or $s$ for $t$-distribution.
df
Degrees of freedom for $t$-distribution.
n
Number of observations per group.
main, xlab, ylab, xlim, ylim, sub
Standard xyplot arguments. Default values are constructed if these arguments are missing. The input value main=NA forces a new constructed main instead of using the
...
number.vars
Number of variables. 1 for a one-sample test, 2 for two-sample tests and paired tests.
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.
zaxis, z1axis
Logical or list. Should the $z$-axis centered on $\mu_0$, or the $z_1$-axis centered on $\mu_1$, be displayed? The list version of the argument must have two components at and labels as specified in
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
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, yhalf.multiplier
Numerical tuning constants to control the width and height 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.
NTmethod
Character string used when shiny=TRUE. It is normally calculated by the methods. NTmethod tells shiny how to use or ignore the df and n sliders.

"htest" objec

power, beta
Logical. If TRUE, then display that graph, else don't display it. Passed forward to powerplot.
##### Details

The graphs produced by this single function cover most of the first semester introductory Statistics course. The htest method plots the results of the stats::t.test function.

NormalAndTplot is built on xyplot. Most of the arguments detailed in xyplot documentation work to control the appearance of the plot.

##### Value

• "trellis" object.

##### Note

This function is built on lattice and latticeExtra. It supersedes the similar function normal.and.t.dist built on base graphics that is used in many displays in the book by Erich Neuwirth and me: R through Excel, Springer (2009). http://www.springer.com/978-1-4419-0051-7. Many details, particularly the alternate color scheme and the concept of floating probability labels, grew out of discussions that Erich and I have had since the book was published. The method for "htest" objects incorporates ideas that Jay Kerns and I developed at the 2011 UseR! conference. This version incorporates some ideas suggested by Moritz Heene.

NTplot

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

x <- rnorm(12, mean=.78)
x.t <- t.test(x)
NTplot(x.t)
NTplot(x.t, type="confidence")
x.tg <- t.test(x, alternative="greater")
NTplot(x.tg)

y <- rnorm(12, mean=-.05)
xy.t <- t.test(x, y)
NTplot(xy.t)
NTplot(xy.t, type="confidence")

NTplot(shiny=TRUE)  ## with any other arguments for initialization of the shiny app.

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

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

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

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

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

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

## confidence intervals

NTplot(mean0=0, xlim=c(-3, 4), type="confidence")
NTplot(xbar=01, xlim=c(-3, 4), type="confidence")
NTplot(mean0=0, xlim=c(-4, 3), type="confidence",
alpha.left=.05,  alpha.right=0)
NTplot(mean0=0, xlim=c(-3, 3), type="confidence",
alpha.left=.025, alpha.right=.025)
NTplot(mean0=95, sd=10, xlim=c(65, 125), type="confidence",
alpha.left=.025, alpha.right=.025)
NTplot(mean0=95, sd=10, xlim=c(65, 125), type="confidence",
alpha.left=.025, alpha.right=.025,
distribution="t", df=10)
Documentation reproduced from package HH, version 3.1-19, License: GPL (>= 2)

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