Title:	Companion to the Book "Investigating Statistical Concepts, Applications, and Methods"
Version:	1.0.0
Description:	Introductory statistics methods to accompany "Investigating Statistical Concepts, Applications, and Methods" (ISCAM) by Beth Chance & Allan Rossman (2024) https://rossmanchance.com/iscam4/. Tools to introduce statistical concepts with a focus on simulation approaches. Functions are verbose, designed to provide ample output for students to understand what each function does. Additionally, most functions are accompanied with plots. The package is designed to be used in an educational setting alongside the ISCAM textbook.
License:	MIT + file LICENSE
URL:	https://iscam4.github.io/ISCAM/, https://github.com/ISCAM4/ISCAM
BugReports:	https://github.com/ISCAM4/ISCAM/issues
Depends:	R (≥ 3.5)
Imports:	graphics, stats
Suggests:	testthat (≥ 3.0.0), usethis, vdiffr (≥ 1.0.8)
Config/testthat/edition:	3
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.3
NeedsCompilation:	no
Packaged:	2025-10-23 17:19:28 UTC; visru
Author:	Beth Chance [cre, aut, cph], Visruth Srimath Kandali [aut]
Maintainer:	Beth Chance <bchance@calpoly.edu>
Repository:	CRAN
Date/Publication:	2025-11-11 09:20:16 UTC

ISCAM: Companion to the Book "Investigating Statistical Concepts, Applications, and Methods"

Description

Introductory statistics methods to accompany "Investigating Statistical Concepts, Applications, and Methods" (ISCAM) by Beth Chance & Allan Rossman. Tools to introduce statistical concepts with a focus on simulation approaches. Functions are verbose, designed to provide ample output for students to understand what each function does. Additionally, most functions are accompanied with plots. The package is designed to be used in an educational setting alongside the ISCAM textbook.

Author(s)

Maintainer: Beth Chance bchance@calpoly.edu [copyright holder]

Authors:

• Visruth Srimath Kandali public@visruth.com (ORCID)

See Also

Useful links:

• https://iscam4.github.io/ISCAM/

• https://github.com/ISCAM4/ISCAM

• Report bugs at https://github.com/ISCAM4/ISCAM/issues

Template documentation for plotting parameters

Description

Template documentation for plotting parameters

Arguments

Template documentation for plotting parameters

Description

Template documentation for plotting parameters

Arguments

Cloud Seeding Data

Description

Our lives depend on rainfall. Consequently, scientists have long investigated whether humans can intervene and, as needed, help nature produce more rainfall. In one study, researchers in southern Florida explored whether injecting silver iodide into cumulus clouds would lead to increased rainfall. On each of 52 days that were judged to be suitable for cloud seeding, a target cloud was identified and a plane flew through the target cloud in order to seed it. Randomization was used to determine whether or not to load a seeding mechanism and seed the target cloud with silver iodide on that day. Radar was used to measure the volume of rainfall from the selected cloud during the next 24 hours. The results from Simpson, Olsen, and Eden, (1975) measure rainfall in volume units of acre-feet, “height” of rain across one acre.

Usage

CloudSeeding

Format

CloudSeeding

A data frame with 52 rows and 2 columns:

treatment

Whether a cloud was seeded with silver iodide or not.

rainfall

Volume of rainfall during the next 24 hours, in acre-feet.

Source

doi:10.2307/1268346

Flint Michigan Lead Data

Description

Lead poisoning can be a serious problem associated with drinking tap water. Many older water pipes are made of lead. Over time, the pipes corrode, releasing lead into the drinking water. In April 2014, the city of Flint Michigan switched its water supply to the Flint River in an effort to save money. The Michigan Department of Environmental Quality (MDEQ) tested the water at the time and declared it safe to drink. Officials were supposed to test at least 100 homes, targeting those most at risk. The U.S. Environmental Protection Agency (EPA)’s Lead and Copper Rule states that if lead concentrations exceed an action level of 15 parts per billion (ppb) in more than 10% of homes sampled, then actions must be undertaken to control corrosion, and the public must be informed.

Usage

FlintMDEQ

Format

flint

A data frame with 71 rows and 1 column:

lead

Lead concentration per household, measured in parts per billion.

Infant Data

Description

In a study reported in the November 2007 issue of Nature, researchers investigated whether infants take into account an individual’s actions towards others in evaluating that individual as appealing or aversive, perhaps laying for the foundation for social interaction (Hamlin, Wynn, and Bloom, 2007). In other words, do children who aren’t even yet talking still form impressions as to someone’s friendliness based on their actions? In one component of the study, 10-month-old infants were shown a “climber” character (a piece of wood with “googly” eyes glued onto it) that could not make it up a hill in two tries. Then the infants were shown two scenarios for the climber’s next try, one where the climber was pushed to the top of the hill by another character (the “helper” toy) and one where the climber was pushed back down the hill by another character (the “hinderer” toy). The infant was alternately shown these two scenarios several times. Then the child was presented with both pieces of wood (the helper and the hinderer characters) and asked to pick one to play with. Videos demonstrating this component of the study can be found at https://campuspress.yale.edu/infantlab/media/.

Usage

Infant

Format

Infant

A data frame with 16 rows and 1 column:

choice

Whether a baby selected the "helper" or "hinderer" toy.

Source

https://pubmed.ncbi.nlm.nih.gov/18033298/

Sleep Deprivation Data

Description

Researchers have established that sleep deprivation has a harmful effect on visual learning (the subject does not consolidate information to improve on the task). Stickgold, James, and Hobson (2000) investigated whether subjects could “make up” for sleep deprivation by getting a full night’s sleep in subsequent nights. This study involved randomly assigning 21 subjects (volunteers between the ages of 18 and 25) to one of two groups: one group was deprived of sleep on the night following training with a visual discrimination task, and the other group was permitted unrestricted sleep on that first night. Both groups were allowed unrestricted sleep on the following two nights, and then were re-tested on the third day. Subjects’ performance on the test was recorded as the minimum time (in milliseconds) between stimuli appearing on a computer screen for which they could accurately report what they had seen on the screen. Previous studies had shown that subjects deprived of sleep performed significantly worse the following day, but it was not clear how long these negative effects would last. The data presented here are the improvements in reaction times (in milliseconds), so a negative value indicates a decrease in performance.

Usage

SleepDeprivation

Format

SleepDeprivation

A data frame with 21 rows and 2 columns:

sleepcondition

The sleep condition the subject was in.

improvement

The subject's improvement in reaction times, measured in milliseconds.

Source

https://www.nature.com/articles/nn1200_1237

Elephant Walking Data

Description

Researchers Holdgate et al. (2016) studied walking behavior of elephants in North American zoos to see whether there is a difference in average distance traveled by African and Asian elephants in captivity. They put GPS loggers on 33 African elephants and 23 Asian elephants, and measured the distance (in kilometers) the elephants walked per day.

Usage

elephants

Format

Elephants

A data frame with 56 rows and 2 columns:

Species

What species this Elephant was.

Distance

How many kilometers they walked per day.

Source

doi:10.1371/journal.pone.0150331

Overlay an Exponential Density Function on Histogram

Description

addexp creates a histogram of x and overlays an exponential density function with \lambda = \frac{1}{mean}.

Usage

iscamaddexp(
  x,
  main = "Histogram with exponential curve",
  xlab = deparse(substitute(x)),
  bins = NULL
)

Arguments

Value

A histogram of x overlayed with an exponential density function.

Examples

set.seed(0)
x <- rexp(100, rate = 0.5)
iscamaddexp(x)
iscamaddexp(x, main = "Your Active Title", xlab = "Exponential Data", bins = 20)

Overlay a Log Normal Density Function on Histogram

Description

addlnorm creates a histogram of x and overlays a log normal density function.

Usage

iscamaddlnorm(
  x,
  main = "Histogram with log-normal curve",
  xlab = deparse(substitute(x)),
  bins = NULL
)

Arguments

Value

A histogram of x overlayed with an log normal density function.

Examples

set.seed(0)
x <- rlnorm(100)
iscamaddlnorm(x)
iscamaddlnorm(x, main = "Your Active Title", xlab = "Log Normal Data", bins = 20)

Overlay a Normal Density Function on Histogram

Description

addnorm creates a histogram of x and overlays a normal density function.

Usage

iscamaddnorm(
  x,
  main = "Histogram with normal curve",
  xlab = deparse(substitute(x)),
  bins = NULL
)

Arguments

Value

A histogram of x overlayed with an normal density function.

Examples

set.seed(0)
x <- rnorm(100)
iscamaddnorm(x)
iscamaddnorm(x, main = "Your Active Title", xlab = "Normal Data", bins = 20)

Overlay a t Density Function on Histogram

Description

Overlay a t Density Function on Histogram

Usage

iscamaddt(
  x,
  df,
  main = "Histogram with t curve",
  xlab = deparse(substitute(x)),
  bins = NULL
)

Arguments

Value

A histogram of x overlayed with an t density function.

Examples

set.seed(0)
x <- rt(100, 30)
iscamaddt(x, 30)
iscamaddt(x, 30, main = "Your Active Title", xlab = "t Data", bins = 20)

Overlay a t Density Function and a Normal Density Function on Histogram

Description

Overlay a t Density Function and a Normal Density Function on Histogram

Usage

iscamaddtnorm(
  x,
  df,
  main = "Histogram with t and normal curve",
  xlab = deparse(substitute(x)),
  bins = NULL
)

Arguments

Value

A histogram of x overlayed with an t density function and a normal density function.

Examples

set.seed(0)
x <- rt(100, 5)
iscamaddtnorm(x, 5)
iscamaddtnorm(x, 5, main = "Your Active Title", xlab = "t Data", bins = 20)

Overlays Normal Approximation onto Binomial

Description

binomnorm creates a binomial distribution of the given inputs and overlays a normal approximation.

Usage

iscambinomnorm(k, n, prob, direction, verbose = TRUE)

Arguments

Value

A plot of the binomial distribution overlayed with the normal approximation

Examples

iscambinomnorm(k = 10, n = 20, prob = 0.5, direction = "two.sided")

Rejection Region for Binomial

Description

binompower determines the rejection region corresponding to the level of significance and the first probability and shows the binomial distribution shading its corresponding region.

Usage

iscambinompower(LOS, n, prob1, alternative, prob2 = NULL, verbose = TRUE)

Arguments

Value

A plot of the binomial distribution with the rejection region highlighted.

Examples

iscambinompower(LOS = 0.05, n = 20, prob1 = 0.5, alternative = "less")

iscambinompower(LOS = 0.05, n = 20, prob1 = 0.5, alternative = "greater", prob2 = 0.75)

iscambinompower(LOS = 0.10, n = 30, prob1 = 0.4, alternative = "two.sided")

iscambinompower(LOS = 0.10, n = 30, prob1 = 0.4, alternative = "two.sided", prob2 = 0.2)

Calculate Binomial Tail Probabilities

Description

binomprob calculates the probability of the number of success of interest using a binomial distribution and plots the distribution.

Usage

iscambinomprob(k, n, prob, lower.tail, verbose = TRUE)

Arguments

Value

The probability of the binomial distribution along with a graph of the distribution.

Examples

iscambinomprob(k = 5, n = 20, prob = 0.4, lower.tail = TRUE)
iscambinomprob(k = 15, n = 30, prob = 0.3, lower.tail = FALSE)
iscambinomprob(k = 22, n = 25, prob = 0.9, lower.tail = TRUE)

Exact Binomial Test

Description

binomtest calculates performs an exact binomial test and graphs the binomial distribution and/or binomial confidence interval.

Usage

iscambinomtest(
  observed,
  n,
  hypothesized = NULL,
  alternative,
  conf.level = NULL,
  verbose = TRUE
)

Arguments

Value

a list of the p-value along with lower and upper bound for the calculated confidence interval.

Examples

iscambinomtest(
  observed = 17,
  n = 25,
  hypothesized = 0.5,
  alternative = "greater"
)

iscambinomtest(
  observed = 12,
  n = 80,
  hypothesized = 0.10,
  alternative = "two.sided",
  conf.level = 0.95
)

iscambinomtest(
  observed = 0.14,
  n = 100,
  hypothesized = 0.20,
  alternative = "less"
)

iscambinomtest(observed = 17, n = 25, conf.level = 0.95)

iscambinomtest(observed = 12, n = 80, conf.level = c(0.90, 0.95, 0.99))

A box plot

Description

boxplot plots the given data in a box plot. If a second categorical variable is given, the data is grouped by this variable.

Usage

iscamboxplot(
  response,
  explanatory = NULL,
  main = "",
  xlab = "",
  ylab = substitute(explanatory)
)

Arguments

Value

A box plot.

Examples

iscamboxplot(
  mtcars$mpg,
  main = "mtcars Cylinders Dotplot",
  xlab = "Number of Cylinders"
)
iscamboxplot(
  mtcars$mpg,
  mtcars$am,
  main = "Automatic Cars Have Better Mileage on Average",
  xlab = "Mileage (miles per gallon)",
  ylab = "Automatic (yes coded as 1)"
)

Chi-Square Probability

Description

chisqrprob returns the upper tail probability for the given chi-square statistic and degrees of freedom.

Usage

iscamchisqprob(xval, df, verbose = TRUE)

Arguments

Value

The upper tail probability for the chi-square distribution, and a plot of the chi-square distribution with the statistic and more extreme shaded.

Examples

iscamchisqprob(5, 3)

A dot plot

Description

dotplot creates a horizontal dot plot. If a second categorical variable is given, the data is grouped by this variable. Use names & mytitle to specify the labels and title.

Usage

iscamdotplot(
  response,
  explanatory = NULL,
  main = "",
  xlab = substitute(response),
  ylab = substitute(explanatory)
)

Arguments

Value

A dot plot.

Examples

iscamdotplot(
  mtcars$cyl,
  main = "mtcars Cylinders Dotplot",
  xlab = "Number of Cylinders"
)
iscamdotplot(
  mtcars$mpg,
  mtcars$am,
  main = "Automatic Cars Have Better Mileage on Average",
  xlab = "Mileage (miles per gallon)",
  ylab = "Automatic (yes coded as 1)"
)

Hypergeometric p-value and Distribution Overlaid with Normal Distribution

Description

Hypergeometric p-value and Distribution Overlaid with Normal Distribution

Usage

iscamhypernorm(k, total, succ, n, lower.tail, verbose = TRUE)

Arguments

Value

Tail probabilities from the hypergeometric distribution, hypergeometric distribution with normal distribution overlayed with the observed statistic and more extreme shaded.

Examples

iscamhypernorm(1, 20, 5, 10, TRUE)

Hypergeometric p-value and Distribution

Description

Hypergeometric p-value and Distribution

Usage

iscamhyperprob(k, total, succ, n, lower.tail, verbose = TRUE)

Arguments

Value

Tail probabilities from the hypergeometric distribution, hypergeometric distribution with the observed statistic and more extreme shaded.

Examples

iscamhyperprob(1, 20, 5, 10, TRUE)

Inverse Binomial Probability

Description

Inverse Binomial Probability

Usage

iscaminvbinom(alpha, n, prob, lower.tail, verbose = TRUE)

Arguments

Value

numeric which achieves at most the stated probability

Examples

iscaminvbinom(alpha = 0.05, n = 30, prob = 0.5, lower.tail = TRUE)

iscaminvbinom(alpha = 0.05, n = 30, prob = 0.5, lower.tail = FALSE)

iscaminvbinom(alpha = 0.01, n = 60, prob = 0.10, lower.tail = FALSE)

Inverse Normal Calculation

Description

Inverse Normal Calculation

Usage

iscaminvnorm(prob1, mean = 0, sd = 1, Sd = sd, direction, verbose = TRUE)

Arguments

Value

a plot of the normal distribution with the quantile of the specified probability highlighted.

Examples

iscaminvnorm(0.05, direction = "below")
iscaminvnorm(0.90, mean = 100, sd = 15, direction = "above")
iscaminvnorm(0.10, direction = "outside")
iscaminvnorm(0.95, direction = "between")

Inverse T Calculation

Description

invt calculates the t quantile of a specified probability.

Usage

iscaminvt(prob, df, direction, verbose = TRUE)

Arguments

Value

The t value for the specified probability.

Examples

iscaminvt(0.05, df = 15, direction = "below")
iscaminvt(0.10, df = 25, direction = "above")
iscaminvt(0.95, df = 30, direction = "between")
iscaminvt(0.05, df = 20, direction = "outside")

Rejection Region for Normal

Description

normpower determines the rejection region corresponding to the level of significance and the first probability and shows the normal distribution shading its corresponding region.

Usage

iscamnormpower(LOS, n, prob1, alternative, prob2, verbose = TRUE)

Arguments

Value

A plot of the normal distribution with the rejection region highlighted.

Examples

iscamnormpower(0.05, n = 100, prob1 = 0.5, alternative = "greater", prob2 = 0.6)
iscamnormpower(0.10, n = 50, prob1 = 0.25, alternative = "less", prob2 = 0.15)
iscamnormpower(0.05, n = 200, prob1 = 0.8, alternative = "two.sided", prob2 = 0.7)

Normal Tail Probability

Description

normprob finds a p-value and plots it onto a normal distribution with mean and standard deviation as specified. The function can find the probability above, below, between, or outside of the observed value, as specified by directions.

Usage

iscamnormprob(
  xval,
  mean = 0,
  sd = 1,
  direction,
  label = NULL,
  xval2 = NULL,
  digits = 4,
  verbose = TRUE
)

Arguments

Value

a p-value and a plot of the normal distribution with shaded area representing probability of the observed value or more extreme occurring.

Examples

iscamnormprob(1.96, direction = "above")
iscamnormprob(-1.5, mean = 1, sd = 2, direction = "below")
iscamnormprob(0, xval2 = 1.5, direction = "between")
iscamnormprob(-1, xval2 = 1, direction = "outside")

One Proportion Z-Test and Interval

Description

iscamonepropztest calculates a one-proportion z-test and/or a corresponding confidence interval.

Usage

iscamonepropztest(
  observed,
  n,
  hypothesized = NULL,
  alternative = "two.sided",
  conf.level = NULL,
  verbose = TRUE
)

Arguments

Value

This function prints the results of the one-proportion z-test and/or the confidence interval. It also generates plots to visualize the test and interval.

Examples

iscamonepropztest(observed = 35, n = 50, hypothesized = 0.5)

iscamonepropztest(
  observed = 0.8,
  n = 100,
  hypothesized = 0.75,
  alternative = "greater",
  conf.level = 0.95
)

iscamonepropztest(observed = 60, n = 100, conf.level = 0.90)

One Sample T-Test

Description

onesamplet calculates a one sample t-test and/or interval from summary statistics. It defaults to a hypothesized population mean of 0. You can optionally set an alternative hypothesis and confidence level for a two-sided confidence interval.

Usage

iscamonesamplet(
  xbar,
  sd,
  n,
  hypothesized = 0,
  alternative = NULL,
  conf.level = NULL,
  verbose = TRUE
)

Arguments

Value

The t value, p value, and confidence interval.

Examples

iscamonesamplet(
  xbar = 2.5,
  sd = 1.2,
  n = 30,
  alternative = "greater",
  hypothesized = 2
)
iscamonesamplet(
  xbar = 10.3,
  sd = 2,
  n = 50,
  alternative = "less",
  hypothesized = 11
)
iscamonesamplet(
  xbar = 98.2,
  sd = 2,
  n = 100,
  alternative = "two.sided",
  conf.level = 0.95
)
iscamonesamplet(xbar = 55, sd = 5, n = 40, conf.level = 0.99)

Some Summary Statistics

Description

summary calculates the five number summary, mean, and standard deviation of the quantitative variable x. An optional second, categorical variable can be specified and values will be calculated separately for each group. The number of digits in output can also be specified. Skewness is sample skewness: g_1 := \frac{m_3}{m_2^{3/2}}, where m_2 := \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2 and m_3 := \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^3 are the second and third central sample moments.

Usage

iscamsummary(x, explanatory = NULL, digits = 3)

Arguments

Value

A table with some summary statistics of x.

Examples

set.seed(0)
fake_data <- rnorm(30) # simulating some data
groups <- sample(c("group1","group2"), 30, TRUE)
iscamsummary(fake_data)
iscamsummary(fake_data, explanatory = groups, digits = 2) # with groups

Tail Probability for t-distribution

Description

Tail Probability for t-distribution

Usage

iscamtprob(xval, df, direction, xval2 = NULL, verbose = TRUE)

Arguments

Value

The tail probability in the specified direction using the given parameters.

Examples

iscamtprob(xval = -2.05, df = 10, direction = "below")
iscamtprob(xval = 1.80, df = 20, direction = "above")
iscamtprob(xval = -2, xval2 = 2, df = 15, direction = "between")
iscamtprob(xval = -2.5, xval2 = 2.5, df = 25, direction = "outside")

Two Proportion Z-Test and Interval

Description

iscamtwopropztest calculates a two-proportion z-test and/or a corresponding confidence interval.

Usage

iscamtwopropztest(
  observed1,
  n1,
  observed2,
  n2,
  hypothesized = 0,
  alternative = NULL,
  conf.level = NULL,
  datatable = NULL,
  verbose = TRUE
)

Arguments

Value

This function prints the results of the two-proportion z-test and/or the confidence interval. It also generates plots to visualize the test and interval.

Examples

iscamtwopropztest(observed1 = 35, n1 = 50, observed2 = 28, n2 = 45)

iscamtwopropztest(
  observed1 = 0.8,
  n1 = 100,
  observed2 = 0.6,
  n2 = 80,
  hypothesized = 0,
  alternative = "greater",
  conf.level = 0.95
)

iscamtwopropztest(observed1 = 60, n1 = 100, observed2 = 45, n2 = 90, conf.level = 0.90)

Two Sample T-Test

Description

twosamplet calculates a two sample t-test and/or interval from summary data. It defaults to a hypothesized population mean difference of 0. You can optionally set an alternative hypothesis and confidence level for a two-sided confidence interval.

Usage

iscamtwosamplet(
  x1,
  sd1,
  n1,
  x2,
  sd2,
  n2,
  hypothesized = 0,
  alternative = NULL,
  conf.level = 0,
  verbose = TRUE
)

Arguments

Value

The t value, p value, and confidence interval.