Package 'CarletonStats'

Anova F test

Description

ANOVA F test when given summarized data (sample sizes, means and standard deviations).

Usage

anovaSummarized(N, mn, stdev)

Arguments

N	a vector with the sample sizes
mn	a vector of means, one for each group in the sample
stdev	a vector of standard deviations, one for each group in the sample

Details

Perform an ANOVA F test when presented with summarized data: sample sizes, sample means and sample standard devations.

Value

Returns invisibly a list

Treatment SS	The treatment sum of squares (also called the "between sum of squares").
Residual SS	Residual sum of squares (also called the "within sum of squares").
Degrees of Freedom	a vector with the numerator and denominator degrees of freedom.
Treatment Mean Square	Treatment SS/numerator DF
Residual Mean Square	Residual SS/denominator DF
Residual Standard Error	Square root of Residual Mean Square
F	the F statistic
P-value	p-value

...

Author(s)

Laura Chihara

Examples

#use the data set chickwts from base R
head(chickwts)

N <- table(chickwts$feed)
stdev <- tapply(chickwts$weight, chickwts$feed, sd)
mn <- tapply(chickwts$weight, chickwts$feed, mean)

anovaSummarized(N, mn, stdev)

---

Bootstrap

Description

Bootstrap a single variable or a grouped variable

Usage

boot(x, ...)

## Default S3 method:
boot(
  x,
  group = NULL,
  statistic = mean,
  conf.level = 0.95,
  B = 10000,
  plot.hist = TRUE,
  plot.qq = FALSE,
  x.name = deparse(substitute(x)),
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  seed = NULL,
  ...
)

## S3 method for class 'formula'
boot(formula, data, subset, ...)

Arguments

x	a numeric vector
...	further arguments to be passed to or from methods.
group	an optional grouping variable (vector), usually a factor variable. If it is a binary numeric variable, it will be coerced to a factor.
statistic	function that computes the statistic of interest. Default is the mean.
conf.level	confidence level for the bootstrap percentile interval. Default is 95%.
B	number of times to resample (positive integer greater than 2).
plot.hist	logical value. If TRUE, plot the histogram of the bootstrap distribution.
plot.qq	Logical value. If TRUE, create a normal quantile-quantile plot of the bootstrap distribution.
x.name	Label for variable name
xlab	an optional character string for the x-axis label
ylab	an optional character string for the y-axis label
title	an optional character string giving the plot title
seed	optional argument to set.seed
formula	a formula y ~ g where y is a numeric vector and g a factor variable with two levels. If g is a binary numeric vector, it will be coerced to a factor variable. For a single numeric variable, formula may also be ~ y.
data	a data frame that contains the variables given in the formula.
subset	an optional expression indicating what observations to use.

Details

Perform a bootstrap of a statistic applied to a single variable, or to the difference of the statistic computed on two samples (using the grouping variable). If x is a binary vector of 0's and 1's and the function is the mean, then the statistic of interest is the proportion.

Observations with missing values are removed.

Value

A vector with the resampled statistics is returned invisibly.

Methods (by class)

• boot(default): Bootstrap a single variable or a grouped variable

• boot(formula): Bootstrap a single variable or a grouped variable

Author(s)

Laura Chihara

References

Tim Hesterberg's website https://www.timhesterberg.net/bootstrap-and-resampling

Examples

#ToothGrowth data (supplied by R)
#bootstrap mean of a single numeric variable
boot(ToothGrowth$len)

#bootstrap difference in mean of tooth length for two groups.
boot(ToothGrowth$len, ToothGrowth$supp, B = 1000)

#same as above using formula syntax
boot(len ~ supp, data = ToothGrowth, B = 1000)

---

Bootstrap the correlation

Description

Bootstrap the correlation of two numeric variables.

Usage

bootCor(x, ...)

## Default S3 method:
bootCor(
  x,
  y,
  conf.level = 0.95,
  B = 10000,
  plot.hist = TRUE,
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  plot.qq = FALSE,
  x.name = deparse(substitute(x)),
  y.name = deparse(substitute(y)),
  seed = NULL,
  ...
)

## S3 method for class 'formula'
bootCor(formula, data, subset, ...)

Arguments

x	a numeric vector.
...	further arguments to be passed to or from methods.
y	a numeric vector.
conf.level	confidence level for the bootstrap ercentile interval.
B	number of times to resample (positive integer greater than 2).
plot.hist	a logical value. If TRUE, plot the bootstrap distribution of the resampled correlation.
xlab	an optional character string for the x-axis label
ylab	an optional character string for the y-axis label
title	an optional character string giving the plot title
plot.qq	a logical value. If TRUE a normal quantile-quantile plot of the bootstraped values is created.
x.name	Label for variable x
y.name	Label for variable y
seed	optional argument to set.seed
formula	a formula of the form lhs ~ rhs where lhs is a numeric variable giving the data values and rhs a factor with two levels giving the corresponding groups.
data	an optional data frame containing the variables in the formula formula. By default the variables are taken from environment(formula).
subset	an optional vector specifying a subset of observations to be used.

Details

Bootstrap the correlation of two numeric variables. The bootstrap mean and standard error are printed as well as a bootstrap percentile confidence interval.

Observations with missing values are removed.

Value

The command returns the correlations of the resampled observations.

Methods (by class)

• bootCor(default): Bootstrap the correlation of two numeric variables.

• bootCor(formula): Bootstrap the correlation of two numeric variables.

Author(s)

Laura Chihara

References

Tim Hesterberg's website https://www.timhesterberg.net/bootstrap-and-resampling

Examples

plot(states03$ColGrad, states03$InfMortality)
bootCor(InfMortality ~ ColGrad, data = states03, B = 1000)
bootCor(states03$ColGrad, states03$InfMortality, B = 1000)

---

Bootstrap paired data

Description

Perform a bootstrap of two paired variables.

Usage

bootPaired(x, ...)

## Default S3 method:
bootPaired(
  x,
  y,
  conf.level = 0.95,
  B = 10000,
  plot.hist = TRUE,
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  plot.qq = FALSE,
  x.name = deparse(substitute(x)),
  y.name = deparse(substitute(y)),
  seed = NULL,
  ...
)

## S3 method for class 'formula'
bootPaired(formula, data, subset, ...)

Arguments

x	a numeric vector.
...	further arguments to be passed to or from methods.
y	a numeric vector.
conf.level	confidence level for the bootstrap percentile interval.
B	number of resamples (positive integer greater than 2).
plot.hist	logical. If TRUE, plot the histogram of the bootstrap distribution.
xlab	an optional character string for the x-axis label
ylab	an optional character string for the y-axis label
title	an optional character string giving the plot title
plot.qq	logical. If TRUE, a normal quantile-quantile plot of the replicates will be created.
x.name	Label for variable x
y.name	Label for variable y
seed	optional argument to set.seed
formula	a formula y ~ x where x, y are both numeric vectors
data	a data frame that contains the variables given in the formula.
subset	an optional expression indicating what observations to use.

Details

The command will compute the difference of x and y and bootstrap the difference. The mean and standard error of the bootstrap distribution will be printed as well as a bootstrap percentile interval.

Observations with missing values are removed.

Value

The command returns a vector with the replicates of the statistic being bootstrapped.

Methods (by class)

• bootPaired(default): Perform a bootstrap of two paired variables.

• bootPaired(formula): Perform a bootstrap of two paired variables.

Author(s)

Laura Chihara

References

Tim Hesterberg's website https://www.timhesterberg.net/bootstrap-and-resampling

Examples

#Bootstrap the mean difference of fat content in vanilla and chocolate ice
#cream. Data are paired becaues ice cream from the same manufacturer will
#have similar content.
Icecream
bootPaired(ChocFat ~ VanillaFat, data = Icecream)
bootPaired(Icecream$VanillaFat, Icecream$ChocFat)

---

Bootstrap the slope of a simple linear regression line

Description

Bootstrap theslope of a simple linear regression line. The bootstrap mean and standard error are printed as well as a bootstrap percentile confidence interval.

Usage

bootSlope(x, ...)

## Default S3 method:
bootSlope(
  x,
  y,
  conf.level = 0.95,
  B = 10000,
  plot.hist = TRUE,
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  plot.qq = FALSE,
  x.name = deparse(substitute(x)),
  y.name = deparse(substitute(y)),
  seed = NULL,
  ...
)

## S3 method for class 'formula'
bootSlope(formula, data, subset, ...)

Arguments

x	a numeric vector.
...	further arguments to be passed to or from methods.
y	a numeric vector.
conf.level	confidence level for the bootstrap percentile interval.
B	number of times to resample (positive integer greater than 2).
plot.hist	a logical value. If TRUE, plot the bootstrap distribution of the resampled slope.
xlab	an optional character string for the x-axis label
ylab	an optional character string for the y-axis label
title	an optional character string giving the plot title
plot.qq	a logical value. If TRUE a normal quantile-quantile plot of the bootstraped values is created.
x.name	Label for variable x
y.name	Label for variable y
seed	optional argument to set.seed
formula	a formula of the form lhs ~ rhs where lhs is a numeric variable giving the data values and rhs a factor with two levels giving the corresponding groups.
data	an optional data frame containing the variables in the formula formula. By default the variables are taken from environment(formula).
subset	an optional vector specifying a subset of observations to be used.

Details

Observations with missing values are removed.

Value

The command returns the slopes of the resampled observations.

Methods (by class)

• bootSlope(default): Bootstrap the slope of a simple linear regression line

• bootSlope(formula): Bootstrap the slope of a simple linear regression line

Author(s)

Adam Loy, Laura Chihara

References

Tim Hesterberg's website https://www.timhesterberg.net/bootstrap-and-resampling

Examples

plot(states03$ColGrad, states03$InfMortality)
bootSlope(InfMortality ~ ColGrad, data = states03, B = 1000)
bootSlope(states03$ColGrad, states03$InfMortality, B = 1000)

---

Calculate a CI from a carlboot object

Description

Calculate percentile confidence intervals for a carlboot object.

Usage

## S3 method for class 'carlboot'
confint(object, parm = NULL, level = 0.95, ...)

Arguments

object	The carlboot object to print.
parm	not used in CarletonStats, just for generic consistency
level	the confidence level
...	not used

---

Confidence Interval Demonstration

Description

Draw many random samples and compute confidence interval. How many intervals capture the true mean?

Usage

confIntDemo(distr = "normal", size = 20, conf.level = 0.95)

Arguments

distr	distribution of the population to be sampled. Options include "normal", "exponential", "uniform" and "binary" (partial match allowed).
size	sample size
conf.level	confidence level.

Details

This simulation will draw 100 random samples from a given population distribution and compute the correpsonding confidence intervals. The 100 intervals will be drawn with an indication of the ones that missed the true mean. A histogram of the population will also be created.

Value

The command invisibly returns the fraction of intervals that capture the true mean.

Author(s)

Laura Chihara

Examples

confIntDemo()

confIntDemo(distr = "exponential", size = 40)

---

Correlation demonstration

Description

For a given r, create a scatterplot of two variables with that correlation.

Usage

corDemo(r = 0)

Arguments

r	a number between -1 and 1. Enter any number r, $latex$, to exit the interactive session[

Details

Demonstrate the concept of correlation by inputting a number between -1 and 1 and seeing a scatter plot of two variables with that correlation. Once you invoke this command, you can continue to enter values for r. Type any number $latex$) to exit.

Author(s)

Laura Chihara

Examples

## Not run: 
corDemo()

## End(Not run)

---

Grouped bar chart

Description

Create a bar chart of a single categorical variable or a grouped bar chart of two categorical variables.

Usage

groupedBar(resp, ...)

## Default S3 method:
groupedBar(
  resp,
  condvar = NULL,
  percent = TRUE,
  print = TRUE,
  cond.name = deparse(substitute(condvar)),
  resp.name = deparse(substitute(resp)),
  ...
)

## S3 method for class 'formula'
groupedBar(formula, data = parent.frame(), subset, ...)

Arguments

resp	a factor variable. If resp is numeric, it will be coerced to a factor variable.
...	further arguments to be passed to or from methods.
condvar	a factor variable to condition on. If NULL, then a bar plot of just the resp variable will be created. If condvar is numeric, it will be coerced to a factor variable.
percent	a logical value. Should the y-axis give percent or counts?
print	a logical value. If TRUE, print out the table.
cond.name	Label for variable condvar.
resp.name	Label for variable resp.
formula	a formula of the form x ~ condvar. If x or condvar is (are) not a factor variable, then it (they) will be coerced into one. Formula can also be ~ x for a single factor variable.
data	a data frame that contains the variables in the formula.
subset	an optional vector specifying a subset of observations to be used.

Details

For a single factor variable, a bar plot. If two factor variables are given, then a bar plot of x conditioned by condvar. This command uses R's table command so missing values are automatically removed.

Value

Returns invisibly a table of the variable(s).

Methods (by class)

• groupedBar(default): Grouped bar chart

• groupedBar(formula): Grouped bar chart

Author(s)

Laura Chihara

Examples

groupedBar(states03$Region)

## Not run: 
groupedBar(states03$DeathPenalty, states03$Region, legend.loc = "topleft")

#Using a formula syntax:

groupedBar(~Region, data = states03)
groupedBar(DeathPenalty ~ Region, data = states03, legend.loc = "topleft")

## End(Not run)

---

Ice cream data

Description

Nutritional information on vanilla and chocolate ice cream from a sample of companies.

Format

A data frame with 39 observations on the following 7 variables.

Brand

Brand name

VanillaCalories

Calories per serving in vanilla

VanillaFat

Fat per serving (g) in vanilla

VanillaSugar

Sugar per serving (g) in vanilla

ChocCalories

Calories per serving in chocolate

ChocFat

Fat per serving (g) in chocolate

ChocSugar

Sugar per serving (g) in chocolate

Source

Data collected by Carleton student Ann Butkowski (2008).

Examples

head(Icecream)
t.test(Icecream$VanillaCalories, Icecream$ChocCalories, paired = TRUE)

---

Milkshakes (chocolate) Nutrional information on chocolate milkshakes from a sample of restaurants.

Description

Milkshakes (chocolate) Nutrional information on chocolate milkshakes from a sample of restaurants.

Format

A data frame with 29 observations on the following 11 variables.

Restaurant

Names of restaurants

Type

Type of restaurant, Dine In Fast Food

Calories

Calories per serving

Fat

Fat per serving (g)

Sodium

Sodium per serving (mg)

Carbs

Carbohydrates per serving (g)

SizeOunces

Size of milkshake (ounces)

CalPerOunce

Calories per ounce

FatPerOunce

Fat per ounce

CarbsPerOunce

Carbohydrates per ounce

Source

Data collected by Carleton students Yoni Blumberg (2013) and Lindsay Guthrie (2013).

---

Missing observations in factors

Description

In data frames with factor variables, convert any observation with "" into <NA>.

Usage

missingLevel(data)

Arguments

data	a data frame with factor variables.

Details

In a factor variable with the level """", this command will convert this to an <NA>.

Value

Returns the same data frame with """" replaced by <NA> in factor variables.

Note

When importing data from comma separated files (for example), missing values in a categorical variable are often denoted by """. We often do not want to treat this as a level of a factor variable in R.

Author(s)

Laura Chihara

---

Permutation test

Description

Permutation test to test a hypothesis involving two samples.

Usage

permTest(x, ...)

## Default S3 method:
permTest(
  x,
  group,
  statistic = mean,
  B = 9999,
  alternative = "two.sided",
  plot.hist = TRUE,
  plot.qq = FALSE,
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  seed = NULL,
  ...
)

## S3 method for class 'formula'
permTest(formula, data = parent.frame(), subset, ...)

Arguments

x	a numeric vector. If the function is the mean (fun = mean) and x is a binary numeric vector of 0's and 1's, then the test is between proportions.
...	further arguments to be passed to or from methods.
group	a factor variable with two levels. If group is a binary numeric vector, it will be coerced into a factor variable.
statistic	the statistic of interest.
B	the number of resamples (positive integer greater than 2).
alternative	the alternative hypothesis. Options are "two.sided", "less" or "greater".
plot.hist	a logical value. If TRUE, the permutation distribution of the statistic is plotted.
plot.qq	a logical value. If TRUE, then a normal quantile-quantile plot of the resampled test statistic is created.
xlab	an optional character string for the x-axis label
ylab	an optional character string for the y-axis label
title	an optional character string giving the plot title
seed	optional argument to set.seed
formula	a formula of the form y ~ group where y is numeric and group is a factor variable.
data	a data frame with the variables in the formula.
subset	an optional expression specifying which observations to keep.

Details

Permutation test to see if a population parameter is the same for two populations. For instance, test $latex$ where $latex$ denotes the population mean. The values of the numeric variable are randomly assigned to the two groups and the difference of the statistic for each group is calculated. The command will print the mean and standard error of the distribution of the test statistic as well as a P-value.

Observations with missing values are removed.

Value

Returns invisibly a vector of the replicates of the test statistic.

Methods (by class)

• permTest(default): Permutation test

• permTest(formula): Permutation test

Author(s)

Laura Chihara

References

Tim Hesteberg's website: https://www.timhesterberg.net/bootstrap-and-resampling

Examples

permTest(states03$ViolentCrime, states03$DeathPenalty)

#using formula syntax
permTest(ViolentCrime ~ DeathPenalty, data = states03, alt = "less")

---

Permutation test for ANOVA F-test

Description

Permutation test to see if the population mean is the same for two or more populations. For instance, test $latex$ where $latex$ denotes the population mean. The values of the numeric variable are randomly assigned to the groups and the ANOVA F statistic is calculated. The command will print the mean and standard error of the distribution of the test statistic as well as a P-value.

Usage

permTestAnova(x, ...)

## Default S3 method:
permTestAnova(
  x,
  group,
  B = 9999,
  plot.hist = TRUE,
  plot.qq = FALSE,
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  seed = NULL,
  ...
)

## S3 method for class 'formula'
permTestAnova(formula, data = parent.frame(), subset, ...)

Arguments

x	a numeric vector.
...	further arguments to be passed to or from methods.
group	a factor variable with two or more levels. If group is a numeric vector, it will be coerced into a factor variable.
B	the number of resamples (positive integer greater than 2).
plot.hist	a logical value. If TRUE, the permutation distribution of the statistic is plotted.
plot.qq	a logical value. If TRUE, then a normal quantile-quantile plot of the resampled test statistic is created.
xlab	an optional character string for the x-axis label
ylab	an optional character string for the y-axis label
title	an optional character string giving the plot title
seed	optional argument to set.seed
formula	a formula of the form y ~ group where y is numeric and group is a factor variable.
data	a data frame with the variables in the formula.
subset	an optional expression specifying which observations to keep.

Details

Observations with missing values are removed.

Value

Returns invisibly a vector of the replicates of the test statistic.

Methods (by class)

• permTestAnova(default): Permutation test for ANOVA F-test

• permTestAnova(formula): Permutation test for ANOVA F-test

Author(s)

Adam Loy, Laura Chihara

References

Tim Hesteberg's website: https://www.timhesterberg.net/bootstrap-and-resampling

Examples

permTestAnova(states03$ViolentCrime, states03$Region, B = 499)

#using formula syntax
## Not run: 
permTestAnova(ViolentCrime ~ Region, data = states03, B = 9999)

## End(Not run)

---

Permutation test for the correlation of two variables.

Description

Hypothesis test for a correlation of two variables. The null hypothesis is that the population correlation is 0.

Usage

permTestCor(x, ...)

## Default S3 method:
permTestCor(
  x,
  y,
  B = 999,
  alternative = "two.sided",
  plot.hist = TRUE,
  plot.qq = FALSE,
  x.name = deparse(substitute(x)),
  y.name = deparse(substitute(y)),
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  seed = NULL,
  ...
)

## S3 method for class 'formula'
permTestCor(formula, data, subset, ...)

Arguments

x	a numeric vector.
...	further arguments to be passed to or from methods.
y	a numeric vector.
B	the number of resamples to draw (positive integer greater than 2).
alternative	alternative hypothesis. Options are "two.sided", "less" or "greater".
plot.hist	a logical value. If TRUE, plot the distribution of the correlations obtained from each resample.
plot.qq	a logical value. If TRUE, plot the normal quantile-quantile plot of the correlations obtained from each resample.
x.name	Label for variable x
y.name	Label for variable y
xlab	an optional character string for the x-axis label
ylab	an optional character string for the y-axis label
title	an optional character string giving the plot title
seed	optional argument to set.seed
formula	a formula y ~ x where x, y are numeric vectors.
data	a data frame that contains the variables given in the formula.
subset	an optional expression indicating what observations to use.

Details

Perform a permutation test to test $latex$, where $latex$is the population correlation. The rows of the second variable are permuted and the correlation is re-computed.

The mean and standard error of the permutation distribution is printed as well as a P-value.

Observations with missing values are removed.

Value

Returns invisibly a vector of the correlations obtained by the randomization.

Methods (by class)

• permTestCor(default): Permutation test for the correlation of two variables.

• permTestCor(formula): Permutation test for the correlation of two variables.

Author(s)

Laura Chihara

References

Tim Hesterberg's website: https://www.timhesterberg.net/bootstrap-and-resampling

Examples

plot(states03$HSGrad, states03$TeenBirths)
cor(states03$HSGrad, states03$TeenBirths)

permTestCor(states03$HSGrad, states03$TeenBirths)
permTestCor(TeenBirths ~ HSGrad, data = states03)

---

Permutation test for paired data.

Description

Permutation test for paired data.

Usage

permTestPaired(x, ...)

## Default S3 method:
permTestPaired(
  x,
  y,
  B = 9999,
  alternative = "two.sided",
  plot.hist = TRUE,
  plot.qq = FALSE,
  x.name = deparse(substitute(x)),
  y.name = deparse(substitute(y)),
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  seed = NULL,
  ...
)

## S3 method for class 'formula'
permTestPaired(formula, data, subset, ...)

Arguments

x	a numeric vector.
...	further arguments to be passed to or from methods.
y	a numeric vector.
B	the number of resamples.
alternative	the alternative hypothesis. Options are "two.sided", "less" and "greater".
plot.hist	a logical value. If TRUE, create a histogram displaying the permutation distribution of the statistic.
plot.qq	a logical value. If TRUE, include a quantile-normal plot of the permuation distribution.
x.name	Label for x variable
y.name	Label for y variable
xlab	an optional character string for the x-axis label
ylab	an optional character string for the y-axis label
title	an optional character string giving the plot title
seed	optional argument to set.seed
formula	a formula of the form y ~ x, where x, y are both numeric variables.
data	an optional data frame containing the variables in the formula. By default the variables are taken from environment(formula).
subset	an optional vector specifying a subset of observations to be used.

Details

For two paired numeric variables with n rows, randomly select k of the n rows (k also is randm) and switch the entries $latex$ and then compute the mean of the difference of the two variables (y-x).

Observations with missing values are removed.

Value

Returns invisibly a vector of the replicates of the test statistic (ex. mean of the difference of the resampled variables).

Methods (by class)

• permTestPaired(default): Permutation test for paired data.

• permTestPaired(formula): Permutation test for paired data.

Author(s)

Laura Chihara

References

Tim Hesterberg's website: https://www.timhesterberg.net/bootstrap-and-resampling

Examples

#Does chocolate ice cream have more calories than vanilla ice cream, on average?
#H0: mean number of calories is the same
#HA: mean number of calories is greater in chocolate ice cream

permTestPaired(Icecream$VanillaCalories, Icecream$ChocCalories, alternative = "less")
permTestPaired(ChocCalories ~ VanillaCalories, data = Icecream, alternative = "greater")

---

Permutation test for the Slope

Description

Hypothesis test for a slope of a simple linear regression model. The null hypothesis is that the population slope is 0.

Usage

permTestSlope(x, ...)

## Default S3 method:
permTestSlope(
  x,
  y,
  B = 999,
  alternative = "two.sided",
  plot.hist = TRUE,
  plot.qq = FALSE,
  x.name = deparse(substitute(x)),
  y.name = deparse(substitute(y)),
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  seed = NULL,
  ...
)

## S3 method for class 'formula'
permTestSlope(formula, data, subset, ...)

Arguments

x	a numeric vector.
...	further arguments to be passed to or from methods.
y	a numeric vector.
B	the number of resamples to draw (positive integer greater than 2).
alternative	alternative hypothesis. Options are "two.sided", "less" or "greater".
plot.hist	a logical value. If TRUE, plot the distribution of the slopes obtained from each resample.
plot.qq	a logical value. If TRUE, plot the normal quantile-quantile plot of the slopes obtained from each resample.
x.name	Label for variable x
y.name	Label for variable y
xlab	an optional character string for the x-axis label
ylab	an optional character string for the y-axis label
title	an optional character string giving the plot title
seed	optional argument to set.seed
formula	a formula y ~ x where x, y are numeric vectors.
data	a data frame that contains the variables given in the formula.
subset	an optional expression indicating what observations to use.

Details

Perform a permutation test to test $latex$, where $latex$is the population slope. The rows of the second variable are permuted and the slope is re-computed.

The mean and standard error of the permutation distribution is printed as well as a P-value.

Observations with missing values are removed.

Value

Returns invisibly a vector of the slopes obtained by the randomization.

Methods (by class)

• permTestSlope(default): Permutation test for the slope

• permTestSlope(formula): Permutation test for the slope

Author(s)

Adam Loy, Laura Chihara

References

Tim Hesterberg's website: https://www.timhesterberg.net/bootstrap-and-resampling

Examples

plot(states03$HSGrad, states03$TeenBirths)
lm(HSGrad ~ TeenBirths, data = states03)

permTestSlope(states03$HSGrad, states03$TeenBirths)
permTestSlope(TeenBirths ~ HSGrad, data = states03)

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Plot the bootstrap distribution in carlboot object

Description

Plot the bootstrap distribution returned as a carlboot object.

Usage

## S3 method for class 'carlboot'
plot(x, bins = 15, size = 5, xlab = NULL, ylab = NULL, title = NULL, ...)

## S3 method for class 'carlperm'
plot(x, bins = 15, size = 5, xlab = NULL, ylab = NULL, title = NULL, ...)

Arguments

x	The carlboot object to print.
bins	number of bins in histogram.
size	size of points.
xlab	an optional character string for the x-axis label
ylab	an optional character string for the y-axis label
title	an optional character string giving the plot title
...	not used

Examples

boot_dist <- boot(ToothGrowth$len, ToothGrowth$supp, B = 1000)
plot(boot_dist)

perm_dist <- permTest(states03$ViolentCrime, states03$DeathPenalty, B = 999)
plot(perm_dist)

---

Print a summary of an carlboot object

Description

Print summary statistics and confidence intervals for an carlboot object.

Usage

## S3 method for class 'carlboot'
print(x, ...)

## S3 method for class 'carlperm'
print(x, ...)

Arguments

x	The carlboot object to print.
...	not used

---

Demonstration of the normal qq-plot.

Description

Demonstrate the normal quantile-quantile plot for samples drawn from different populations.

Usage

qqPlotDemo(
  n = 25,
  distribution = "normal",
  mu = 0,
  sigma = 1,
  df = 10,
  lambda = 10,
  numdf = 10,
  dendf = 16,
  shape1 = 40,
  shape2 = 5
)

Arguments

n	sample size
distribution	population distribution. Options are "normal", "t","exponential", "chi.square", "F" or "beta" (partial matches are accepted).
mu	mean for the normal distribution.
sigma	(positive) standard deviation for the normal distribution.
df	(positive) degrees of freedom for the t-distribution.
lambda	positive rate for the exponential distribution.
numdf	(positive) numerator degrees of freedom for the chi-square distribution.
dendf	(positive) denominator degrees of freedom for the chi-square distribution.
shape1	positive parameter for the beta distribution (shape1 = a).
shape2	positive parameter for the beta distribution (shape2 = b).

Details

Draw a random sample from the chosen sample and display the normal qq-plot as well as the histogram of its distribution.

Value

Returns invisibly the random sample.

Author(s)

Laura Chihara

Examples

qqPlotDemo(n = 30, distr = "exponential", lambda = 1/3)

---

US government data, 2003

Description

Census data on the 50 states from 2003.

Format

A data frame with 50 observations on the following 24 variables.

State

the 50 states

Region

a factor with levels Midwest, Northeast, South, West

Pop

Population in 1000

Births

Number of births

Deaths

Number of deaths

Pop18

Percent of population 18 years of age or younger

Pop65

Percent of population 65 years of age or older

HSGrad

Percent of population 25 years of age or older with a high school degree

ColGrad

Percent of population 25 years of age or older with a college degree

TeacherPay

Average teachers salary in dollars

InfMortality

Infant mortality per 1000 live births

TeenBirths

Live births per 1000 15-19 year old females

ViolentCrime

Violent crime per 100000 population

PropertyCrime

Property crime per 100000 population

DeathPenalty

State has death penalty?

Executions

Number of executions 1977-2003

Poverty

Percent of populaton below the poverty level

Unemp

Percent unemployed (of population 16 years or older)

Uninsured

Percent uninsured (3 year aveage)

Income

Median household income in 1998 dollars

Earnings

Average hourly earnings of production workers in manufacturing

Heart

Deaths by heart disease per 100000 population

Vehicles

Deaths by motor vehicle accidents per 100000 population

Homeowners

Home ownership rate

Source

United States Census Bureau https://www.census.gov/

---

Stem and leaf plot

Description

Stem and leaf plot. Will accept a factor variable as a second argument to create stem plots for each of the levels.

Usage

stemPlot(x, ...)

## Default S3 method:
stemPlot(x, grpvar = NULL, varname = NULL, grpvarname = NULL, ...)

## S3 method for class 'formula'
stemPlot(formula, data = parent.frame(), subset, ...)

Arguments

x	a numeric variable.
...	further arguments to be passed to or from methods.
grpvar	a factor variable. A stem plot of x will be created for each level of the factor variable.
varname	name of the numeric variable. This is for printing the output only. Change if you want to print out a name different from the actual variable name.
grpvarname	name of the factor variable. This is for printing the output only. Change if you want to print out a name different from the actual variable name.
formula	a formula of the form x ~ grpvar where x is numeric and grpvar is a factor variable.
data	a data frame with the variables in the formula.
subset	an optional expression specifying which observations to keep.

Details

This command is just an enhanced version of R's stem command. It allows the user to create the stem plot for a numeric variable grouped by the levels of a factor variable.

Methods (by class)

• stemPlot(default): Stem and leaf plot

• stemPlot(formula): Stem and leaf plot

Author(s)

Laura Chihara

Examples

stemPlot(states03$Births, states03$Region)

stemPlot(Births ~ Region, data = states03)

---

Print a summary of an carlboot object

Description

Print summary statistics and confidence intervals, if desired, for an lmeresamp object.

Usage

## S3 method for class 'carlboot'
summary(object, ...)

## S3 method for class 'carlperm'
summary(object, ...)

Arguments

object	The carlboot object to print.
...	not used

Examples

boot_dist <- boot(ToothGrowth$len, ToothGrowth$supp, B = 1000)
summary(boot_dist)
perm_dist <- permTest(states03$ViolentCrime, states03$DeathPenalty, B = 999)
summary(perm_dist)

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