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()

Examples

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

Simple check to determine if code is being run in RStudio with the shiny runtime internal function

Description

Simple check to determine if code is being run in RStudio with the shiny runtime internal function

Usage

allow_shiny()

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

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()

Examples

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

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

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)
)

Arguments

Value

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

See Also

bandit_sim to generate data and plot_bandit_posterior to visualize.

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)

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()

See Also

bandit_posterior and plot_bandit_posterior

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)

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
)

Arguments

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")               

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

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)

Arguments

Value

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

Examples

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()

Examples

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

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
)

Arguments

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")
                

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

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

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

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

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)
)

Arguments

See Also

bandit_sim to generate data to use below

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)

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)

Arguments

Examples

## 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

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)

Arguments

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)

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

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

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

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