In apjacobson/iscam: Introduction to Fundamental Concepts and Various Applications of Statistics

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Introduction

This package contains a variety of R functions to accompany the introductory statistics textbook, Investigating Statistical Concepts, Applications, and Methods (ISCAM), written by Dr. Allan Rossman and Dr. Beth Chance. These functions are to aid students in their investigations, assignments, and projects. The functions are categorized into 5 groups: Data Visualization, Summary Statistics, Hypothesis Testing, Quantiles, Rejection Regions & Power, Probability Distributions, Normal Approximations, and Overlaying Probability Distributions.

library(ISCAM)

Data Visualization

iscam_boxplot

This function displays horizontal boxplot(s).

data("chickwts")
iscam_boxplot(x = chickwts$weight, explanatory = chickwts$feed, names = c("Weight", "Feed"))

iscam_dotplot

This function displays horizontal dotplot(s). Optional: A second, categorical variable can also be specified and values will be calculated separately for each group.

iscam_dotplot(response = chickwts$weight, explanatory = chickwts$feed, names = c("Weight", "Feed"))

Summary Statistics

iscam_summary

This function calculates the five number summary, mean, and standard deviation of the quantitative variable x.

iscam_summary(x = chickwts$weight)

Hypothesis Testing

iscam_onepropztest

This function calculates a one proportion z-test and/or interval.

iscam_onepropztest(observed = 12, n = 15, hypothesized = .5, alternative = "two.sided", conf.level = 0.95)

iscam_twopropztest

This function calculates a two proportion z-test and/or interval.

iscam_twopropztest(observed1 = 6, n1 = 17, observed2 = 12, n2 = 20, hypothesized = 0, alternative = "less")

iscam_onesamplet

This function calculates a one sample t-test and/or interval from summary statistics.

iscam_onesamplet(xbar = 70, sd = 4, n = 25, hypothesized = 68, alternative = "greater")

iscam_twosamplet

This function calculates a two sample t-test and/or interval from summary data.

iscam_twosamplet(x1 = 97.25, sd1 = 3.65, n1 = 8, x2 = 87.25, sd2 = 9.60, n2 = 12, hypothesized = 0, alternative = "less", conf.level = 0.95)

iscam_binomtest

This function performs an exact binomial test and graphs the binomial distribution and/or binomial confidence interval.

iscam_binomtest(10, 40, hypothesized = .50, alternative = "two.sided", conf.level = 0.90)

Quantiles

iscam_invbinom

This function calculates the binomial quantile of a specified probability. The integer that achieves at most the stated probability will be returned.

iscam_invbinom(alpha = .05, n = 15, prob = .20, lower.tail = FALSE)

iscam_invnorm

This function calculates the normal quantile of a specified probability.

iscam_invnorm(prob1 = .55, mean = 15, sd = 2, direction = "below")

iscam_invt

This function calculates the t quantile of a specified probability.

iscam_invt(prob1 = .35, df = 2, direction = "above")

Rejection Regions & Power

iscam_binompower

This function determines the rejection region corresponding to the level of significance and the first probability. A second, optional probability can be specified to determine the power of the test.

iscam_binompower(LOS = .05, n = 20, prob1 = 0.25, alternative = "greater", prob2 = 0.333, explain = T)

iscam_normpower

This function determines the rejection region corresponding to the level of significance and the first probability and shows the second distribution shading its corresponding region.

iscam_normpower(LOS = .05, n = 20, prob1 = .5, alternative = "less", prob2 = .7)

Probability Distributions

iscam_binom

This function calculates either a tail probability or the inverse cumulative probability depending on whether k or prob is passed a question mark.

iscam_binom("?", 0.05, 20, 0.3, lower.tail = TRUE)
iscam_binom(10, "?", 20, 0.3, TRUE)

iscam_binomprob

This function calculates tail probabilities from the binomial distribution.

iscam_binomprob(k = 20, n = 30, prob = 0.5, lower.tail = TRUE)

iscam_hyperprob

This function calculates tail probabilities from the hypergeometric distribution.

iscam_hyperprob(k = 2, total = 52, succ = 5, n = 13, lower.tail = FALSE)

iscam_normprob

This function calculates tail probability for the normal distribution.

iscam_normprob(xval = 2.2, direction = "above", label = "sample proportions")

iscam_chisqprob

This function calculates the upper tail probability for the chi-square distribution.

iscam_chisqprob(xval = 10, df = 4)

iscam_tprob

This function calculates tail probability for the t distribution.

iscam_tprob(xval = 4, df = 5, direction = "above")

Normal Approximations

iscam_binomnorm

This function illustrates the normal approximation to the binomial.

iscam_binomnorm(k = 20, n = 30, prob = 0.5, direction = "above")

iscam_hypernorm

This function calculates tail probabilities from the hypergeometric distribution.

iscam_hypernorm(k = 2, total = 52, succ = 5, n = 26, lower.tail = T)

Histograms with Overlaid Density Curves

iscam_addexp

This function creates a histogram of the inputted variable and overlays an exponential density function with lambda = 1/mean.

expdata <- rexp(50)
iscam_addexp(expdata)

iscam_addlnorm

This function creates a histogram of the inputted variable and overlays a log normal density function.

lnormdata <- rlnorm(50)
iscam_addlnorm(lnormdata)

iscam_addnorm

This function creates a histogram of the inputted variable and overlays a normal density function.

normdata <- rnorm(50)
iscam_addnorm(normdata)

iscam_addt

This function creates a histogram of the inputted variable and overlays a t density function with df degrees of freedom.

tdata <- rt(50, df = 5)
iscam_addt(tdata, df = 5)

iscam_addtnorm

This function creates a histogram of the inputted variable and overlays a t density function with df degrees of freedom and a normal density function.