Package 'statsr' reference manual

Title:	Companion Software for the Coursera Statistics with R Specialization
Description:	Data and functions to support Bayesian and frequentist inference and decision making for the Coursera Specialization "Statistics with R". See <https://github.com/StatsWithR/statsr> for more information.
Authors:	Colin Rundel [aut], Mine Cetinkaya-Rundel [aut], Merlise Clyde [aut, cre], David Banks [aut]
Maintainer:	Merlise Clyde <[email protected]>
License:	MIT + file LICENSE
Version:	0.3.0
Built:	2024-11-23 05:04:43 UTC
Source:	https://github.com/statswithr/statsr

Housing prices in Ames, Iowa

Description

Data set contains information from the Ames Assessor's Office used in computing assessed values for individual residential properties sold in Ames, IA from 2006 to 2010. See http://www.amstat.org/publications/jse/v19n3/decock/datadocumentation.txt for detailed variable descriptions.

Usage

ames
ames

Format

A tbl_df with with 2930 rows and 82 variables:

Order: Observation number.
PID: Parcel identification number - can be used with city web site for parcel review.
area: Above grade (ground) living area square feet.
price: Sale price in USD.
MS.SubClass: Identifies the type of dwelling involved in the sale.
MS.Zoning: Identifies the general zoning classification of the sale.
Lot.Frontage: Linear feet of street connected to property.
Lot.Area: Lot size in square feet.
Street: Type of road access to property.
Alley: Type of alley access to property.
Lot.Shape: General shape of property.
Land.Contour: Flatness of the property.
Utilities: Type of utilities available.
Lot.Config: Lot configuration.
Land.Slope: Slope of property.
Neighborhood: Physical locations within Ames city limits (map available).
Condition.1: Proximity to various conditions.
Condition.2: Proximity to various conditions (if more than one is present).
Bldg.Type: Type of dwelling.
House.Style: Style of dwelling.
Overall.Qual: Rates the overall material and finish of the house.
Overall.Cond: Rates the overall condition of the house.
Year.Built: Original construction date.
Year.Remod.Add: Remodel date (same as construction date if no remodeling or additions).
Roof.Style: Type of roof.
Roof.Matl: Roof material.
Exterior.1st: Exterior covering on house.
Exterior.2nd: Exterior covering on house (if more than one material).
Mas.Vnr.Type: Masonry veneer type.
Mas.Vnr.Area: Masonry veneer area in square feet.
Exter.Qual: Evaluates the quality of the material on the exterior.
Exter.Cond: Evaluates the present condition of the material on the exterior.
Foundation: Type of foundation.
Bsmt.Qual: Evaluates the height of the basement.
Bsmt.Cond: Evaluates the general condition of the basement.
Bsmt.Exposure: Refers to walkout or garden level walls.
BsmtFin.Type.1: Rating of basement finished area.
BsmtFin.SF.1: Type 1 finished square feet.
BsmtFin.Type.2: Rating of basement finished area (if multiple types).
BsmtFin.SF.2: Type 2 finished square feet.
Bsmt.Unf.SF: Unfinished square feet of basement area.
Total.Bsmt.SF: Total square feet of basement area.
Heating: Type of heating.
Heating.QC: Heating quality and condition.
Central.Air: Central air conditioning.
Electrical: Electrical system.
X1st.Flr.SF: First Floor square feet.
X2nd.Flr.SF: Second floor square feet.
Low.Qual.Fin.SF: Low quality finished square feet (all floors).
Bsmt.Full.Bath: Basement full bathrooms.
Bsmt.Half.Bath: Basement half bathrooms.
Full.Bath: Full bathrooms above grade.
Half.Bath: Half baths above grade.
Bedroom.AbvGr: Bedrooms above grade (does NOT include basement bedrooms).
Kitchen.AbvGr: Kitchens above grade.
Kitchen.Qual: Kitchen quality.
TotRms.AbvGrd: Total rooms above grade (does not include bathrooms).
Functional: Home functionality (Assume typical unless deductions are warranted).
Fireplaces: Number of fireplaces.
Fireplace.Qu: Fireplace quality.
Garage.Type: Garage location.
Garage.Yr.Blt: Year garage was built.
Garage.Finish: Interior finish of the garage.
Garage.Cars: Size of garage in car capacity.
Garage.Area: Size of garage in square feet.
Garage.Qual: Garage quality.
Garage.Cond: Garage condition.
Paved.Drive: Paved driveway.
Wood.Deck.SF: Wood deck area in square feet.
Open.Porch.SF: Open porch area in square feet.
Enclosed.Porch: Enclosed porch area in square feet.
X3Ssn.Porch: Three season porch area in square feet.
Screen.Porch: Screen porch area in square feet.
Pool.Area: Pool area in square feet.
Pool.QC: Pool quality.
Fence: Fence quality.
Misc.Feature: Miscellaneous feature not covered in other categories.
Misc.Val: Dollar value of miscellaneous feature.
Mo.Sold: Month Sold (MM).
Yr.Sold: Year Sold (YYYY).
Sale.Type: Type of sale.
Sale.Condition: Condition of sale.

Source

De Cock, Dean. "Ames, Iowa: Alternative to the Boston housing data as an end of semester regression project." Journal of Statistics Education 19.3 (2011).

Simulate Sampling Distribution

Description

Run the interactive ames sampling distribution shiny app to illustrate sampling distributions using variables from the 'ames' dataset.

Usage

ames_sampling_dist()
ames_sampling_dist()

Examples

if (interactive()) { 
  ames_sampling_dist()
}
if (interactive()) { 
  ames_sampling_dist()
}

Male and female births in London

Description

Arbuthnot's data describes male and female christenings (births) for London from 1629-1710.

Usage

arbuthnot
arbuthnot

Format

A tbl_df with with 82 rows and 3 variables:

year: year, ranging from 1629 to 1710
boys: number of male christenings (births)
girls: number of female christenings (births)

Details

John Arbuthnot (1710) used these time series data to carry out the first known significance test. During every one of the 82 years, there were more male christenings than female christenings. As Arbuthnot wondered, we might also wonder if this could be due to chance, or whether it meant the birth ratio was not actually 1:1.

Source

These data are excerpted from the Arbuthnot data set in the HistData package.

Atheism in the world data

Description

Survey results on atheism across several countries and years. Each row represents a single respondent.

Usage

atheism
atheism

Format

A tbl_df with 88032 rows and 3 variables:

nationality: Country of the individual surveyed.
response: A categorical variable with two levels: atheist and non-atheist.
year: Year in which the person was surveyed.

Source

WIN-Gallup International Press Release

bandit posterior

Description

Utility function for calculating the posterior probability of each machine being "good" in two armed bandit problem. Calculated result is based on observed win loss data, prior belief about which machine is good and the probability of the good and bad machine paying out.

Usage

bandit_posterior(
  data,
  prior = c(m1_good = 0.5, m2_good = 0.5),
  win_probs = c(good = 1/2, bad = 1/3)
)
bandit_posterior(
  data,
  prior = c(m1_good = 0.5, m2_good = 0.5),
  win_probs = c(good = 1/2, bad = 1/3)
)

Arguments

`data`	data frame containing win loss data
`prior`	prior vector containing the probabilities of Machine 1 and Machine 2 being good, defaults to 0.5 and 0.5 respectively.
`win_probs`	vector containing the probabilities of winning on the good and bad machine respectively.

Value

A vector containing the posterior probability of Machine 1 and Machine 2 being the good machine.

Examples

data = data.frame(machine = c(1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L), 
                  outcome = c("W", "L", "W", "L", "L", "W", "L", "L", "L", "W"))
bandit_posterior(data)
plot_bandit_posterior(data)

data = data.frame(machine = c(1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L), 
                  outcome = c("W", "L", "W", "L", "L", "W", "L", "L", "L", "W"))
bandit_posterior(data)
plot_bandit_posterior(data)

Run the Bandit Simulation shiny app

Description

Simulate data from a two armed-bandit (two slot machines) by clicking on the images for Machine 1 or Machine 2 and guess/learn which machine has the higher probability of winning as the number of outcomes of wins and losses accumulate.

Usage

bandit_sim()
bandit_sim()

Examples

if (interactive()) {
# run interactive shiny app to generate wins and losses
bandit_sim()
}
# paste data from the shiny app into varible
data = data.frame(
 machine = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
   1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
   2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
   2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
   2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 
   1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
   2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 
   1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L), 
 outcome = c("W", "W", "W", "L", "W", "W", "W", "L", "W", "L", "W", "L",
  "L", "L", "W", "L", "W", "L", "L", "L", "W", "W", "W", "L", "L", "L", 
  "L", "L", "W", "W", "L", "L", "W", "L", "L", "W", "L", "L", "W", "L",
  "L", "L", "L", "L", "W", "L", "L", "W", "W", "W", "W", "L", "L", "L",
  "L", "L", "L", "W", "L", "W", "L", "W", "L", "L", "L", "L", "L", "L", "L",
  "L", "L", "L", "W", "W", "W", "L", "W", "L", "L", "L", "L", "L", "L", "L",
  "L", "L", "L", "W", "W", "W", "W", "W", "L", "W", "W", "L", "W", "L", "L",
  "L", "L", "L", "W", "L", "W", "L", "L", "L", "W", "W", "W", "W", "L", "L",
  "W", "L", "W", "L", "L", "W"))
  bandit_posterior(data)
  plot_bandit_posterior(data)

if (interactive()) {
# run interactive shiny app to generate wins and losses
bandit_sim()
}
# paste data from the shiny app into varible
data = data.frame(
 machine = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
   1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
   2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
   2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
   2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 
   1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
   2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 
   1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L), 
 outcome = c("W", "W", "W", "L", "W", "W", "W", "L", "W", "L", "W", "L",
  "L", "L", "W", "L", "W", "L", "L", "L", "W", "W", "W", "L", "L", "L", 
  "L", "L", "W", "W", "L", "L", "W", "L", "L", "W", "L", "L", "W", "L",
  "L", "L", "L", "L", "W", "L", "L", "W", "W", "W", "W", "L", "L", "L",
  "L", "L", "L", "W", "L", "W", "L", "W", "L", "L", "L", "L", "L", "L", "L",
  "L", "L", "L", "W", "W", "W", "L", "W", "L", "L", "L", "L", "L", "L", "L",
  "L", "L", "L", "W", "W", "W", "W", "W", "L", "W", "W", "L", "W", "L", "L",
  "L", "L", "L", "W", "L", "W", "L", "L", "L", "W", "W", "W", "W", "L", "L",
  "W", "L", "W", "L", "L", "W"))
  bandit_posterior(data)
  plot_bandit_posterior(data)

Bayesian hypothesis tests and credible intervals

Description

Bayesian hypothesis tests and credible intervals

Usage

bayes_inference(
  y,
  x = NULL,
  data,
  type = c("ci", "ht"),
  statistic = c("mean", "proportion"),
  method = c("theoretical", "simulation"),
  success = NULL,
  null = NULL,
  cred_level = 0.95,
  alternative = c("twosided", "less", "greater"),
  hypothesis_prior = c(H1 = 0.5, H2 = 0.5),
  prior_family = "JZS",
  n_0 = 1,
  mu_0 = null,
  s_0 = 0,
  v_0 = -1,
  rscale = 1,
  beta_prior = NULL,
  beta_prior1 = NULL,
  beta_prior2 = NULL,
  nsim = 10000,
  verbose = TRUE,
  show_summ = verbose,
  show_res = verbose,
  show_plot = verbose
)
bayes_inference(
  y,
  x = NULL,
  data,
  type = c("ci", "ht"),
  statistic = c("mean", "proportion"),
  method = c("theoretical", "simulation"),
  success = NULL,
  null = NULL,
  cred_level = 0.95,
  alternative = c("twosided", "less", "greater"),
  hypothesis_prior = c(H1 = 0.5, H2 = 0.5),
  prior_family = "JZS",
  n_0 = 1,
  mu_0 = null,
  s_0 = 0,
  v_0 = -1,
  rscale = 1,
  beta_prior = NULL,
  beta_prior1 = NULL,
  beta_prior2 = NULL,
  nsim = 10000,
  verbose = TRUE,
  show_summ = verbose,
  show_res = verbose,
  show_plot = verbose
)

Arguments

`y`	Response variable, can be numerical or categorical
`x`	Explanatory variable, categorical (optional)
`data`	Name of data frame that y and x are in
`type`	of inference; "ci" (credible interval) or "ht" (hypothesis test)
`statistic`	population parameter to estimate: mean or proportion
`method`	of inference; "theoretical" (quantile based) or "simulation"
`success`	which level of the categorical variable to call "success", i.e. do inference on
`null`	null value for the hypothesis test
`cred_level`	confidence level, value between 0 and 1
`alternative`	direction of the alternative hypothesis; "less","greater", or "twosided"
`hypothesis_prior`	discrete prior for H1 and H2, default is the uniform prior: c(H1=0.5,H2=0.5)
`prior_family`	character string representing default priors for inference or testing ("JSZ", "JUI","ref"). See notes for details.
`n_0`	n_0 is the prior sample size in the Normal prior for the mean
`mu_0`	the prior mean in one sample mean problems or the prior difference in two sample problems. For hypothesis testing, this is all the null value if null is not supplied.
`s_0`	the prior standard deviation of the data for the conjugate Gamma prior on 1/sigma^2
`v_0`	prior degrees of freedom for conjugate Gamma prior on 1/sigma^2
`rscale`	is the scaling parameter in the Cauchy prior: 1/n_0 ~ Gamma(1/2, rscale^2/2) leads to mu_0 having a Cauchy(0, rscale^2*sigma^2) prior distribution for prior_family="JZS".
`beta_prior`, `beta_prior1`, `beta_prior2`	beta priors for p (or p_1 and p_2) for one or two proportion inference
`nsim`	number of Monte Carlo draws; default is 10,000
`verbose`	whether output should be verbose or not, default is TRUE
`show_summ`	print summary stats, set to verbose by default
`show_res`	print results, set to verbose by default
`show_plot`	print inference plot, set to verbose by default

Value

Results of inference task performed.

Note

For inference and testing for normal means several default options are available. "JZS" corresponds to using the Jeffreys reference prior on sigma^2, p(sigma^2) = 1/sigma^2, and the Zellner-Siow Cauchy prior on the standardized effect size mu/sigma or ( mu_1 - mu_2)/sigma with a location of mu_0 and scale rscale. The "JUI" option also uses the Jeffreys reference prior on sigma^2, but the Unit Information prior on the standardized effect, N(mu_0, 1). The option "ref" uses the improper uniform prior on the standardized effect and the Jeffreys reference prior on sigma^2. The latter cannot be used for hypothesis testing due to the ill-determination of Bayes factors. Finally "NG" corresponds to the conjugate Normal-Gamma prior.

References

https://statswithr.github.io/book/

Examples


# inference for the mean from a single normal population using
# Jeffreys Reference prior, p(mu, sigma^2) = 1/sigma^2

library(BayesFactor)
data(tapwater)

# Calculate 95% CI using quantiles from Student t derived from ref prior
bayes_inference(tthm, data=tapwater,
                statistic="mean", 
                type="ci", prior_family="ref",
                method="theoretical")
 
# Calculate 95% CI using simulation from Student t using an informative mean and ref
# prior for sigma^2

bayes_inference(tthm, data=tapwater,
                statistic="mean", mu_0=9.8,
                type="ci",  prior_family="JUI",
                method="theo")

# Calculate 95% CI using simulation  with the 
# Cauchy prior on mu and reference prior on sigma^2


bayes_inference(tthm, data=tapwater,
                statistic="mean", mu_0 = 9.8, rscale=sqrt(2)/2,
                type="ci", prior_family="JZS",
                method="simulation")

                
# Bayesian t-test mu = 0 with ZJS prior  
bayes_inference(tthm, data=tapwater,
                statistic="mean",
                type="ht", alternative="twosided", null=80,
                prior_family="JZS",
                method="sim")
                
               
# Bayesian t-test for two means 

data(chickwts)
chickwts = chickwts[chickwts$feed %in% c("horsebean","linseed"),]
# Drop unused factor levels
chickwts$feed = factor(chickwts$feed)                
bayes_inference(y=weight, x=feed, data=chickwts,
                statistic="mean", mu_0 = 0, alt="twosided",
                type="ht", prior_family="JZS",
                method="simulation")               

# inference for the mean from a single normal population using
# Jeffreys Reference prior, p(mu, sigma^2) = 1/sigma^2

library(BayesFactor)
data(tapwater)

# Calculate 95% CI using quantiles from Student t derived from ref prior
bayes_inference(tthm, data=tapwater,
                statistic="mean", 
                type="ci", prior_family="ref",
                method="theoretical")
 
# Calculate 95% CI using simulation from Student t using an informative mean and ref
# prior for sigma^2

bayes_inference(tthm, data=tapwater,
                statistic="mean", mu_0=9.8,
                type="ci",  prior_family="JUI",
                method="theo")

# Calculate 95% CI using simulation  with the 
# Cauchy prior on mu and reference prior on sigma^2


bayes_inference(tthm, data=tapwater,
                statistic="mean", mu_0 = 9.8, rscale=sqrt(2)/2,
                type="ci", prior_family="JZS",
                method="simulation")

                
# Bayesian t-test mu = 0 with ZJS prior  
bayes_inference(tthm, data=tapwater,
                statistic="mean",
                type="ht", alternative="twosided", null=80,
                prior_family="JZS",
                method="sim")
                
               
# Bayesian t-test for two means 

data(chickwts)
chickwts = chickwts[chickwts$feed %in% c("horsebean","linseed"),]
# Drop unused factor levels
chickwts$feed = factor(chickwts$feed)                
bayes_inference(y=weight, x=feed, data=chickwts,
                statistic="mean", mu_0 = 0, alt="twosided",
                type="ht", prior_family="JZS",
                method="simulation")

Run the interactive Bayes Factor shiny app

Description

This app illustrates how changing the Z score and prior precision affects the Bayes Factor for testing H1 that the mean is zero versus H2 that the mean is not zero for data arising from a normal population. Lindley's paradox occurs for large sample sizes when the Bayes factor favors H1 even though the Z score is large or the p-value is small enough to reach statistical significance and the values of the sample mean do not reflex practical significance based on the prior distribution. Bartlett's paradox may occur when the prior precision goes to zero, leading to Bayes factors that favor H1 regardless of the data. A prior precision of one corresponds to the unit information prior.

Usage

BF_app()
BF_app()

Examples

if (interactive()) { 
BF.app()
}
if (interactive()) { 
BF.app()
}

Behavioral Risk Factor Surveillance System 2013 (Subset)

Description

This data set is a small subset of BRFSS results from the 2013 survey, each row represents an individual respondent.

Usage

brfss
brfss

Format

A tbl_df with with 5000 rows and 6 variables:

weight: Weight in pounds.
height: Height in inches.
sex: Sex
exercise: Any exercise in the last 30 days
fruit_per_day: Number of servings of fruit consumed per day.
vege_per_day: Number of servings of dark green vegetables consumed per day.

Source

Centers for Disease Control and Prevention (CDC). Behavioral Risk Factor Surveillance System Survey Data. Atlanta, Georgia: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, 2013.

Calculate hitting streaks

Description

Calculate hitting streaks

Usage

calc_streak(x)
calc_streak(x)

Arguments

`x`	A data frame or character vector of hits (`"H"`) and misses (`"M"`).

Value

A data frame with one column, length, containing the length of each hit streak.

Examples

data(kobe_basket)
calc_streak(kobe_basket$shot)

data(kobe_basket)
calc_streak(kobe_basket$shot)

Credible Interval shiny app

Description

Run the 'shiny' credible interval app to generate credible intervals under the prior or posterior distribution for Beta, Gamma and Gaussian families. Sliders are used to adjust the hyperparameters in the distribution so that one may see how the resulting credible intervals and plotted distributions change.

Usage

credible_interval_app()
credible_interval_app()

Examples

if (interactive()) {
   credible_interval_app()
}
if (interactive()) {
   credible_interval_app()
}

Teachers evaluations at the University of Texas at Austin

Description

The data were gathered from end of semester student evaluations for a large sample of professors from the University of Texas at Austin (variables beginning with cls). In addition, six students rated the professors' physical appearance (variables beginning with bty). (This is a slightly modified version of the original data set that was released as part of the replication data for Data Analysis Using Regression and Multilevel/Hierarchical Models (Gelman and Hill, 2007).

Usage

evals
evals

Format

A data frame with 463 rows and 21 variables:

score: Average professor evaluation score: (1) very unsatisfactory - (5) excellent
rank: Rank of professor: teaching, tenure track, tenure
ethnicity: Ethnicity of professor: not minority, minority
gender: Gender of professor: female, male
language: Language of school where professor received education: english or non-english
age: Age of professor
cls_perc_eval: Percent of students in class who completed evaluation
cls_did_eval: Number of students in class who completed evaluation
cls_students: Total number of students in class
cls_level: Class level: lower, upper
cls_profs: Number of professors teaching sections in course in sample: single, multiple
cls_credits: Number of credits of class: one credit (lab, PE, etc.), multi credit
bty_f1lower: Beauty rating of professor from lower level female: (1) lowest - (10) highest
bty_f1upper: Beauty rating of professor from upper level female: (1) lowest - (10) highest
bty_f2upper: Beauty rating of professor from second upper level female: (1) lowest - (10) highest
bty_m1lower: Beauty rating of professor from lower level male: (1) lowest - (10) highest
bty_m1upper: Beauty rating of professor from upper level male: (1) lowest - (10) highest
bty_m2upper: Beauty rating of professor from second upper level male: (1) lowest - (10) highest
bty_avg: Average beauty rating of professor
pic_outfit: Outfit of professor in picture: not formal, formal
pic_color: Color of professor's picture: color, black & white

Source

These data appear in Hamermesh DS, and Parker A. 2005. Beauty in the classroom: instructors pulchritude and putative pedagogical productivity. Economics of Education Review 24(4):369-376.

Hypothesis tests and confidence intervals

Description

Hypothesis tests and confidence intervals

Usage

inference(
  y,
  x = NULL,
  data,
  type = c("ci", "ht"),
  statistic = c("mean", "median", "proportion"),
  success = NULL,
  order = NULL,
  method = c("theoretical", "simulation"),
  null = NULL,
  alternative = c("less", "greater", "twosided"),
  sig_level = 0.05,
  conf_level = 0.95,
  boot_method = c("perc", "se"),
  nsim = 15000,
  seed = NULL,
  verbose = TRUE,
  show_var_types = verbose,
  show_summ_stats = verbose,
  show_eda_plot = verbose,
  show_inf_plot = verbose,
  show_res = verbose
)
inference(
  y,
  x = NULL,
  data,
  type = c("ci", "ht"),
  statistic = c("mean", "median", "proportion"),
  success = NULL,
  order = NULL,
  method = c("theoretical", "simulation"),
  null = NULL,
  alternative = c("less", "greater", "twosided"),
  sig_level = 0.05,
  conf_level = 0.95,
  boot_method = c("perc", "se"),
  nsim = 15000,
  seed = NULL,
  verbose = TRUE,
  show_var_types = verbose,
  show_summ_stats = verbose,
  show_eda_plot = verbose,
  show_inf_plot = verbose,
  show_res = verbose
)

Arguments

`y`	Response variable, can be numerical or categorical
`x`	Explanatory variable, categorical (optional)
`data`	Name of data frame that y and x are in
`type`	of inference; "ci" (confidence interval) or "ht" (hypothesis test)
`statistic`	parameter to estimate: mean, median, or proportion
`success`	which level of the categorical variable to call "success", i.e. do inference on
`order`	when x is given, order of levels of x in which to subtract parameters
`method`	of inference; "theoretical" (CLT based) or "simulation" (randomization/bootstrap)
`null`	null value for a hypothesis test
`alternative`	direction of the alternative hypothesis; "less","greater", or "twosided"
`sig_level`	significance level, value between 0 and 1 (used only for ANOVA to determine if posttests are necessary)
`conf_level`	confidence level, value between 0 and 1
`boot_method`	bootstrap method; "perc" (percentile) or "se" (standard error)
`nsim`	number of simulations
`seed`	seed to be set, default is NULL
`verbose`	whether output should be verbose or not, default is TRUE
`show_var_types`	print variable types, set to verbose by default
`show_summ_stats`	print summary stats, set to verbose by default
`show_eda_plot`	print EDA plot, set to verbose by default
`show_inf_plot`	print inference plot, set to verbose by default
`show_res`	print results, set to verbose by default

Value

Results of inference task performed

Examples

data(tapwater)

# Calculate 95% CI using quantiles using a Student t distribution
inference(tthm, data=tapwater,
                statistic="mean", 
                type="ci",
                method="theoretical")
                
inference(tthm, data=tapwater,
                statistic="mean", 
                type="ci",
                boot_method = "perc",
                method="simulation")
                
# Inference for a proportion
# Calculate 95% confidence intervals for the proportion of atheists

data("atheism")
library("dplyr")
us12 <- atheism %>%
        filter(nationality == "United States" , atheism$year == "2012")
inference(y = response, data = us12, statistic = "proportion",
          type = "ci",
          method = "theoretical", 
          success = "atheist")
                
data(tapwater)

# Calculate 95% CI using quantiles using a Student t distribution
inference(tthm, data=tapwater,
                statistic="mean", 
                type="ci",
                method="theoretical")
                
inference(tthm, data=tapwater,
                statistic="mean", 
                type="ci",
                boot_method = "perc",
                method="simulation")
                
# Inference for a proportion
# Calculate 95% confidence intervals for the proportion of atheists

data("atheism")
library("dplyr")
us12 <- atheism %>%
        filter(nationality == "United States" , atheism$year == "2012")
inference(y = response, data = us12, statistic = "proportion",
          type = "ci",
          method = "theoretical", 
          success = "atheist")

Kobe Bryant basketball performance

Description

Data from the five games the Los Angeles Lakers played against the Orlando Magic in the 2009 NBA finals.

Usage

kobe_basket
kobe_basket

Format

A data frame with 133 rows and 6 variables:

vs: A categorical vector, ORL if the Los Angeles Lakers played against Orlando
game: A numerical vector, game in the 2009 NBA finals
quarter: A categorical vector, quarter in the game, OT stands for overtime
time: A character vector, time at which Kobe took a shot
description: A character vector, description of the shot
shot: A categorical vector, H if the shot was a hit, M if the shot was a miss

Details

Each row represents a shot Kobe Bryant took during the five games of the 2009 NBA finals. Kobe Bryant's performance earned him the title of Most Valuable Player and many spectators commented on how he appeared to show a hot hand.

Major League Baseball team data

Description

Data from all 30 Major League Baseball teams from the 2011 season.

Usage

mlb11
mlb11

Format

A data frame with 30 rows and 12 variables:

team: Team name.
runs: Number of runs.
at_bats: Number of at bats.
hits: Number of hits.
homeruns: Number of home runs.
bat_avg: Batting average.
strikeouts: Number of strikeouts.
stolen_bases: Number of stolen bases.
wins: Number of wins.
new_onbase: Newer variable: on-base percentage, a measure of how often a batter reaches base for any reason other than a fielding error, fielder's choice, dropped/uncaught third strike, fielder's obstruction, or catcher's interference.
new_slug: Newer variable: slugging percentage, popular measure of the power of a hitter calculated as the total bases divided by at bats.
new_obs: Newer variable: on-base plus slugging, calculated as the sum of the on-base and slugging percentages.

Source

mlb.com

North Carolina births

Description

In 2004, the state of North Carolina released a large data set containing information on births recorded in this state. This data set is useful to researchers studying the relation between habits and practices of expectant mothers and the birth of their children. We will work with a random sample of observations from this data set.

Usage

nc
nc

Format

A tbl_df with 1000 rows and 13 variables:

fage: father's age in years
mage: mother's age in years
mature: maturity status of mother
weeks: length of pregnancy in weeks
premie: whether the birth was classified as premature (premie) or full-term
visits: number of hospital visits during pregnancy
marital: whether mother is 'married' or 'not married' at birth
gained: weight gained by mother during pregnancy in pounds
weight: weight of the baby at birth in pounds
lowbirthweight: whether baby was classified as low birthweight ('low') or not ('not low')
gender: gender of the baby, 'female' or 'male'
habit: status of the mother as a 'nonsmoker' or a 'smoker'
whitemom: whether mom is 'white' or 'not white'

Source

State of North Carolina.

Flights data

Description

On-time data for a random sample of flights that departed NYC (i.e. JFK, LGA or EWR) in 2013.

Usage

nycflights
nycflights

Format

A tbl_df with 32,735 rows and 16 variables:

year,month,day: Date of departure
dep_time,arr_time: Departure and arrival times, local tz.
dep_delay,arr_delay: Departure and arrival delays, in minutes. Negative times represent early departures/arrivals.
hour,minute: Time of departure broken in to hour and minutes
carrier: Two letter carrier abbreviation. See airlines in the nycflights13 package for more information
tailnum: Plane tail number
flight: Flight number
origin,dest: Origin and destination. See airports in the nycflights13 package for more information, or google airport the code.
air_time: Amount of time spent in the air
distance: Distance flown

Source

Hadley Wickham (2014). nycflights13: Data about flights departing NYC in 2013. R package version 0.1. https://CRAN.R-project.org/package=nycflights13

plot_bandit_posterior

Description

Generates a plot that shows the bandit posterior values as they are sequentially updated by the provided win / loss data.

Usage

plot_bandit_posterior(
  data,
  prior = c(m1_good = 0.5, m2_good = 0.5),
  win_probs = c(good = 1/2, bad = 1/3)
)
plot_bandit_posterior(
  data,
  prior = c(m1_good = 0.5, m2_good = 0.5),
  win_probs = c(good = 1/2, bad = 1/3)
)

Arguments

`data`	data frame containing win loss data
`prior`	prior vector containing the probabilities of Machine 1 and Machine 2 being good, defaults to 50-50.
`win_probs`	vector containing the probabilities of winning on the good and bad machine respectively.

Examples

# capture data from the `shiny` app `bandit_sim`.
data = data.frame(machine = c(1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L), 
                  outcome = c("W", "L", "W", "L", "L", "W", "L", "L", "L", "W"))
plot_bandit_posterior(data)

# capture data from the `shiny` app `bandit_sim`.
data = data.frame(machine = c(1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L), 
                  outcome = c("W", "L", "W", "L", "L", "W", "L", "L", "L", "W"))
plot_bandit_posterior(data)

plot_ss

Description

An interactive shiny app that will generate a scatterplot of two variables, then allow the user to click the plot in two locations to draw a best fitting line. Residuals are drawn by default; boxes representing the squared residuals are optional.

Usage

plot_ss(x, y, data, showSquares = FALSE, leastSquares = FALSE)
plot_ss(x, y, data, showSquares = FALSE, leastSquares = FALSE)

Arguments

`x`	the name of numerical vector 1 on x-axis
`y`	the name of numerical vector 2 on y-axis
`data`	the dataframe in which x and y can be found
`showSquares`	logical option to show boxes representing the squared residuals
`leastSquares`	logical option to bypass point entry and automatically draw the least squares line

Examples

## Not run: plot_ss
## Not run: plot_ss

Male and female births in the US

Description

Counts of the total number of male and female births in the United States from 1940 to 2013.

Usage

present
present

Format

A tbl_df with 74 rows and 3 variables:

year: year, ranging from 1940 to 2013
boys: number of male births
girls: number of female births

Source

Data up to 2002 appear in Mathews TJ, and Hamilton BE. 2005. Trend analysis of the sex ratio at birth in the United States. National Vital Statistics Reports 53(20):1-17. Data for 2003 - 2013 have been collected from annual National Vital Statistics Reports published by the US Department of Health and Human Services, Centers for Disease Control and Prevention, National Center for Health Statistics.

Repeating Sampling from a Tibble

Description

Repeating Sampling from a Tibble

Usage

rep_sample_n(tbl, size, replace = FALSE, reps = 1)
rep_sample_n(tbl, size, replace = FALSE, reps = 1)

Arguments

`tbl`	tbl of data.
`size`	The number of rows to select.
`replace`	Sample with or without replacement?
`reps`	The number of samples to collect.

Value

A tbl_df that aggregates all created samples, with the addition of a replicate column that the tbl_df is also grouped by

Examples

data(nc)
rep_sample_n(nc, size=10, replace=FALSE, reps=1)
data(nc)
rep_sample_n(nc, size=10, replace=FALSE, reps=1)

statsr: A companion package for Statistics with R

Description

R package to support the online open access book "An Introduction to Bayesian Thinking" available at https://statswithr.github.io/book/ and videos for the Coursera "Statistics with R" Specialization. The package includes data sets, functions and Shiny Applications for learning frequentist and Bayesian statistics with R. The two main functions for inference and decision making are 'inference' and 'bayes_inference' which support confidence/credible intervals and hypothesis testing with one sample or two samples from Gaussian and Bernoulli populations. Shiny apps are used to illustrate how prior hyperparameters or changes in the data may influence posterior distributions.

Details

See https://github.com/StatsWithR/statsr for the development version and additional information or for additional background and illustrations of functions the online book https://statswithr.github.io/book/.

Total Trihalomethanes in Tapwater

Description

Trihalomethanes are formed as a by-product predominantly when chlorine is used to disinfect water for drinking. They result from the reaction of chlorine or bromine with organic matter present in the water being treated. THMs have been associated through epidemiological studies with some adverse health effects and many are considered carcinogenic. In the United States, the EPA limits the total concentration of the four chief constituents (chloroform, bromoform, bromodichloromethane, and dibromochloromethane), referred to as total trihalomethanes (TTHM), to 80 parts per billion in treated water.

Usage

tapwater
tapwater

Format

A dataframe with 28 rows and 6 variables:

date: Date of collection
tthm: average total trihalomethanes in ppb
samples: number of samples
nondetects: number of samples where tthm not detected (0)
min: min tthm in ppb in samples
max: max tthm in ppb in samples

Source

National Drinking Water Database for Durham, NC. https://www.ewg.org

Wage data

Description

The data were gathered as part of a random sample of 935 respondents throughout the United States.

Usage

wage
wage

Format

A tbl_df with with 935 rows and 17 variables:

wage: weekly earnings (dollars)
hours: average hours worked per week
iq: IQ score
kww: Knowledge of world work score
educ: years of education
exper: years of work experience
tenure: years with current employer
age: age in years
married: =1 if married
black: =1 if black
south: =1 if live in south
urban: =1 if live in a Standard Metropolitan Statistical Area
sibs: number of siblings
brthord: birth order
meduc: mother's education (years)
feduc: father's education (years)
lwage: natural log of wage

Source

Jeffrey M. Wooldridge (2000). Introductory Econometrics: A Modern Approach. South-Western College Publishing.

Zinc Concentration in Water

Description

Trace metals in drinking water affect the flavor and an unusually high concentration can pose a health hazard. Ten pairs of data were taken measuring zinc concentration in bottom water and surface water.

Usage

zinc
zinc

Format

A data frame with 10 observations on the following 4 variables.

location: sample number
bottom: zinc concentration in bottom water
surface: zinc concentration in surface water
difference: difference between zinc concentration at the bottom and surface

Source

PennState Eberly College of Science Online Courses

Examples

 data(zinc)
 str(zinc)
 plot(bottom ~ surface, data=zinc)
 # use paired t-test to test if difference in means is zero

data(zinc)
 str(zinc)
 plot(bottom ~ surface, data=zinc)
 # use paired t-test to test if difference in means is zero

Package 'statsr'

Help Index

Housing prices in Ames, Iowa

Description

Usage

Format

Source

Simulate Sampling Distribution

Description

Usage

Examples

Male and female births in London

Description

Usage

Format

Details

Source

Atheism in the world data

Description

Usage

Format

Source

bandit posterior

Description

Usage

Arguments

Value

See Also

Examples

Run the Bandit Simulation shiny app

Description

Usage

See Also

Examples

Bayesian hypothesis tests and credible intervals

Description

Usage

Arguments

Value

Note

References

Examples

Run the interactive Bayes Factor shiny app

Description

Usage

Examples

Behavioral Risk Factor Surveillance System 2013 (Subset)

Description

Usage

Format

Source

Calculate hitting streaks

Description

Usage

Arguments

Value

Examples

Credible Interval shiny app

Description

Usage

Examples

Teachers evaluations at the University of Texas at Austin

Description

Usage

Format

Source

Hypothesis tests and confidence intervals

Description

Usage

Arguments

Value

Examples

Kobe Bryant basketball performance

Description

Usage

Format

Details

Major League Baseball team data

Description

Usage