Help for package HistData

Type:

Package

Title:

Data Sets from the History of Statistics and Data Visualization

Version:

0.9-3

Date:

2025-04-08

Maintainer:

Michael Friendly <friendly@yorku.ca>

Description:

The 'HistData' package provides a collection of small data sets that are interesting and important in the history of statistics and data visualization. The goal of the package is to make these available, both for instructional use and for historical research. Some of these present interesting challenges for graphics or analysis in R.

Depends:

R (≥ 4.1.0)

Suggests:

gtools, KernSmooth, maps, ggplot2, dplyr, scales, proto, grid, reshape, plyr, lattice, jpeg, car, gplots, sp, heplots, knitr, rmarkdown, effects, lubridate, gridExtra, vcd, MASS, forcats

License:

GPL-2 | GPL-3 [expanded from: GPL]

LazyLoad:

yes

LazyData:

yes

VignetteBuilder:

knitr

Language:

en-US

RoxygenNote:

7.3.1

Encoding:

UTF-8

BugReports:

https://github.com/friendly/HistData/issues

URL:

https://friendly.github.io/HistData/

NeedsCompilation:

Packaged:

2025-04-09 14:09:50 UTC; friendly

Author:

Michael Friendly

[aut, cre], Stephane Dray

[ctb], Hadley Wickham [ctb], James Hanley [ctb], Dennis Murphy [ctb], Peter Li [ctb], Luiz Droubi [ctb], James Riley [ctb], Antoine de Falguerolles [ctb], Monique Graf [ctb], Neville Verlander [ctb], Brian Clair [ctb], Jim Oeppen [ctb], David Bellhouse [ctb]

Repository:

CRAN

Date/Publication:

2025-04-09 14:40:02 UTC

Data sets from the History of Statistics and Data Visualization

Description

The HistData package provides a collection of data sets that are interesting and important in the history of statistics and data visualization. The goal of the package is to make these available, both for instructional use and for historical research.

Some of the data sets have examples which reproduce an historical graph or analysis. These are meant mainly as starters for more extensive re-analysis or graphical elaboration. Some of these present graphical challenges to reproduce in R.

They are part of a program of research called statistical historiography, meaning the use of statistical methods to study problems and questions in the history of statistics and graphics. A main aspect of this is the increased understanding of historical problems in science and data analysis trough the process of trying to reproduce a graph or analysis using modern methods. I call this "Re-visioning", meaning to see again, hopefully in a new light.

A number of these are illustrated in our book, Friendly & Wainer (2021), A History of Data Visualization and Graphic Communication, and some are re-produced in R in the companion web site, https://friendly.github.io/HistDataVis/.

Details

Descriptions of each DataSet can be found using help(DataSet); example(DataSet) will likely show applications similar to the historical use.

Data sets included in the HistData package are:

Arbuthnot: Arbuthnot's data on male and female birth ratios in London from 1629-1710
Armada: The Spanish Armada
Bowley: Bowley's data on values of British and Irish trade, 1855-1899
Breslau: Halley's Breslau Life Table
Cavendish: Cavendish's 1798 determinations of the density of the earth
ChestSizes: Quetelet's data on chest measurements of Scottish militiamen
Cholera: William Farr's Data on Cholera in London, 1849
CholeraDeaths1849: Daily Deaths from Cholera and Diarrhaea in England, 1849
CushnyPeebles: Cushny-Peebles data: Soporific effects of scopolamine derivatives
Dactyl: Edgeworth's counts of dactyls in Virgil's Aeneid
DrinksWages: Elderton and Pearson's (1910) data on drinking and wages
EdgeworthDeaths: Edgeworth's Data on Death Rates in British Counties
Fingerprints: Waite's data on Patterns in Fingerprints
Galton: Galton's data on the heights of parents and their children
GaltonFamilies: Galton's data on the heights of parents and their children, by family
Guerry: Data from A.-M. Guerry, "Essay on the Moral Statistics of France"
HalleyLifeTable: Halley's Life Table
Jevons: W. Stanley Jevons' data on numerical discrimination
Langren: van Langren's data on longitude distance between Toledo and Rome
Macdonell: Macdonell's data on height and finger length of criminals, used by Gosset (1908)
Mayer: Mayer's data on the libration of the moon
Michelson: Michelson's 1879 determinations of the velocity of light
Minard: Data from Minard's famous graphic map of Napoleon's march on Moscow
Nightingale: Florence Nightingale's data on deaths from various causes in the Crimean War
OldMaps: Latitudes and Longitudes of 39 Points in 11 Old Maps
PearsonLee: Pearson and Lee's 1896 data on the heights of parents and children classified by gender
PolioTrials: Polio Field Trials Data on the Salk vaccine
Pollen: 5D dataset from the 1986 JSM Challenge
Prostitutes: Parent-Duchatelet's time-series data on the number of prostitutes in Paris
Pyx: Trial of the Pyx
Quarrels: Statistics of Deadly Quarrels
Saturn: Laplace's Saturn data
Snow: John Snow's map and data on the 1854 London Cholera outbreak
Virginis: J. F. W. Herschel's data on the orbit of the twin star gamma Virginis
Wheat: Playfair's data on wages and the price of wheat
Yeast: Student's (1906) Yeast Cell Counts
ZeaMays: Darwin's Heights of Cross- and Self-fertilized Zea May Pairs

Author(s)

Michael Friendly

Maintainer: Michael Friendly <friendly@yorku.ca>

References

Friendly, M. (2007). A Brief History of Data Visualization. In Chen, C., Hardle, W. & Unwin, A. (eds.) Handbook of Computational Statistics: Data Visualization, Springer-Verlag, III, Ch. 1, 1-34.

Friendly, M. & Denis, D. (2001). Milestones in the history of thematic cartography, statistical graphics, and data visualization. http://datavis.ca/milestones/

Friendly, M. & Denis, D. (2005). The early origins and development of the scatterplot. Journal of the History of the Behavioral Sciences, 41, 103-130.

Friendly, M. & Sigal, M. & Harnanansingh, D. (2016). "The Milestones Project: A Database for the History of Data Visualization," In Kostelnick, C. & Kimball, M. (ed.), Visible Numbers: The History of Data Visualization, Ashgate Press, Chapter 10.

Friendly, M. & Wainer, H. (2021). A History of Data Visualization and Graphic Communication. Harvard University Press. Book: https://www.hup.harvard.edu/books/9780674975231, Web site: https://friendly.github.io/HistDataVis/.

Examples

# see examples for the separate data sets

Arbuthnot's data on male and female birth ratios

Description

John Arbuthnot (1710) used these time series data on the ratios of male to female christenings in London from 1629-1710 to carry out the first known significance test, comparing observed data to a null hypothesis. The data for these 81 years showed that in every year there were more male than female christenings.

On the assumption that male and female births were equally likely, he showed that the probability of observing 82 years with more males than females was vanishingly small (~ 4.14 x 10^{-25}). He used this to argue that a nearly constant birth ratio > 1 could be interpreted to show the guiding hand of a devine being. The data set adds variables of deaths from the plague and total mortality obtained by Campbell and from Creighton (1965).

Usage

data(Arbuthnot)

Format

A data frame with 82 observations on the following 7 variables.

Year: a numeric vector, 1629-1710
Males: a numeric vector, number of male christenings
Females: a numeric vector, number of female christenings
Plague: a numeric vector, number of deaths from plague
Mortality: a numeric vector, total mortality
Ratio: a numeric vector, ratio of Males/Females
Total: a numeric vector, total christenings in London (000s)

Details

Sandy Zabell (1976) pointed out several errors and inconsistencies in the Arbuthnot data. In particular, the values for 1674 and 1704 are identical, suggesting that the latter were copied erroneously from the former.

Jim Oeppen <joeppen@health.sdu.dk> points out that: "Arbuthnot's data are annual counts of public baptisms, not births. Birth-baptism delay meant that infant deaths could occur before baptism. As male infants are more likely to die than females, the sex ratio at baptism might be expected to be lower than the 'normal' male- female birth ratio of 105:100. These effects were not constant as there were trends in birth-baptism delay, and in early infant mortality. In addition, the English Civil War and Commonwealth period 1642-1660 is thought to have been a period of both under-registration and lower fertility, but it is not clear whether these had sex-specific effects."

Source

Arbuthnot, John (1710). "An argument for Devine Providence, taken from the constant Regularity observ'd in the Births of both Sexes," Philosophical transactions, 27, 186-190. Published in 1711.

References

Campbell, R. B., Arbuthnot and the Human Sex Ratio (2001). Human Biology, 73:4, 605-610.

Creighton, C. (1965). A History of Epidemics in Britain, 2nd edition, vol. 1 and 2. NY: Barnes and Noble.

S. Zabell (1976). Arbuthnot, Heberden, and the Bills of Mortality. Technical Report No. 40, Department of Statistics, University of Chicago.

Examples

data(Arbuthnot)
# plot the sex ratios
with(Arbuthnot, plot(Year,Ratio, type='b', ylim=c(1, 1.20), ylab="Sex Ratio (M/F)"))
abline(h=1, col="red")
#  add loess smooth
Arb.smooth <- with(Arbuthnot, loess.smooth(Year,Ratio))
lines(Arb.smooth$x, Arb.smooth$y, col="blue", lwd=2)

# plot the total christenings to observe the anomalie in 1704
with(Arbuthnot, plot(Year,Total, type='b', ylab="Total Christenings"))

La Felicisima Armada

Description

The Spanish Armada (Spanish: Grande y Felicisima Armada, literally "Great and Most Fortunate Navy") was a Spanish fleet of 130 ships that sailed from La Coruna in August 1588. During its preparation, several accounts of its formidable strength were circulated to reassure allied powers of Spain or to intimidate its enemies. One such account was given by Paz Salas et Alvarez (1588). The intent was bring the forces of Spain to invade England, overthrow Queen Elizabeth I, and re-establish Spanish control of the Netherlands. However the Armada was not as fortunate as hoped: it was all destroyed in one week's fighting.

de Falguerolles (2008) reports the table given here as Armada as an early example of data to which multivariate methods might be applied.

Usage

data("Armada")

Format

A data frame with 10 observations on the following 11 variables.

Fleet: designation of the origin of the fleet, a factor with levels Andalucia, Castilla, Galeras, Guipuscua, Napoles, Pataches, Portugal, Uantiscas, Vizca, Vrcas
ships: number of ships, a numeric vector
tons: total tons of the ships, a numeric vector
soldiers: number of soldiers, a numeric vector
sailors: number of sailors, a numeric vector
men: total of soldiers plus sailors, a numeric vector
artillery: number of canons, a numeric vector
balls: number of canonballs, a numeric vector
gunpowder: amount of gunpowder loaded, a numeric vector
lead: a numeric vector
rope: a numeric vector

Details

Note that men = soldiers + sailors, so this variable is redundant in a multivariate analysis.

A complete list of the ships of the Spanish Armada, their types, armaments and fate can be found at https://en.wikipedia.org/wiki/List_of_ships_of_the_Spanish_Armada. An enterprising data historian might attempt to square the data given there with this table.

The fleet of Portugal, under the command of Alonso Pérez de Guzmán, 7th Duke of Medina Sidonia was largely in control of the attempted invasion of England.

Source

de Falguerolles, A. (2008). L'analyse des donnees; before and around. Journal Electronique d'Histoire des Probabilites et de la Statistique, 4 (2), Link: https://www.jehps.net/Decembre2008/Falguerolles.pdf

References

Pedro de Paz Salas and Antonio Alvares. La felicisima armada que elrey Don Felipe nuestro Senor mando juntar enel puerto de la ciudad de Lisboa enel Reyno de Portugal. Lisbon, 1588.

Examples

data(Armada)
# delete character and redundant variable
armada <- Armada[,-c(1,6)]
# use fleet as labels
fleet <- Armada[, 1]

# do a PCA of the standardized data
armada.pca <- prcomp(armada, scale.=TRUE)
summary(armada.pca)

# screeplot
plot(armada.pca, type="lines", pch=16, cex=2)

biplot(armada.pca, xlabs = fleet,
  xlab = "PC1 (Fleet size)",
  ylab = "PC2 (Fleet configuration)")

Bowley's data on values of British and Irish trade, 1855-1899

Description

In one of the first statistical textbooks, Arthur Bowley (1901) used these data to illustrate an arithmetic and graphical analysis of time-series data using the total value of British and Irish exports from 1855-1899. He presented a line graph of the time-series data, supplemented by overlaid line graphs of 3-, 5- and 10-year moving averages. His goal was to show that while the initial series showed wide variability, moving averages made the series progressively smoother.

Usage

data(Bowley)

Format

A data frame with 45 observations on the following 2 variables.

Year: Year, from 1855-1899
Value: total value of British and Irish exports (millions of Pounds)

Source

Bowley, A. L. (1901). Elements of Statistics. London: P. S. King and Son, p. 151-154.

Digitized from Bowley's graph.

Examples

data(Bowley)

# plot the data 
with(Bowley,plot(Year, Value, type='b', lwd=2, 
	ylab="Value of British and Irish Exports",
	main="Bowley's example of the method of smoothing curves"))

# find moving averages
# simpler version using stats::filter
running <- function(x, width = 5){
  as.vector(stats::filter(x, rep(1 / width, width), sides = 2))
  }

mav3<-running(Bowley$Value, width=3)
mav5<-running(Bowley$Value, width=5)
mav9<-running(Bowley$Value, width=9)
lines(Bowley$Year, mav3, col='blue', lty=2)
lines(Bowley$Year, mav5, col='green3', lty=3)
lines(Bowley$Year, mav9, col='brown', lty=4)

# add lowess smooth
lines(lowess(Bowley), col='red', lwd=2)

# Initial version, using ggplot
library(ggplot2)
ggplot(aes(x=Year, y=Value), data=Bowley) +
  geom_point() +
  geom_smooth(method="loess", formula=y~x)

Halley's Breslau Life Table

Description

Edmond Halley published his Breslau life table in 1693, which was arguably the first in the world based on population data. David Bellhouse (2011) resurrected the original sources of these data, collected by Caspar Neumann in the city of Breslau (now called Wroclaw), and then reconstructed in the 1880s by Jonas Graetzer, the medical officer in Breslau at that time.

The dataset here follows Graetzer, and gives the number of deaths at ages 1:100 recorded in each of the years 1687:1691. Halley's analysis was based on the total over those years.

Usage

data("Breslau")

Format

A data frame with 100 observations on the following 8 variables. The yearXXXX variables give the number of deaths for persons of a given age recorded in that year.

age: a numeric vector
year1687: a numeric vector
year1688: a numeric vector
year1689: a numeric vector
year1690: a numeric vector
year1691: a numeric vector
total: a numeric vector
average: a numeric vector

Details

This dataset was kindly provided by David Bellhouse.

Source

Bellhouse, D.R. (2011), A new look at Halley's life table. Journal of the Royal Statistical Society: Series A, 174, 823-832. doi:10.1111/j.1467-985X.2010.00684.x

References

Halley, E. (1693). An estimate of the degrees of mortality of mankind, drawn from the curious tables of births and funerals in the City of Breslaw; with an attempt to ascertain the price of annuities upon lives. Phil. Trans., 17, 596-610.

Examples

data(Breslau)

# Reproduce Figure 1 in Bellhouse (2011)
# He excluded age < 5 and made a point of the over-representation of deaths in quinquennial years.
library(ggplot2)
library(dplyr, warn.conflicts = FALSE)
Breslau5 <- Breslau |>
  filter(age >= 5) |>
  mutate(div5 = factor(age %% 5 == 0))

ggplot(Breslau5, aes(x=age, y=total), size=1.5) +
  geom_point(aes(color=div5)) +
  scale_color_manual(labels = c(FALSE, TRUE), 
                     values = c("blue", "red")) +
  guides(color=guide_legend("Age divisible by 5")) +
  theme(legend.position = "top") +
  labs(x = "Age current at death",
       y = "Total number of deaths") +
  theme_bw()

Cavendish's Determinations of the Density of the Earth

Description

Henry Cavendish carried out a series of experiments in 1798 to determine the mean density of the earth, as an indirect means to calculate the gravitational constant, G, in Newton's formula for the force (f) of gravitational attraction, f = G m M / r^2 between two bodies of mass m and M.

Stigler (1977) used these data to illustrate properties of robust estimators with real, historical data. For these data sets, he found that trimmed means performed as well or better than more elaborate robust estimators.

Usage

data(Cavendish)

Format

A data frame with 29 observations on the following 3 variables.

density: Cavendish's 29 determinations of the mean density of the earth
density2: same as density, with the third value (4.88) replaced by 5.88
density3: same as density, omitting the the first 6 observations

Details

Density values (D) of the earth are given as relative to that of water. If the earth is regarded as a sphere of radius R, Newton's law can be expressed as G D = 3 g / (4 \pi R), where g=9.806 m/s^2 is the acceleration due to gravity; so G is proportional to 1/D.

density contains Cavendish's measurements as analyzed, where he treated the value 4.88 as if it were 5.88. density2 corrects this. Cavendish also changed his experimental apparatus after the sixth determination, using a stiffer wire in the torsion balance. density3 replaces the first 6 values with NA.

The modern "true" value of D is taken as 5.517. The gravitational constant can be expressed as G = 6.674 * 10^-11 m^3/kg/s^2.

Source

Kyle Siegrist, "Virtual Laboratories in Probability and Statistics", https://www.math.uah.edu/stat/data/Cavendish.html

Stephen M. Stigler (1977), "Do robust estimators work with real data?", Annals of Statistics, 5, 1055-1098

References

Cavendish, H. (1798). Experiments to determine the density of the earth. Philosophical Transactions of the Royal Society of London, 88 (Part II), 469-527. Reprinted in A. S. Mackenzie (ed.), The Laws of Gravitation, 1900, New York: American.

Brownlee, K. A. (1965). Statistical theory and methodology in science and engineering, NY: Wiley, p. 520.

Examples

data(Cavendish)
summary(Cavendish)
boxplot(Cavendish, ylab='Density', xlab='Data set')
abline(h=5.517, col="red", lwd=2)

# trimmed means
sapply(Cavendish, mean, trim=.1, na.rm=TRUE)

# express in terms of G
G <- function(D, g=9.806, R=6371) 3*g / (4 * pi * R * D)
 
boxplot(10^5 * G(Cavendish), ylab='~ Gravitational constant (G)', xlab='Data set')
abline(h=10^5 * G(5.517), col="red", lwd=2)

Chest measurements of Scottish Militiamen

Description

Quetelet's data on chest measurements of 5738 Scottish Militiamen. Quetelet (1846) used this data as a demonstration of the normal distribution of physical characteristics and the concept of l'homme moyen.

Stigler (1986) compared this table to the original 1817 source, and discovered some transcription errors, which he corrected (p. 208). These data are given separately in ChestStigler. Gallagher (2020) used these data sets to re-consider the question of normality in these distributions.

Usage

data(ChestSizes)

Format

A data frame with 16 observations on the following 2 variables. Total count=5738.

chest: Chest size (in inches)
count: Number of soldiers with this chest size

Source

Velleman, P. F. and Hoaglin, D. C. (1981). Applications, Basics, and Computing of Exploratory Data Analysis. Belmont. CA: Wadsworth. Retrieved from Statlib: https://www.stat.cmu.edu/StatDat/Datafiles/MilitiamenChests.html

References

A. Quetelet, Lettres a S.A.R. le Duc Regnant de Saxe-Cobourg et Gotha, sur la Theorie des Probabilites, Appliquee aux Sciences Morales et Politiques. Brussels: M. Hayes, 1846, p. 400.

Eugene D. Gallagher (2020). Was Quetelet's Average Man Normal?, The American Statistician, 74:3, 301-306, DOI: 10.1080/00031305.2019.1706635

Stephen M. Stigler (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Cambridge, MA: Harvard University Press, 1986, p. 208.

Examples

data(ChestSizes)

# frequency polygon
plot(ChestSizes, type='b')
# barplot
barplot(ChestSizes[,2], ylab="Frequency", xlab="Chest size")

# calculate expected frequencies under normality, chest ~ N(xbar, std)
n_obs <- sum(ChestSizes$count)
xbar  <- with(ChestSizes, weighted.mean(chest, count))
std   <- with(ChestSizes, sd(rep(chest, count)))

expected <- 
with(ChestSizes, diff(pnorm(c(32, chest) + .5, xbar, std)) * sum(count))

William Farr's Data on Cholera in London, 1849

Description

In 1852, William Farr, published a report of the Registrar-General on mortality due to cholera in England in the years 1848-1849, during which there was a large epidemic throughout the country. Farr initially believed that cholera arose from bad air ("miasma") associated with low elevation above the River Thames. John Snow (1855) later showed that the disease was principally spread by contaminated water.

This data set comes from a paper by Brigham et al. (2003) that analyses some tables from Farr's report to examine the prevalence of death from cholera in the districts of London in relation to the available predictors from Farr's table.

Usage

data("Cholera")

Format

A data frame with 38 observations on the following 15 variables.

district: name of the district in London, a character vector
cholera_drate: deaths from cholera in 1849 per 10,000 inhabitants, a numeric vector
cholera_deaths: number of deaths registered from cholera in 1849, a numeric vector
popn: population, in the middle of 1849, a numeric vector
elevation: elevation, in feet above the high water mark, a numeric vector
region: a grouping of the London districts, a factor with levels West North Central South Kent
water: water supply region, a factor with levels Battersea New River Kew; see Details
annual_deaths: annual deaths from all causes, 1838-1844, a numeric vector
pop_dens: population density (persons per acre), a numeric vector
persons_house: persons per inhabited house, a numeric vector
house_valpp: average annual value of house, per person (pounds), a numeric vector
poor_rate: poor rate precept per pound of house value, a numeric vector
area: district area, a numeric vector
houses: number of houses, a numeric vector
house_val: total house values, a numeric vector

Details

The supply of water was classified as “Thames, between Battersea and Waterloo Bridges” (central London), “New River, Rivers Lea and Ravensbourne”, and “Thames, at Kew and Hammersmith” (western London). The factor levels use abbreviations for these.

The data frame is sorted by increasing elevation above the high water mark.

Source

Bingham P., Verlander, N. Q., Cheal M. J. (2004). John Snow, William Farr and the 1849 outbreak of cholera that affected London: a reworking of the data highlights the importance of the water supply. Public Health, 118(6), 387-394, Table 2. (The data was kindly supplied by Neville Verlander, including additional variables not shown in their Table 2.)

References

Registrar-General (1852). Report on the Mortality of Cholera in England 1848-49, W. Clowes and Sons, for Her Majesty's Stationary Office. Written by William Farr. https://ia600208.us.archive.org/11/items/b24751297/b24751297.pdf The relevant tables are at pages clii – clvii.

Examples

data(Cholera)

# plot cholera deaths vs. elevation
plot(cholera_drate ~ elevation, data=Cholera, 
	pch=16, cex.lab=1.2, cex=1.2,
	xlab="Elevation above high water mark (ft)",
	ylab="Deaths from cholera in 1849 per 10,000")

# Farr's mortality ~ 1/ elevation law
elev <- c(0, 10, 30, 50, 70, 90, 100, 350)
mort <- c(174, 99, 53, 34, 27, 22, 20, 6)
lines(mort ~ elev, lwd=2, col="blue")

# better plots, using car::scatterplot

if(require("car", quietly=TRUE)) {
# show separate regression lines for each water supply
  scatterplot(cholera_drate ~ elevation | water, data=Cholera, 
              smooth=FALSE, pch=15:17,
              id=list(n=2, labels=sub(",.*", "", Cholera$district)),
              col=c("red", "darkgreen", "blue"),
              legend=list(coords="topleft", title="Water supply"),
              xlab="Elevation above high water mark (ft)",
              ylab="Deaths from cholera in 1849 per 10,000")
  
  scatterplot(cholera_drate ~ poor_rate | water, data=Cholera, 
              smooth=FALSE, pch=15:17,
              id=list(n=2, labels=sub(",.*", "", Cholera$district)),
              col=c("red", "darkgreen", "blue"),
              legend=list(coords="topleft", title="Water supply"),
              xlab="Poor rate per pound of house value",
              ylab="Deaths from cholera in 1849 per 10,000")
  }

# fit a logistic regression model a la Bingham etal.
fit <- glm( cbind(cholera_deaths, popn) ~ 
            water + elevation + poor_rate + annual_deaths +
            pop_dens + persons_house,
            data=Cholera, family=binomial)
summary(fit)

# odds ratios
cbind( OR = exp(coef(fit))[-1], exp(confint(fit))[-1,] )

if (require(effects)) {
  eff <- allEffects(fit)
  plot(eff)
}

Daily Deaths from Cholera and Diarrhaea in England, 1849

Description

Deaths from Cholera and Diarrhaea, for each day of the month of each of the 12 months of 1849.

This was used by William Farr (GRO & Farr, 1852, Plate 2) to produce a time series chart of these deaths, in which he also recorded various meteorological phenomena (barometer, wind, rain), to see if he could find any patterns. This chart is available on the web site for Friendly & Wainer (2021) as Fig 4.1, https://friendly.github.io/HistDataVis/figs-web/04_1-cholera-diarrhea.png.

James Riley (2023) notes, "Cholera 1849 has special significance — it is likely to be one of few modern pandemics that was completely unmitigated."

Usage

data("CholeraDeaths1849")

Format

A data frame with 730 observations on the following 6 variables.

month: a character vector
cause_of_death: a factor with levels Cholera Diarrhaea
day_of_month: a character vector
deaths: a numeric vector
date: a Date
day_of_week: an ordered factor with levels Mon < Tue < Wed < Thu < Fri < Sat < Sun

Details

The data set was transcribed by James Riley to a spreadsheet, https://github.com/jimr1603/1849-cholera. He notes, "the scan at Internet Archive has a fold on day 11. I have derived this column from the row totals."

Source

The original source is: General Register Office, William Farr (1852), Report on the Mortality of Cholera in England, 1848-49. London: Printed by W. Clowes, for HMSO; scanned by the Internet Archive from the collection of King's College London and available at https://archive.org/details/b21308251/page/20/mode/2up.

References

Friendly, M. & Wainer, H. (2021). A History of Data Visualization and Graphic Communication, Harvard University Press.

Riley, J. (2023). "Cholera in Victorian England", blog post, https://openor.blog/2023/07/27/cholera-in-victorian-england/.

Examples

data(CholeraDeaths1849)
str(CholeraDeaths1849)

# Reproduce Farr's (1852) plate 2
library(ggplot2)
CholeraDeaths1849  |>
  ggplot(aes(x = date, y = deaths, colour = cause_of_death)) +
  geom_line(linewidth = 1.2) +
  theme_bw(base_size = 14) +
  theme(legend.position = "top")

Cushny-Peebles Data: Soporific Effects of Scopolamine Derivatives

Description

Cushny and Peebles (1905) studied the effects of hydrobromides related to scopolamine and atropine in producing sleep. The sleep of mental patients was measured without hypnotic (Control) and after treatment with one of three drugs: L. hyoscyamine hydrobromide (L_hyoscyamine), L. hyoscine hydrobromide (L_hyoscyine), and a mixture (racemic) form, DL_hyoscine, called atropine. The L (levo) and D (detro) form of a given molecule are optical isomers (mirror images).

The drugs were given on alternate evenings, and the hours of sleep were compared with the intervening control night. Each of the drugs was tested in this manner a varying number of times in each subject. The average number of hours of sleep for each treatment is the response.

Student (1908) used these data to illustrate the paired-sample t-test in small samples, testing the hypothesis that the mean difference between a given drug and the control condition was zero. This data set became well known when used by Fisher (1925). Both Student and Fisher had problems labeling the drugs correctly (see Senn & Richardson (1994)), and consequently came to wrong conclusions.

But as well, the sample sizes (number of nights) for each mean differed widely, ranging from 3-9, and this was not taken into account in their analyses. To allow weighted analyses, the number of observations for each mean is contained in the data frame CushnyPeeblesN.

Usage

data(CushnyPeebles)
data(CushnyPeeblesN)

Format

CushnyPeebles: A data frame with 11 observations on the following 4 variables.

Control: a numeric vector: mean hours of sleep
L_hyoscyamine: a numeric vector: mean hours of sleep
L_hyoscine: a numeric vector: mean hours of sleep
D_hyoscine: a numeric vector: mean hours of sleep

CushnyPeeblesN: A data frame with 11 observations on the following 4 variables.

Control: a numeric vector: number of observations
L_hyoscyamine: a numeric vector: number of observations
L_hyoscine: a numeric vector: number of observations
DL_hyoscine: a numeric vector: number of observations

Details

The last patient (11) has no Control observations, and so is often excluded in analyses or other versions of this data set.

Source

Cushny, A. R., and Peebles, A. R. (1905), "The Action of Optical Isomers. II: Hyoscines," Journal of Physiology, 32, 501-510.

References

Fisher, R. A. (1925), Statistical Methods for Research Workers, Edinburgh and London: Oliver & Boyd.

Student (1908), "The Probable Error of a Mean," Biometrika, 6, 1-25.

Senn, S.J. and Richardson, W. (1994), "The first t-test", Statistics in Medicine, 13, 785-803.

Examples

data(CushnyPeebles)
# quick looks at the data
plot(CushnyPeebles)
boxplot(CushnyPeebles, ylab="Hours of Sleep", xlab="Treatment")

##########################
# Repeated measures MANOVA

CPmod <- lm(cbind(Control, L_hyoscyamine, L_hyoscine, DL_hyoscine) ~ 1, data=CushnyPeebles)

# Assign within-S factor and contrasts
Treatment <- factor(colnames(CushnyPeebles), levels=colnames(CushnyPeebles))
contrasts(Treatment) <- matrix(
	c(-3, 1, 1, 1,
	   0,-2, 1, 1,
	   0, 0,-1, 1), ncol=3)
colnames(contrasts(Treatment)) <- c("Control.Drug", "L.DL", "L_hy.DL_hy")

Treats <- data.frame(Treatment)
if (require(car)) {
(CPaov <- Anova(CPmod, idata=Treats, idesign= ~Treatment))
}
summary(CPaov, univariate=FALSE)

if (require(heplots)) {
  heplot(CPmod, idata=Treats, idesign= ~Treatment, iterm="Treatment", 
	xlab="Control vs Drugs", ylab="L vs DL drug")
  pairs(CPmod, idata=Treats, idesign= ~Treatment, iterm="Treatment")
}

################################
# reshape to long format, add Ns

CPlong <- stack(CushnyPeebles)[,2:1]
colnames(CPlong) <- c("treatment", "sleep")
CPN <- stack(CushnyPeeblesN)
CPlong <- data.frame(patient=rep(1:11,4), CPlong, n=CPN$values)
str(CPlong)

Edgeworth's counts of dactyls in Virgil's Aeneid

Description

Edgeworth (1885) took the first 75 lines in Book XI of Virgil's Aeneid and classified each of the first four "feet" of the line as a dactyl (one long syllable followed by two short ones) or not.

Grouping the lines in blocks of five gave a 4 x 25 table of counts, represented here as a data frame with ordered factors, Foot and Lines. Edgeworth used this table in what was among the first examples of analysis of variance applied to a two-way classification.

Usage

data(Dactyl)

Format

A data frame with 60 observations on the following 3 variables.

Foot: an ordered factor with levels 1 < 2 < 3 < 4
Lines: an ordered factor with levels 1:5 < 6:10 < 11:15 < 16:20 < 21:25 < 26:30 < 31:35 < 36:40 < 41:45 < 46:50 < 51:55 < 56:60 < 61:65 < 66:70 < 71:75
count: number of dactyls

Source

Stigler, S. (1999) Statistics on the Table Cambridge, MA: Harvard University Press, table 5.1.

References

Edgeworth, F. Y. (1885). On methods of ascertaining variations in the rate of births, deaths and marriages. Journal of the [Royal] Statistical Society, 48, 628-649.

Examples

data(Dactyl)

# display the basic table
xtabs(count ~ Foot+Lines, data=Dactyl)

# simple two-way anova
anova(dact.lm <- lm(count ~ Foot+Lines, data=Dactyl))

# plot the lm-quartet
op <- par(mfrow=c(2,2))
plot(dact.lm)
par(op)

# show table as a simple mosaicplot
mosaicplot(xtabs(count ~ Foot+Lines, data=Dactyl), shade=TRUE)

Elderton and Pearson's (1910) data on drinking and wages

Description

In 1910, Karl Pearson weighed in on the debate, fostered by the temperance movement, on the evils done by alcohol not only to drinkers, but to their families. The report "A first study of the influence of parental alcoholism on the physique and ability of their offspring" was an ambitious attempt to the new methods of statistics to bear on an important question of social policy, to see if the hypothesis that children were damaged by parental alcoholism would stand up to statistical scrutiny.

Working with his assistant, Ethel M. Elderton, Pearson collected voluminous data in Edinburgh and Manchester on many aspects of health, stature, intelligence, etc. of children classified according to the drinking habits of their parents. His conclusions where almost invariably negative: the tendency of parents to drink appeared unrelated to any thing he had measured.

The firestorm that this report set off is well described by Stigler (1999), Chapter 1. The data set DrinksWages is just one of Pearson's many tables, that he published in a letter to The Times, August 10, 1910.

Usage

data(DrinksWages)

Format

A data frame with 70 observations on the following 6 variables, giving the number of non-drinkers (sober) and drinkers (drinks) in various occupational categories (trade).

class: wage class: a factor with levels A B C
trade: a factor with levels baker barman billposter ... wellsinker wireworker
sober: the number of non-drinkers, a numeric vector
drinks: the number of drinkers, a numeric vector
wage: weekly wage (in shillings), a numeric vector
n: total number, a numeric vector

Details

The data give Karl Pearson's tabulation of the father's trades from an Edinburgh sample, classified by whether they drink or are sober, and giving average weekly wage.

The wages are averages of the individuals' nominal wages. Class A is those with wages under 2.5s.; B: those with wages 2.5s. to 30s.; C: wages over 30s.

Source

Pearson, K. (1910). The Times, August 10, 1910.

Stigler, S. M. (1999). Statistics on the Table: The History of Statistical Concepts and Methods. Harvard University Press, Table 1.1

References

M. E. Elderton & K. Pearson (1910). A first study of the influence of parental alcoholism on the physique and ability of their offspring, Eugenics Laboratory Memoirs, 10.

Examples

data(DrinksWages)
plot(DrinksWages) 

# plot proportion sober vs. wage | class
with(DrinksWages, plot(wage, sober/n, col=c("blue","red","green")[class]))

# fit logistic regression model of sober on wage
mod.sober <- glm(cbind(sober, n) ~ wage, family=binomial, data=DrinksWages)
summary(mod.sober)
op <- par(mfrow=c(2,2))
plot(mod.sober)
par(op)

# TODO: plot fitted model

Edgeworth's Data on Death Rates in British Counties

Description

In 1885, Francis Edgeworth published a paper, On methods of ascertaining variations in the rate of births, deaths and marriages. It contained among the first examples of two-way tables, analyzed to show variation among row and column factors, in a way that Fisher would later formulate as the Analysis of Variance.

Although the data are rates per 1000, they provide a good example of a two-way ANOVA with n=1 per cell, where an additive model fits reasonably well.

Treated as frequencies, the data is also a good example of a case where the independence model fits reasonably well.

Usage

data("EdgeworthDeaths")

Format

A data frame with 42 observations on the following 3 variables.

County: a factor with levels Berks Herts Bucks Oxford Bedford Cambridge
year: an ordered factor with levels 1876 < 1877 < 1878 < 1879 < 1880 < 1881 < 1882
Freq: a numeric vector, death rate per 1000 population

Details

Edgeworth's data came from the Registrar General's report for the final year, 1883. The Freq variable represents death rates per 1000 population in the six counties listed.

Source

The data were scanned from Table 5.2 in Stigler, S. M. (1999) Statistics on the Table: The History of Statistical Concepts and Methods, Harvard University Press.

References

Edgeworth, F. Y. (1885). On Methods of Ascertaining Variations in the Rate of Births, Deaths, and Marriages. Journal of the Statistical Society of London, 48(4), 628-649. doi:10.2307/2979201

Examples

data(EdgeworthDeaths)

# fit the additive ANOVA model
library(car)  # for Anova()
EDmod <- lm(Freq ~ County + year, data=EdgeworthDeaths)
Anova(EDmod)

# now, consider as a two-way table of frequencies

library(vcd)
library(MASS)
structable( ~ County + year, data=EdgeworthDeaths)
loglm( Freq ~ County + year, data=EdgeworthDeaths)

mosaic( ~ County + year, data=EdgeworthDeaths, 
	shade=TRUE, legend=FALSE, labeling=labeling_values, 
	gp=shading_Friendly)

Waite's data on Patterns in Fingerprints

Description

Waite (1915) was interested in analyzing the association of patterns in fingerprints, and produced a table of counts for 2000 right hands, classified by the number of fingers describable as a "whorl", a "small loop" (or neither). Because each hand contributes five fingers, the number of Whorls + Loops cannot exceed 5, so the contingency table is necessarily triangular.

Karl Pearson (1904) introduced the test for independence in contingency tables, and by 1913 had developed methods for "restricted contingency tables," such as the triangular table analyzed by Waite. The general formulation of such tests for association in restricted tables is now referred to as models for quasi-independence.

Usage

data(Fingerprints)

Format

A frequency data frame with 36 observations on the following 3 variables, representing a 6 x 6 table giving the cross-classification of the fingers on 2000 right hands as a whorl, small loop or neither.

Whorls: Number of whorls, an ordered factor with levels 0 < 1 < 2 < 3 < 4 < 5
Loops: Number of small loops, an ordered factor with levels 0 < 1 < 2 < 3 < 4 < 5
count: Number of hands

Details

Cells for which Whorls + Loops>5 have NA for count

Source

Stigler, S. M. (1999). Statistics on the Table. Cambridge, MA: Harvard University Press, table 19.4.

References

Pearson, K. (1904). Mathematical contributions to the theory of evolution. XIII. On the theory of contingency and its relation to association and normal correlation. Reprinted in Karl Pearson's Early Statistical Papers, Cambridge: Cambridge University Press, 1948, 443-475.

Waite, H. (1915). The analysis of fingerprints, Biometrika, 10, 421-478.

Examples

data(Fingerprints)
xtabs(count ~ Whorls + Loops, data=Fingerprints)

Galton's data on the heights of parents and their children

Description

Galton (1886) presented these data in a table, showing a cross-tabulation of 928 adult children born to 205 fathers and mothers, by their height and their mid-parent's height. He visually smoothed the bivariate frequency distribution and showed that the contours formed concentric and similar ellipses, thus setting the stage for correlation, regression and the bivariate normal distribution.

Usage

data(Galton)

Format

A data frame with 928 observations on the following 2 variables.

parent: a numeric vector: height of the mid-parent (average of father and mother)
child: a numeric vector: height of the child

Details

The data are recorded in class intervals of width 1.0 in. He used non-integer values for the center of each class interval because of the strong bias toward integral inches.

All of the heights of female children were multiplied by 1.08 before tabulation to compensate for sex differences. See Hanley (2004) for a reanalysis of Galton's raw data questioning whether this was appropriate.

Source

Galton, F. (1886). Regression Towards Mediocrity in Hereditary Stature Journal of the Anthropological Institute, 15, 246-263

References

Friendly, M. & Denis, D. (2005). The early origins and development of the scatterplot. Journal of the History of the Behavioral Sciences, 41, 103-130.

Galton, F. (1869). Hereditary Genius: An Inquiry into its Laws and Consequences. London: Macmillan.

Hanley, J. A. (2004). "Transmuting" Women into Men: Galton's Family Data on Human Stature. The American Statistician, 58, 237-243. See: http://www.medicine.mcgill.ca/epidemiology/hanley/galton/ for source materials.

Stigler, S. M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Cambridge, MA: Harvard University Press, Table 8.1

Wachsmuth, A. W., Wilkinson L., Dallal G. E. (2003). Galton's bend: A previously undiscovered nonlinearity in Galton's family stature regression data. The American Statistician, 57, 190-192. doi:10.1198/0003130031874

Examples


data(Galton)

###########################################################################
# sunflower plot with regression line and data ellipses and lowess smooth
###########################################################################

with(Galton, 
	{
	sunflowerplot(parent,child, xlim=c(62,74), ylim=c(62,74))
	reg <- lm(child ~ parent)
	abline(reg)
	lines(lowess(parent, child), col="blue", lwd=2)
	if(require(car)) {
	dataEllipse(parent,child, xlim=c(62,74), ylim=c(62,74), plot.points=FALSE)
		}
  })

Galton's data on the heights of parents and their children, by child

Description

This data set lists the individual observations for 934 children in 205 families on which Galton (1886) based his cross-tabulation.

In addition to the question of the relation between heights of parents and their offspring, for which this data is mainly famous, Galton had another purpose which the data in this form allows to address: Does marriage selection indicate a relationship between the heights of husbands and wives, a topic he called assortative mating? Keen [p. 297-298](2010) provides a brief discussion of this topic.

Usage

data(GaltonFamilies)

Format

A data frame with 934 observations on the following 8 variables.

family: family ID, a factor with levels 001-204
father: height of father
mother: height of mother
midparentHeight: mid-parent height, calculated as (father + 1.08*mother)/2
children: number of children in this family
childNum: number of this child within family. Children are listed in decreasing order of height for boys followed by girls
gender: child gender, a factor with levels female male
childHeight: height of child

Details

Galton's notebook lists 963 children in 205 families ranging from 1-15 adult children children. Of these, 29 had non-numeric heights recorded and are not included here.

Families are largely listed in descending order of fathers and mothers height.

Source

Galton's notebook, http://www.medicine.mcgill.ca/epidemiology/hanley/galton/notebook/, transcribed by Beverley Shipley in 2001.

References

Galton, F. (1886). Regression Towards Mediocrity in Hereditary Stature Journal of the Anthropological Institute, 15, 246-263

Keen, K. J. (2010). Graphics for Statistics and Data Analysis with R, Boca Raton: CRC Press, https://www.unbc.ca/keen/textbook.

Examples

data(GaltonFamilies)
str(GaltonFamilies)

## reproduce Fig 2 in Hanley (2004)
library(car)
scatterplot(childHeight ~ midparentHeight | gender, data=GaltonFamilies, 
    ellipse=TRUE, levels=0.68, legend.coords=list(x=64, y=78))

# multiply daughters' heights by 1.08
GF1 <- within(GaltonFamilies, 
              {childHeight <- ifelse (gender=="female", 1.08*childHeight, childHeight)} )
scatterplot(childHeight ~ midparentHeight | gender, data=GF1, 
    ellipse=TRUE, levels=0.68, legend.coords=list(x=64, y=78))

# add 5.2 to daughters' heights 
GF2 <- within(GaltonFamilies, 
              {childHeight <- ifelse (gender=="female", childHeight+5.2, childHeight)} )
scatterplot(childHeight ~ midparentHeight | gender, data=GF2, 
    ellipse=TRUE, levels=0.68, legend.coords=list(x=64, y=78))

#########################################
# relationship between heights of parents
#########################################

Parents <- subset(GaltonFamilies, !duplicated(GaltonFamilies$family))

with(Parents, {
  sunflowerplot(mother, father, rotate=TRUE, pch=16, 
     xlab="Mother height", ylab="Father height")
	dataEllipse(mother, father, add=TRUE, plot.points=FALSE, 
     center.pch=NULL, levels=0.68)
	abline(lm(father ~ mother), col="red", lwd=2)
	}
	)

Data from A.-M. Guerry, "Essay on the Moral Statistics of France"

Description

Andre-Michel Guerry (1833) was the first to systematically collect and analyze social data on such things as crime, literacy and suicide with the view to determining social laws and the relations among these variables.

The Guerry data frame comprises a collection of 'moral variables' on the 86 departments of France around 1830. A few additional variables have been added from other sources.

Usage

data(Guerry)

Format

A data frame with 86 observations (the departments of France) on the following 23 variables.

dept: Department ID: Standard numbers for the departments, except for Corsica (200)
Region: Region of France ('N'='North', 'S'='South', 'E'='East', 'W'='West', 'C'='Central'). Corsica is coded as NA
Department: Department name: Departments are named according to usage in 1830, but without accents. A factor with levels Ain Aisne Allier ... Vosges Yonne
Crime_pers: Population per Crime against persons. Source: A2 (Compte general, 1825-1830)
Crime_prop: Population per Crime against property. Source: A2 (Compte general, 1825-1830)
Literacy: Percent Read & Write: Percent of military conscripts who can read and write. Source: A2
Donations: Donations to the poor. Source: A2 (Bulletin des lois)
Infants: Population per illegitimate birth. Source: A2 (Bureau des Longitudes, 1817-1821)
Suicides: Population per suicide. Source: A2 (Compte general, 1827-1830)
MainCity: Size of principal city ('1:Sm', '2:Med', '3:Lg'), used as a surrogate for population density. Large refers to the top 10, small to the bottom 10; all the rest are classed Medium. Source: A1. An ordered factor with levels 1:Sm < 2:Med < 3:Lg
Wealth: Per capita tax on personal property. A ranked index based on taxes on personal and movable property per inhabitant. Source: A1
Commerce: Commerce and Industry, measured by the rank of the number of patents / population. Source: A1
Clergy: Distribution of clergy, measured by the rank of the number of Catholic priests in active service / population. Source: A1 (Almanach officiel du clergy, 1829)
Crime_parents: Crimes against parents, measured by the rank of the ratio of crimes against parents to all crimes– Average for the years 1825-1830. Source: A1 (Compte general)
Infanticide: Infanticides per capita. A ranked ratio of number of infanticides to population– Average for the years 1825-1830. Source: A1 (Compte general)
Donation_clergy: Donations to the clergy. A ranked ratio of the number of bequests and donations inter vivios to population– Average for the years 1815-1824. Source: A1 (Bull. des lois, ordunn. d'autorisation)
Lottery: Per capita wager on Royal Lottery. Ranked ratio of the proceeds bet on the royal lottery to population— Average for the years 1822-1826. Source: A1 (Compte rendus par le ministere des finances)
Desertion: Military desertion, ratio of the number of young soldiers accused of desertion to the force of the military contingent, minus the deficit produced by the insufficiency of available billets– Average of the years 1825-1827. Source: A1 (Compte du ministere du guerre, 1829 etat V)
Instruction: Instruction. Ranks recorded from Guerry's map of Instruction. Note: this is inversely related to Literacy (as defined here)
Prostitutes: Prostitutes in Paris. Number of prostitutes registered in Paris from 1816 to 1834, classified by the department of their birth Source: Parent-Duchatelet (1836), De la prostitution en Paris
Distance: Distance to Paris (km). Distance of each department centroid to the centroid of the Seine (Paris) Source: calculated from department centroids
Area: Area (1000 km^2). Source: Angeville (1836)
Pop1831: 1831 population. Population in 1831, taken from Angeville (1836), Essai sur la Statistique de la Population fran?ais, in 1000s

Details

Note that most of the variables (e.g., Crime_pers) are scaled so that 'more is better' morally.

Values for the quantitative variables displayed on Guerry's maps were taken from Table A2 in the English translation of Guerry (1833) by Whitt and Reinking. Values for the ranked variables were taken from Table A1, with some corrections applied. The maximum is indicated by rank 1, and the minimum by rank 86.

Source

Angeville, A. (1836). Essai sur la Statistique de la Population fran?aise Paris: F. Doufour.

Guerry, A.-M. (1833). Essai sur la statistique morale de la France Paris: Crochard. English translation: Hugh P. Whitt and Victor W. Reinking, Lewiston, N.Y. : Edwin Mellen Press, 2002.

Parent-Duchatelet, A. (1836). De la prostitution dans la ville de Paris, 3rd ed, 1857, p. 32, 36

References

Dray, S. and Jombart, T. (2011). A Revisit Of Guerry's Data: Introducing Spatial Constraints In Multivariate Analysis. The Annals of Applied Statistics, Vol. 5, No. 4, 2278-2299. http://arxiv.org/pdf/1202.6485, DOI: 10.1214/10-AOAS356.

Brunsdon, C. and Dykes, J. (2007). Geographically weighted visualization: interactive graphics for scale-varying exploratory analysis. Geographical Information Science Research Conference (GISRUK 07), NUI Maynooth, Ireland, April, 2007.

Friendly, M. (2007). A.-M. Guerry's Moral Statistics of France: Challenges for Multivariable Spatial Analysis. Statistical Science, 22, 368-399.

Friendly, M. (2007). Data from A.-M. Guerry, Essay on the Moral Statistics of France (1833), http://datavis.ca/gallery/guerry/guerrydat.html.

Examples

data(Guerry)
## maybe str(Guerry) ; plot(Guerry) ...

Halley's Life Table

Description

In 1693 the famous English astronomer Edmond Halley studied the birth and death records of the city of Breslau, which had been transmitted to the Royal Society by Caspar Neumann. He produced a life table showing the number of people surviving to any age from a cohort born the same year. He also used his table to compute the price of life annuities.

Usage

data("HalleyLifeTable")

Format

A data frame with 84 observations on the following 4 variables.

age: a numeric vector
deaths: number of deaths, D_k, among people of age k, a numeric vector
number: size of the population, P_k surviving until this age, a numeric vector
ratio: the ratio P_{k+1}/P_k, the conditional probability of surviving until age k + 1 given that one had already reached age k, a numeric vector

Details

Halley's table contained only age and number. For people aged over 84 years, Halley just noted that their total number was 107. This value is not included in the data set.

The data from Breslau had a mean of 1,238 births per year: this is the value that Halley took for the size, P_0 of the population cohort at age 0. From the data, he could compute the annual mean D_k of the number of deaths among people aged k for all k >= 0. From this, he calculated the number P_{k+1} surviving one more year,

P_{k+1} = P_k - D_k

This method had the great advantage of not requiring a general census but only knowledge of the number of births and deaths and of the age at which people died during a few years.

Source

N. Bacaer (2011), "Halley's life table (1693)", Ch 2, pp 5-10. In A Short History of Mathematical Population Dynamics, Springer-Verlag London, DOI 10.1007/978-0-85729-115-8_2. Data taken from Table 1.

References

Halley, E. (1693). An estimate of the degrees of the mortality of mankind, drawn from curious tables of the births and funerals at the city of Breslau; with an attempt to ascertain the price of annuities upon lives. Philosophical Transactions of the Royal Society, London, 17, 596-610.

The text of Halley's paper was found at http://www.pierre-marteau.com/editions/1693-mortality.html

Examples

data(HalleyLifeTable)
# what was the estimated population of Breslau?
sum(HalleyLifeTable$number)

# plot survival vs. age
plot(number ~ age, data=HalleyLifeTable, type="h", ylab="Number surviving")

# population pyramid is transpose of this
plot(age ~ number, data=HalleyLifeTable, type="l", xlab="Number surviving")
with(HalleyLifeTable, segments(0, age, number, age, lwd=2))

# conditional probability of survival, one more year
plot(ratio ~ age, data=HalleyLifeTable, ylab="Probability survive one more year")

W. Stanley Jevons' data on numerical discrimination

Description

In a remarkable brief note in Nature, 1871, W. Stanley Jevons described the results of an experiment he had conducted on himself to determine the limits of the number of objects an observer could comprehend immediately without counting them. This was an important philosophical question: How many objects can the mind embrace at once?

He carried out 1027 trials in which he tossed an "uncertain number" of uniform black beans into a box and immediately attempted to estimate the number "without the least hesitation". His questions, procedure and analysis anticipated by 75 years one of the most influential papers in modern cognitive psychology by George Miller (1956), "The magical number 7 plus or minus 2: Some limits on ..." For Jevons, the magical number was 4.5, representing an empirical law of complete accuracy.

Usage

data(Jevons)

Format

A frequency data frame with 50 observations on the following 4 variables.

actual: Actual number: a numeric vector
estimated: Estimated number: a numeric vector
frequency: Frequency of this combination of (actual, estimated): a numeric vector
error: actual-estimated: a numeric vector

Details

The original data were presented in a two-way, 13 x 13 frequency table, estimated (3:15) x actual (3:15).

Source

Jevons, W. S. (1871). The Power of Numerical Discrimination, Nature, 1871, III (281-282)

References

Miller, G. A. (1956). The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information, Psychological Review, 63, 81-97, http://www.musanim.com/miller1956/

Examples

data(Jevons)
# show as tables
xtabs(frequency ~ estimated+actual, data=Jevons)
xtabs(frequency ~ error+actual, data=Jevons)

# show as sunflowerplot with regression line
with(Jevons, sunflowerplot(actual, estimated, frequency, 
  main="Jevons data on numerical estimation"))
Jmod <-lm(estimated ~ actual, data=Jevons, weights=frequency)
abline(Jmod)

# show as balloonplots
if (require(gplots)) {

with(Jevons, balloonplot(actual, estimated, frequency, xlab="actual", ylab="estimated", 
  main="Jevons data on numerical estimation\nBubble area proportional to frequency",
  text.size=0.8))

with(Jevons, balloonplot(actual, error, frequency, xlab="actual", ylab="error", 
  main="Jevons data on numerical estimation: Errors\nBubble area proportional to frequency", 
  text.size=0.8))
}

# plot average error
if(require(reshape)) {
unJevons <- untable(Jevons, Jevons$frequency)
str(unJevons)

require(plyr)
mean_error <- function(df) mean(df$error, na.rm=TRUE)
Jmean <- ddply(unJevons, .(actual), mean_error)
with(Jmean, plot(actual, V1, ylab='Mean error', xlab='Actual number', type='b', main='Jevons data'))
abline(h=0)
}

van Langren's Data on Longitude Distance between Toledo and Rome

Description

Michael Florent van Langren (1598-1675) was a Dutch mathematician and astronomer, who served as a royal mathematician to King Phillip IV of Spain, and who worked on one of the most significant problems of his time— the accurate determination of longitude, particularly for navigation at sea.

In order to convince the Spanish court of the seriousness of the problem (often resulting in great losses through ship wrecks), he prepared a 1-dimensional line graph, showing all the available estimates of the distance in longitude between Toledo and Rome, which showed large errors, for even this modest distance. This 1D line graph, from Langren (1644), is believed to be the first known graph of statistical data (Friendly etal., 2010). It provides a compelling example of the notions of statistical variability and bias.

The data frame Langren1644 gives the estimates and other information derived from the previously known 1644 graph. It turns out that van Langren produced other versions of this graph, as early as 1628. The data frame Langren.all gives the estimates derived from all known versions of this graph.

Usage

	data(Langren1644)
	data(Langren.all)

Format

Langren1644: A data frame with 12 observations on the following 9 variables, giving determinations of the distance in longitude between Toledo and Rome, from the 1644 graph.

Name: The name of the person giving a determination, a factor with levels A. Argelius ... T. Brahe
Longitude: Estimated value of the longitude distance between Toledo and Rome
Year: Year associated with this determination
Longname: A longer version of the Name, where appropriate; a factor with levels Andrea Argoli Christoph Clavius Tycho Brahe
City: The principal city where this person worked; a factor with levels Alexandria Amsterdam Bamberg Bologna Frankfurt Hven Leuven Middelburg Nuremberg Padua Paris Rome
Country: The country where this person worked; a factor with levels Belgium Denmark Egypt Flanders France Germany Italy Italy
Latitude: Latitude of this City; a numeric vector
Source: Likely source for this determination of Longitude; a factor with levels Astron Map
Gap: A numeric vector indicating whether the Longitude value is below or above the median

Langren.all: A data frame with 61 observations on the following 4 variables, giving determinations of Longitude between Toledo and Rome from all known versions of van Langren's graph.

Author: Author of the graph, a factor with levels Langren Lelewel
Year: Year of publication
Name: The name of the person giving a determination, a factor with levels Algunos1 Algunos2 Apianus ... Schonerus
Longitude: Estimated value of the longitude distance between Toledo and Rome

Details

In all the graphs, Toledo is implicitly at the origin and Rome is located relatively at the value of Longitude To judge correspondence with an actual map, the positions in (lat, long) are

toledo <- c(39.86, -4.03); rome <- c(41.89, 12.5)

Source

The longitude values were digitized from images of the various graphs, which may be found on the Supplementary materials page for Friendly etal. (2009).

References

Friendly, M., Valero-Mora, P. and Ulargui, J. I. (2010). The First (Known) Statistical Graph: Michael Florent van Langren and the "Secret" of Longitude. The American Statistician, 64 (2), 185-191. Supplementary materials: http://datavis.ca/gallery/langren/.

Langren, M. F. van. (1644). La Verdadera Longitud por Mar y Tierra. Antwerp: (n.p.), 1644. English translation available at http://datavis.ca/gallery/langren/verdadera.pdf.

Lelewel, J. (1851). Geographie du Moyen Age. Paris: Pilliet, 1851.

Examples

data(Langren1644)

####################################################
# reproductions of Langren's graph overlaid on a map
####################################################

if (require(jpeg, quietly=TRUE)) {

  gimage <- readJPEG(system.file("images", "google-toledo-rome3.jpg", package="HistData"))
  # NB: dimensions from readJPEG are y, x, colors

  gdim <- dim(gimage)[1:2]
  ylim <- c(1,gdim[1])
  xlim <- c(1,gdim[2])
  op <- par(bty="n", xaxt="n", yaxt="n", mar=c(2, 1, 1, 1) + 0.1)
  # NB: necessary to scale the plot to the pixel coordinates, and use asp=1
  plot(xlim, ylim, xlim=xlim, ylim=ylim, type="n", ann=FALSE, asp=1 )
  rasterImage(gimage, 1, 1, gdim[2], gdim[1])

  # pixel coordinates of Toledo and Rome in the image, measured from the bottom left corner
  toledo.map <- c(131, 59)
  rome.map <- c(506, 119)
  
  # confirm locations of Toledo and Rome
  points(rbind(toledo.map, rome.map), cex=2)
  text(131, 95, "Toledo", cex=1.5)
  text(506, 104, "Roma", cex=1.5)

  # set a scale for translation of lat,long to pixel x,y
  scale <- data.frame(x=c(131, 856), y=c(52,52))
  rownames(scale)=c(0,30)

  # translate from degrees longitude to pixels
  xlate <- function(x) {
    131+x*726/30	
  }

  # draw an axis
  lines(scale)
  ticks <- xlate(seq(0,30,5))
  segments(ticks, 52, ticks, 45)
  text(ticks, 40, seq(0,30,5))
  text(xlate(8), 17, "Grados de la Longitud", cex=1.7)

  # label the observations with the names
  points(x=xlate(Langren1644$Longitude), y=rep(57, nrow(Langren1644)), 
         pch=25, col="blue", bg="blue")
  text(x=xlate(Langren1644$Longitude), y=rep(57, nrow(Langren1644)), 
       labels=Langren1644$Name, srt=90, adj=c(-.1, .5), cex=0.8)
  par(op)
}

### Original implementation using ReadImages, now deprecated & shortly to be removed
## Not run: 
if (require(ReadImages)) {
  gimage <- read.jpeg(system.file("images", "google-toledo-rome3.jpg", package="HistData"))
  plot(gimage)
  
  # pixel coordinates of Toledo and Rome in the image, measured from the bottom left corner
  toledo.map <- c(130, 59)
  rome.map <- c(505, 119)
  
  # confirm locations of Toledo and Rome
  points(rbind(toledo.map, rome.map), cex=2)
  
  # set a scale for translation of lat,long to pixel x,y
  scale <- data.frame(x=c(130, 856), y=c(52,52))
  rownames(scale)=c(0,30)
  lines(scale)
  
  xlate <- function(x) {
    130+x*726/30	
  }
  points(x=xlate(Langren1644$Longitude), y=rep(57, nrow(Langren1644)), 
         pch=25, col="blue")
  text(x=xlate(Langren1644$Longitude), y=rep(57, nrow(Langren1644)), 
         labels=Langren1644$Name, srt=90, adj=c(0, 0.5), cex=0.8)
}

## End(Not run)

### First attempt using ggplot2; temporarily abandonned.
## Not run: 
require(maps)
require(ggplot2)
require(reshape)
require(plyr)
require(scales)

# set latitude to that of Toledo
Langren1644$Latitude <- 39.68

#          x/long   y/lat
bbox <- c( 38.186, -9.184,
           43.692, 28.674 )
bbox <- matrix(bbox, 2, 2, byrow=TRUE)

borders <- as.data.frame(map("world", plot = FALSE,
  xlim = expand_range(bbox[,2], 0.2),
  ylim = expand_range(bbox[,1], 0.2))[c("x", "y")])

data(world.cities)
# get actual locations of Toledo & Rome
cities <- subset(world.cities,
  name %in% c("Rome", "Toledo") & country.etc %in% c("Spain", "Italy"))
colnames(cities)[4:5]<-c("Latitude", "Longitude")

mplot <- ggplot(Langren1644, aes(Longitude, Latitude) ) +
  geom_path(aes(x, y), borders, colour = "grey60") +
  geom_point(y = 40) +
  geom_text(aes(label = Name), y = 40.1, angle = 90, hjust = 0, size = 3)
mplot <- mplot +
	geom_segment(aes(x=-4.03, y=40, xend=30, yend=40))

mplot <- mplot +
  geom_point(data = cities, colour = "red", size = 2) +
  geom_text(data=cities, aes(label=name), color="red", size=3, vjust=-0.5) +
  coord_cartesian(xlim=bbox[,2], ylim=bbox[,1])

# make the plot have approximately aspect ratio = 1
windows(width=10, height=2)
mplot

## End(Not run)


###########################################
# show variation in estimates across graphs
###########################################

library(lattice)
graph <- paste(Langren.all$Author, Langren.all$Year)
dotplot(Name ~ Longitude, data=Langren.all)

dotplot( as.factor(Year) ~ Longitude, data=Langren.all, groups=Name, type="o")

dotplot(Name ~ Longitude|graph, data=Langren.all, groups=graph)

# why the gap?
gap.mod <- glm(Gap ~ Year + Source + Latitude, family=binomial, data=Langren1644)
anova(gap.mod, test="Chisq")

Macdonell's Data on Height and Finger Length of Criminals, used by Gosset (1908)

Description

In the second issue of Biometrika, W. R. Macdonell (1902) published an extensive paper, On Criminal Anthropometry and the Identification of Criminals in which he included numerous tables of physical characteristics 3000 non-habitual male criminals serving their sentences in England and Wales. His Table III (p. 216) recorded a bivariate frequency distribution of height by finger length. His main purpose was to show that Scotland Yard could have indexed their material more efficiently, and find a given profile more quickly.

W. S. Gosset (aka "Student") used these data in two classic papers in 1908, in which he derived various characteristics of the sampling distributions of the mean, standard deviation and Pearson's r. He said, "Before I had succeeded in solving my problem analytically, I had endeavoured to do so empirically." Among his experiments, he randomly shuffled the 3000 observations from Macdonell's table, and then grouped them into samples of size 4, 8, ..., calculating the sample means, standard deviations and correlations for each sample.

Usage

data(Macdonell)
data(MacdonellDF)

Format

Macdonell: A frequency data frame with 924 observations on the following 3 variables giving the bivariate frequency distribution of height and finger.

height: lower class boundaries of height, in decimal ft.
finger: length of the left middle finger, in mm.
frequency: frequency of this combination of height and finger

MacdonellDF: A data frame with 3000 observations on the following 2 variables.

height: a numeric vector
finger: a numeric vector

Details

Class intervals for height in Macdonell's table were given in 1 in. ranges, from (4' 7" 9/16 - 4' 8" 9/16), to (6' 4" 9/16 - 6' 5" 9/16). The values of height are taken as the lower class boundaries.

For convenience, the data frame MacdonellDF presents the same data, in expanded form, with each combination of height and finger replicated frequency times.

Source

Macdonell, W. R. (1902). On Criminal Anthropometry and the Identification of Criminals. Biometrika, 1(2), 177-227. doi:10.1093/biomet/1.2.177

The data used here were obtained from:

Hanley, J. (2008). Macdonell data used by Student. http://www.medicine.mcgill.ca/epidemiology/hanley/Student/

References

Hanley, J. and Julien, M. and Moodie, E. (2008). Student's z, t, and s: What if Gosset had R? The American Statistician, 62(1), 64-69.

Gosset, W. S. [Student] (1908). Probable error of a mean. Biometrika, 6(1), 1-25. https://www.york.ac.uk/depts/maths/histstat/student.pdf

Gosset, W. S. [Student] (1908). Probable error of a correlation coefficient. Biometrika, 6, 302-310.

Examples

data(Macdonell)

# display the frequency table
xtabs(frequency ~ finger+round(height,3), data=Macdonell)

## Some examples by james.hanley@mcgill.ca    October 16, 2011
## http://www.biostat.mcgill.ca/hanley/
## See:  http://www.biostat.mcgill.ca/hanley/Student/

###############################################
##  naive contour plots of height and finger ##
###############################################
 
# make a 22 x 42 table
attach(Macdonell)
ht <- unique(height) 
fi <- unique(finger)
fr <- t(matrix(frequency, nrow=42))
detach(Macdonell)


dev.new(width=10, height=5)  # make plot double wide
op <- par(mfrow=c(1,2),mar=c(0.5,0.5,0.5,0.5),oma=c(2,2,0,0))

dx <- 0.5/12
dy <- 0.5/12

plot(ht,ht,xlim=c(min(ht)-dx,max(ht)+dx),
           ylim=c(min(fi)-dy,max(fi)+dy), xlab="", ylab="", type="n" )

# unpack  3000 heights while looping though the frequencies 
heights <- c()
for(i in 1:22) {
	for (j in 1:42) {
	 f  <-  fr[i,j]
	 if(f>0) heights <- c(heights,rep(ht[i],f))
	 if(f>0) text(ht[i], fi[j], toString(f), cex=0.4, col="grey40" ) 
	}
}
text(4.65,13.5, "Finger length (cm)",adj=c(0,1), col="black") ;
text(5.75,9.5, "Height (feet)", adj=c(0,1), col="black") ;
text(6.1,11, "Observed bin\nfrequencies", adj=c(0.5,1), col="grey40",cex=0.85) ;
# crude countour plot
contour(ht, fi, fr, add=TRUE, drawlabels=FALSE, col="grey60")


# smoother contour plot (Galton smoothed 2-D frequencies this way)
# [Galton had experience with plotting isobars for meteorological data]
# it was the smoothed plot that made him remember his 'conic sections'
# and ask a mathematician to work out for him the iso-density
# contours of a bivariate Gaussian distribution... 

dx <- 0.5/12; dy <- 0.05  ; # shifts caused by averaging

plot(ht,ht,xlim=c(min(ht),max(ht)),ylim=c(min(fi),max(fi)), xlab="", ylab="", type="n"  )
 
sm.fr <- matrix(rep(0,21*41),nrow <- 21)
for(i in 1:21) {
	for (j in 1:41) {
	   smooth.freq  <-  (1/4) * sum( fr[i:(i+1), j:(j+1)] ) 
	   sm.fr[i,j]  <-  smooth.freq
	   if(smooth.freq > 0 )
	   text(ht[i]+dx, fi[j]+dy, sub("^0.", ".",toString(smooth.freq)), cex=0.4, col="grey40" )
	   }
	}
 
contour(ht[1:21]+dx, fi[1:41]+dy, sm.fr, add=TRUE, drawlabels=FALSE, col="grey60")
text(6.05,11, "Smoothed bin\nfrequencies", adj=c(0.5,1), col="grey40", cex=0.85) ;
par(op)
dev.new()    # new default device

#######################################
## bivariate kernel density estimate
#######################################

if(require(KernSmooth)) {
MDest <- bkde2D(MacdonellDF, bandwidth=c(1/8, 1/8))
contour(x=MDest$x1, y=MDest$x2, z=MDest$fhat,
	xlab="Height (feet)", ylab="Finger length (cm)", col="red", lwd=2)
with(MacdonellDF, points(jitter(height), jitter(finger), cex=0.5))
}

#############################################################
## sunflower plot of height and finger with data ellipses  ##
#############################################################

with(MacdonellDF, 
	{
	sunflowerplot(height, finger, size=1/12, seg.col="green3",
		xlab="Height (feet)", ylab="Finger length (cm)")
	reg <- lm(finger ~ height)
	abline(reg, lwd=2)
	if(require(car)) {
	dataEllipse(height, finger, plot.points=FALSE, levels=c(.40, .68, .95))
		}
  })


############################################################
## Sampling distributions of sample sd (s) and z=(ybar-mu)/s
############################################################

# note that Gosset used a divisor of n (not n-1) to get the sd.
# He also used Sheppard's correction for the 'binning' or grouping.
# with concatenated height measurements...

mu <- mean(heights) ; sigma <- sqrt( 3000 * var(heights)/2999 )
c(mu,sigma)

# 750 samples of size n=4 (as Gosset did)

# see Student's z, t, and s: What if Gosset had R? 
# [Hanley J, Julien M, and Moodie E. The American Statistician, February 2008] 

# see also the photographs from Student's notebook ('Original small sample data and notes")
# under the link "Gosset' 750 samples of size n=4" 
# on website http://www.biostat.mcgill.ca/hanley/Student/
# and while there, look at the cover of the Notebook containing his yeast-cell counts
# http://www.medicine.mcgill.ca/epidemiology/hanley/Student/750samplesOf4/Covers.JPG
# (Biometrika 1907) and decide for yourself why Gosset, when forced to write under a 
# pen-name, might have taken the name he did!

# PS: Can you figure out what the 750 pairs of numbers signify?
# hint: look again at the numbers of rows and columns in Macdonell's (frequency) Table III.


n <- 4
Nsamples <- 750

y.bar.values <- s.over.sigma.values <- z.values <- c()
for (samp in 1:Nsamples) {
	y <- sample(heights,n)
	y.bar <- mean(y)
	s  <-  sqrt( (n/(n-1))*var(y) ) 
	z <- (y.bar-mu)/s
	y.bar.values <- c(y.bar.values,y.bar) 
	s.over.sigma.values <- c(s.over.sigma.values,s/sigma)
	z.values <- c(z.values,z)
	}

	
op <- par(mfrow=c(2,2),mar=c(2.5,2.5,2.5,2.5),oma=c(2,2,0,0))
# sampling distributions
hist(heights,breaks=seq(4.5,6.5,1/12), main="Histogram of heights (N=3000)")
hist(y.bar.values, main=paste("Histogram of y.bar (n=",n,")",sep=""))

hist(s.over.sigma.values,breaks=seq(0,4,0.1),
	main=paste("Histogram of s/sigma (n=",n,")",sep="")); 
z=seq(-5,5,0.25)+0.125
hist(z.values,breaks=z-0.125, main="Histogram of z=(ybar-mu)/s")
# theoretical
lines(z, 750*0.25*sqrt(n-1)*dt(sqrt(n-1)*z,3), col="red", lwd=1)
par(op)

#####################################################
## Chisquare probability plot for bivariate normality
#####################################################

mu <- colMeans(MacdonellDF)
sigma <- var(MacdonellDF)
Dsq <- mahalanobis(MacdonellDF, mu, sigma)

Q <- qchisq(1:3000/3000, 2)
plot(Q, sort(Dsq), xlab="Chisquare (2) quantile", ylab="Squared distance")
abline(a=0, b=1, col="red", lwd=2)

Mayer's Data on the Libration of the Moon.

Description

Mayer had twenty-seven days' observations of Manilius and only three unknowns. The form of Mayer's problem is almost the same as that of Legendre, who developed later the least squares method.

"How did Mayer address his overdetermined system of equations? His approach was a simple and straightforward one, so simple and straightforward that a twentieth-century reader might arrive at the very mistaken opinion that the procedure was not remarkable at all. Mayer divided his equations into three groups of nine equations each, added each of the three groups separately, and solved the resulting three linear equations for \alpha, \beta and \alpha sin\theta (and then solved for \theta). His choice of which equations belonged in which groups was based upon the coefficients of \alpha and \alpha sin \theta. The first group consisted of the nine equations with the largest positive values for the coefficient of a, namely, equations 1,2, 3, 6, 9, 10, 11,12, and 27. The second group were those with the nine largest negative values for this coefficient: equations 8, 18, 19, 21, 22, 23, 24, 25, and 26. The remaining nine equations formed the third group, which he described as having the largest values for the coefficient of \alpha sin \theta."

Stigler (1986, p.21)

Usage

data(Mayer)

Format

A data frame with 27 observations on the following 4 variables.

Equation: an integer vector, id of the Equation
Y: a numeric vector, representing the term (h-90) (see details)
X1: a numeric vector, representing \beta
X2: a numeric vector, representing \alpha
X3: a numeric vector, representing the term \alpha sin\theta
Group: a character vector, representing the Mayer grouping

Details

Stigler (1986):

"The development of the method of least squares was closely associated with three of the major scientific problems of the eighteenth century: (1) to determine and represent mathematically the motions of the moon; (2) to account for an apparently secular (that is, nonperiodic) inequality that had been observed in the motions of the planets Jupiter and Saturn; and (3) to determine the shape or figure of the earth. These problems all involved astronomical observations and the theory of gravitational attraction, and they all presented intellectual challenges that engaged the attention of many of the ablest mathematical scientists of the period.

Over the period from April 1748 to March 1749, Mayer made numerous observations of the positions of several prominent lunar features; and in his 1750 memoir he showed how these data could be used to determine various characteristics of the moon's orbit. His method of handling the data was novel, and it is well worth considering this method in detail, both for the light it sheds on his pioneering, if limited, understanding of the problem and because his approach was widely circulated in the major contemporary treatise on astronomy, having signal influence upon later work."

His analysis led to this equation:

\beta - (90-h) = \alpha sin(g-k) - \alpha sin\theta cos(g-k)

According to Stigler (1986, p. 21), this "equation would hold if no errors were present. The modern tendency would be to write, say":

(h - 90) = - \beta + \alpha sin (g - k) - \alpha sin\theta cos(g - k) + E

treating (h - 90) as the dependent variable and -\beta, \alpha, and -\alpha sin \theta as the parameters in a linear regression model.

Author(s)

Luiz Fernando Palin Droubi

Source

Stigler, Stephen M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Cambridge, MA: Harvard University Press, 1986, Table 1.1, p. 22.

Examples

library(sp)
library(effects)
data(Mayer)

# some scatterplots
plot(Y ~ X2, pch=(15:17)[as.factor(Group)], 
             col=c("red", "blue", "darkgreen")[as.factor(Group)], data=Mayer)
abline(lm(Y ~ X2, data=Mayer), lwd=2)

plot(Y ~ X3, pch=(15:17)[as.factor(Group)], 
             col=c("red", "blue", "darkgreen")[as.factor(Group)], data=Mayer)
abline(lm(Y ~ X3, data=Mayer), lwd=2)


fit <- lm(Y ~ X2 + X3, data=Mayer)
plot(predictorEffects(fit, residuals=TRUE))


Avg_Method <- aggregate(Mayer[, 2:5], by = list(Group = Mayer$Group), FUN=sum)
fit_Mayer <- lm(Y ~ X1 + X2 + X3 - 1, Avg_Method)

## See Stigler (1986, p. 23)
## W means that the angle found is negative.

coeffs <- coef(fit_Mayer)
(alpha <- dd2dms(coeffs[2]))
(beta <- dd2dms(coeffs[1]))
(theta <- dd2dms(asin(coeffs[3]/coeffs[2])*180/pi))

Michelson's Determinations of the Velocity of Light

Description

The data frame Michelson gives Albert Michelson's measurements of the velocity of light in air, made from June 5 to July 2, 1879, reported in Michelson (1882). The given values + 299,000 are Michelson's measurements in km/sec. The number of cases is 100 and the "true" value on this scale is 734.5.

Stigler (1977) used these data to illustrate properties of robust estimators with real, historical data. For this purpose, he divided the 100 measurements into 5 sets of 20 each. These are contained in MichelsonSets.

Usage

data(Michelson)
data(MichelsonSets)

Format

Michelson: A data frame with 100 observations on the following variable, given in time order of data collection

velocity: a numeric vector

MichelsonSets: A 20 x 5 matrix, with format int [1:20, 1:5] 850 850 1000 810 960 800 830 830 880 720 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr [1:5] "ds12" "ds13" "ds14" "ds15" ...

Details

The "true" value is taken to be 734.5, arrived at by taking the "true" speed of light in a vacuum to be 299,792.5 km/sec, and adjusting for the velocity in air.

The data values are recorded in order, and so may also be taken as a time series.

Source

Kyle Siegrist, "Virtual Laboratories in Probability and Statistics", https://www.math.uah.edu/stat/data/Michelson.html

Stephen M. Stigler (1977), "Do robust estimators work with real data?", Annals of Statistics, 5, 1055-1098

References

Michelson, A. A. (1882). "Experimental determination of the velocity of light made at the United States Naval Academy, Anapolis". Astronomical Papers, 1,109-145, U. S. Nautical Almanac Office.

Examples

data(Michelson)

# density plot (default bandwidth & 0.6 * bw)
plot(density(Michelson$velocity), xlab="Speed of light - 299000 (km/s)",
	main="Density plots of Michelson data")
lines(density(Michelson$velocity, adjust=0.6), lty=2)
rug(jitter(Michelson$velocity))
abline(v=mean(Michelson$velocity), col="blue")
abline(v=734.5, col="red", lwd=2)
text(mean(Michelson$velocity), .004, "mean", srt=90, pos=2)
text(734.5, .004, "true", srt=90, pos=2)

# index / time series plot
plot(Michelson$velocity, type="b")
abline(h=734.5, col="red", lwd=2)
lines(lowess(Michelson$velocity), col="blue", lwd=2)

# examine lag=1 differences
plot(diff(Michelson$velocity), type="b")
lines(lowess(diff(Michelson$velocity)), col="blue", lwd=2)

# examine different data sets
boxplot(MichelsonSets, ylab="Velocity of light - 299000 (km/s)", xlab="Data set")
abline(h=734.5, col="red", lwd=2)

# means and trimmed means
(mn <-apply(MichelsonSets, 2, mean))
(tm <- apply(MichelsonSets, 2, mean, trim=.1))
points(1:5, mn)
points(1:5+.05, tm, pch=16, col="blue")

Data from Minard's famous graphic map of Napoleon's march on Moscow

Description

Charles Joseph Minard's graphic depiction of the fate of Napoleon's Grand Army in the Russian campaign of 1815 has been called the "greatest statistical graphic ever drawn" (Tufte, 1983). Friendly (2002) describes some background for this graphic, and presented it as Minard's Challenge: to reproduce it using modern statistical or graphic software, in a way that showed the elegance of some computer language to both describe and produce this graphic.

Usage

data(Minard.troops)
data(Minard.cities)
data(Minard.temp)

Format

Minard.troops: A data frame with 51 observations on the following 5 variables giving the number of surviving troops.

long: Longitude
lat: Latitude
survivors: Number of surviving troops, a numeric vector
direction: a factor with levels A ("Advance") R ("Retreat")
group: a numeric vector

Minard.cities: A data frame with 20 observations on the following 3 variables giving the locations of various places along the path of Napoleon's army.

long: Longitude
lat: Latitude
city: City name: a factor with levels Bobr Chjat ... Witebsk Wixma

Minard.temp: A data frame with 9 observations on the following 4 variables, giving the temperature at various places along the march of retreat from Moscow.

long: Longitude
temp: Temperature
days: Number of days on the retreat march
date: a factor with levels Dec01 Dec06 Dec07 Nov09 Nov14 Nov28 Oct18 Oct24

Details

date in Minard.temp should be made a real date in 1815.

Source

Originally given by Lee Wilkinson, in a text file associated with The Grammar of Graphics (1990). Springer.

References

Friendly, M. (2002). Visions and Re-visions of Charles Joseph Minard, Journal of Educational and Behavioral Statistics, 27, No. 1, 31-51.

Friendly, M. (2003). Re-Visions of Minard. http://datavis.ca/gallery/re-minard.html

Examples

data(Minard.troops)
data(Minard.cities)
data(Minard.temp)

#' ## Load required packages
require(ggplot2)
require(scales)
require(gridExtra)

#' ## plot path of troops, and another layer for city names
 plot_troops <- ggplot(Minard.troops, aes(long, lat)) +
		geom_path(aes(linewidth = survivors, colour = direction, group = group),
                 lineend = "round", linejoin = "round")
 plot_cities <- geom_text(aes(label = city), size = 4, data = Minard.cities)
 
#' ## Combine these, and add scale information, labels, etc.
#' Set the x-axis limits for longitude explicitly, to coincide with those for temperature

breaks <- c(1, 2, 3) * 10^5 
plot_minard <- plot_troops + plot_cities +
 	scale_size("Survivors", range = c(1, 10), 
 	            breaks = breaks, labels = scales::comma(breaks)) +
  scale_color_manual("Direction", 
                     values = c("grey50", "red"), 
                     labels=c("Advance", "Retreat")) +
  coord_cartesian(xlim = c(24, 38)) +
  xlab(NULL) + 
  ylab("Latitude") + 
  ggtitle("Napoleon's March on Moscow") +
  theme_bw() +
  theme(legend.position = "inside", 
        legend.position.inside=c(.8, .2), 
        legend.box="horizontal")
 
#' ## plot temperature vs. longitude, with labels for dates
plot_temp <- ggplot(Minard.temp, aes(long, temp)) +
	geom_path(color="grey", size=1.5) +
	geom_point(size=2) +
	geom_text(aes(label=date)) +
	xlab("Longitude") + ylab("Temperature") +
	coord_cartesian(xlim = c(24, 38)) + 
	theme_bw()
	

#' The plot works best if we  re-scale the plot window to an aspect ratio of ~ 2 x 1
# windows(width=10, height=5)

#' Combine the two plots into one
grid.arrange(plot_minard, plot_temp, nrow=2, heights=c(3,1))

Florence Nightingale's data on deaths from various causes in the Crimean War

Description

In the history of data visualization, Florence Nightingale is best remembered for her role as a social activist and her view that statistical data, presented in charts and diagrams, could be used as powerful arguments for medical reform.

After witnessing deplorable sanitary conditions in the Crimea, she wrote several influential texts (Nightingale, 1858, 1859), including polar-area graphs (sometimes called "Coxcombs" or rose diagrams), showing the number of deaths in the Crimean from battle compared to disease or preventable causes that could be reduced by better battlefield nursing care.

Her Diagram of the Causes of Mortality in the Army in the East showed that most of the British soldiers who died during the Crimean War died of sickness rather than of wounds or other causes. It also showed that the death rate was higher in the first year of the war, before a Sanitary Commissioners arrived in March 1855 to improve hygiene in the camps and hospitals.

Usage

data(Nightingale)

Format

A data frame with 24 observations on the following 10 variables.

Date: a Date, composed as as.Date(paste(Year, Month, 1, sep='-'), "%Y-%b-%d")
Month: Month of the Crimean War, an ordered factor
Year: Year of the Crimean War
Army: Estimated average monthly strength of the British army
Disease: Number of deaths from preventable or mitagable zymotic diseases
Wounds: Number of deaths directly from battle wounds
Other: Number of deaths from other causes
Disease.rate: Annual rate of deaths from preventable or mitagable zymotic diseases, per 1000
Wounds.rate: Annual rate of deaths directly from battle wounds, per 1000
Other.rate: Annual rate of deaths from other causes, per 1000

Details

For a given cause of death, D, annual rates per 1000 are calculated as 12 * 1000 * D / Army, rounded to 1 decimal.

The two panels of Nightingale's Coxcomb correspond to dates before and after March 1855

Source

The data were obtained from:

Pearson, M. and Short, I. (2007). Understanding Uncertainty: Mathematics of the Coxcomb. http://understandinguncertainty.org/node/214.

References

Nightingale, F. (1858) Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army Harrison and Sons, 1858

Nightingale, F. (1859) A Contribution to the Sanitary History of the British Army during the Late War with Russia London: John W. Parker and Son.

Small, H. (1998) Florence Nightingale's statistical diagrams http://www.florence-nightingale-avenging-angel.co.uk/GraphicsPaper/Graphics.htm

Pearson, M. and Short, I. (2008) Nightingale's Rose (flash animation). http://understandinguncertainty.org/files/animations/Nightingale11/Nightingale1.html

Examples

data(Nightingale)

# For some graphs, it is more convenient to reshape death rates to long format
#  keep only Date and death rates
require(reshape)
Night<- Nightingale[,c(1,8:10)]
melted <- melt(Night, "Date")
names(melted) <- c("Date", "Cause", "Deaths")
melted$Cause <- sub("\\.rate", "", melted$Cause)
melted$Regime <- ordered( rep(c(rep('Before', 12), rep('After', 12)), 3), 
                          levels=c('Before', 'After'))
Night <- melted

# subsets, to facilitate separate plotting
Night1 <- subset(Night, Date < as.Date("1855-04-01"))
Night2 <- subset(Night, Date >= as.Date("1855-04-01"))

# sort according to Deaths in decreasing order, so counts are not obscured [thx: Monique Graf]
Night1 <- Night1[order(Night1$Deaths, decreasing=TRUE),]
Night2 <- Night2[order(Night2$Deaths, decreasing=TRUE),]

# merge the two sorted files
Night <- rbind(Night1, Night2)


require(ggplot2)
# Before plot
cxc1 <- ggplot(Night1, aes(x = factor(Date), y=Deaths, fill = Cause)) +
		# do it as a stacked bar chart first
   geom_bar(width = 1, position="identity", stat="identity", color="black") +
		# set scale so area ~ Deaths	
   scale_y_sqrt() 
		# A coxcomb plot = bar chart + polar coordinates
cxc1 + coord_polar(start=3*pi/2) + 
	ggtitle("Causes of Mortality in the Army in the East") + 
	xlab("")

# After plot
cxc2 <- ggplot(Night2, aes(x = factor(Date), y=Deaths, fill = Cause)) +
   geom_bar(width = 1, position="identity", stat="identity", color="black") +
   scale_y_sqrt()
cxc2 + coord_polar(start=3*pi/2) +
	ggtitle("Causes of Mortality in the Army in the East") + 
	xlab("")

## Not run: 
# do both together, with faceting
cxc <- ggplot(Night, aes(x = factor(Date), y=Deaths, fill = Cause)) +
 geom_bar(width = 1, position="identity", stat="identity", color="black") + 
 scale_y_sqrt() +
 facet_grid(. ~ Regime, scales="free", labeller=label_both)
cxc + coord_polar(start=3*pi/2) +
	ggtitle("Causes of Mortality in the Army in the East") + 
	xlab("")

## End(Not run)

## What if she had made a set of line graphs?

# these plots are best viewed with width ~ 2 * height 
colors <- c("blue", "red", "black")
with(Nightingale, {
	plot(Date, Disease.rate, type="n", cex.lab=1.25, 
		ylab="Annual Death Rate", xlab="Date", xaxt="n",
		main="Causes of Mortality of the British Army in the East");
	# background, to separate before, after
	rect(as.Date("1854/4/1"), -10, as.Date("1855/3/1"), 
		1.02*max(Disease.rate), col=gray(.90), border="transparent");
	text( as.Date("1854/4/1"), .98*max(Disease.rate), "Before Sanitary\nCommission", pos=4);
	text( as.Date("1855/4/1"), .98*max(Disease.rate), "After Sanitary\nCommission", pos=4);
	# plot the data
	points(Date, Disease.rate, type="b", col=colors[1], lwd=3);
	points(Date, Wounds.rate, type="b", col=colors[2], lwd=2);
	points(Date, Other.rate, type="b", col=colors[3], lwd=2)
	}
)
# add custom Date axis and legend
axis.Date(1, at=seq(as.Date("1854/4/1"), as.Date("1856/3/1"), "3 months"), format="%b %Y")
legend(as.Date("1855/10/20"), 700, c("Preventable disease", "Wounds and injuries", "Other"),
	col=colors, fill=colors, title="Cause", cex=1.25)

# Alternatively, show each cause of death as percent of total
Nightingale <- within(Nightingale, {
	Total <- Disease + Wounds + Other
	Disease.pct <- 100*Disease/Total
	Wounds.pct <- 100*Wounds/Total
	Other.pct <- 100*Other/Total
	})

colors <- c("blue", "red", "black")
with(Nightingale, {
	plot(Date, Disease.pct, type="n",  ylim=c(0,100), cex.lab=1.25,
		ylab="Percent deaths", xlab="Date", xaxt="n",
		main="Percentage of Deaths by Cause");
	# background, to separate before, after
	rect(as.Date("1854/4/1"), -10, as.Date("1855/3/1"), 
		1.02*max(Disease.rate), col=gray(.90), border="transparent");
	text( as.Date("1854/4/1"), .98*max(Disease.pct), "Before Sanitary\nCommission", pos=4);
	text( as.Date("1855/4/1"), .98*max(Disease.pct), "After Sanitary\nCommission", pos=4);
	# plot the data
	points(Date, Disease.pct, type="b", col=colors[1], lwd=3);
	points(Date, Wounds.pct, type="b", col=colors[2], lwd=2);
	points(Date, Other.pct, type="b", col=colors[3], lwd=2)
	}
)
# add custom Date axis and legend
axis.Date(1, at=seq(as.Date("1854/4/1"), as.Date("1856/3/1"), "3 months"), format="%b %Y")
legend(as.Date("1854/8/20"), 60, c("Preventable disease", "Wounds and injuries", "Other"),
	col=colors, fill=colors, title="Cause", cex=1.25)

Latitudes and Longitudes of 39 Points in 11 Old Maps

Description

The data set is concerned with the problem of aligning the coordinates of points read from old maps (1688 - 1818) of the Great Lakes area. 39 easily identifiable points were selected in the Great Lakes area, and their (lat, long) coordinates were recorded using a grid overlaid on each of 11 old maps, and using linear interpolation.

It was conjectured that maps might be systematically in error in five key ways: (a) constant error in latitude; (b)constant error in longitude; (c) proportional error in latitude; (d)proportional error in longitude; (e) angular error from a non-zero difference between true North and the map's North.

One challenge from these data is to produce useful analyses and graphical displays that relate to these characteristics or to other aspects of the data.

Usage

data(OldMaps)

Format

A data frame with 468 observations on the following 6 variables, giving the latitude and longitude of 39 points recorded from 12 sources (Actual + 11 maps).

point: a numeric vector
col: Column in the table a numeric vector
name: Name of the map maker, using Actual for the true coordinates of the points. A factor with levels Actual Arrowsmith Belin Cary Coronelli D'Anville} \code{Del'Isle Lattre Melish Mitchell Popple
year: Year of the map
lat: Latitude
long: Longitude

Details

Some of the latitude and longitude values are inexplicably negative. It is probable that this is an error in type setting, because the table footnote says "* denotes that interpolation accuracy is not good," yet no "*"s appear in the body of the table.

Source

Andrews, D. F., and Herzberg, A. M. (1985). Data: A Collection of Problems from Many fields for the Student and Research Worker. New York: Springer, Table 10.1. The data were obtained from http://www.stat.duke.edu/courses/Spring01/sta114/data/Andrews/T10.1.

Examples

data(OldMaps)
## maybe str(OldMaps) ; plot(OldMaps) ...

with(OldMaps, plot(abs(long),abs(lat), pch=col, col=colors()[point]))

Pearson and Lee's data on the heights of parents and children classified by gender

Description

Wachsmuth et. al (2003) noticed that a loess smooth through Galton's data on heights of mid-parents and their offspring exhibited a slightly non-linear trend, and asked whether this might be due to Galton having pooled the heights of fathers and mothers and sons and daughters in constructing his tables and graphs.

To answer this question, they used analogous data from English families at about the same time, tabulated by Karl Pearson and Alice Lee (1896, 1903), but where the heights of parents and children were each classified by gender of the parent.

Usage

data(PearsonLee)

Format

A frequency data frame with 746 observations on the following 6 variables.

child: child height in inches, a numeric vector
parent: parent height in inches, a numeric vector
frequency: a numeric vector
gp: a factor with levels fd fs md ms
par: a factor with levels Father Mother
chl: a factor with levels Daughter Son

Details

The variables gp, par and chl are provided to allow stratifying the data according to the gender of the father/mother and son/daughter.

Source

Pearson, K. and Lee, A. (1896). Mathematical contributions to the theory of evolution. On telegony in man, etc. Proceedings of the Royal Society of London, 60 , 273-283.

Pearson, K. and Lee, A. (1903). On the laws of inheritance in man: I. Inheritance of physical characters. Biometrika, 2(4), 357-462. (Tables XXII, p. 415; XXV, p. 417; XXVIII, p. 419 and XXXI, p. 421.)

References

Wachsmuth, A.W., Wilkinson L., Dallal G.E. (2003). Galton's bend: A previously undiscovered nonlinearity in Galton's family stature regression data. The American Statistician, 57, 190-192. doi:10.1198/0003130031874

Examples

data(PearsonLee)
str(PearsonLee)

with(PearsonLee, 
    {
    lim <- c(55,80)
    xv <- seq(55,80, .5)
    sunflowerplot(parent,child, number=frequency, xlim=lim, ylim=lim, seg.col="gray", size=.1)
    abline(lm(child ~ parent, weights=frequency), col="blue", lwd=2)
    lines(xv, predict(loess(child ~ parent, weights=frequency), data.frame(parent=xv)), 
          col="blue", lwd=2)
    # NB: dataEllipse doesn't take frequency into account
    if(require(car)) {
    dataEllipse(parent,child, xlim=lim, ylim=lim, plot.points=FALSE)
        }
  })

## separate plots for combinations of (chl, par)

# this doesn't quite work, because xyplot can't handle weights
require(lattice)
xyplot(child ~ parent|par+chl, data=PearsonLee, type=c("p", "r", "smooth"), col.line="red")

# Using ggplot [thx: Dennis Murphy]
require(ggplot2)
ggplot(PearsonLee, aes(x = parent, y = child, weight=frequency)) +
   geom_point(size = 1.5, position = position_jitter(width = 0.2)) +
   geom_smooth(method = lm, aes(weight = PearsonLee$frequency,
               colour = 'Linear'), se = FALSE, size = 1.5) +
   geom_smooth(aes(weight = PearsonLee$frequency,
               colour = 'Loess'), se = FALSE, size = 1.5) +
   facet_grid(chl ~ par) +
   scale_colour_manual(breaks = c('Linear', 'Loess'),
                       values = c('green', 'red')) +
   theme(legend.position = c(0.14, 0.885),
        legend.background = element_rect(fill = 'white'))

# inverse regression, as in Wachmuth et al. (2003)

ggplot(PearsonLee, aes(x = child, y = parent, weight=frequency)) +
   geom_point(size = 1.5, position = position_jitter(width = 0.2)) +
   geom_smooth(method = lm, aes(weight = PearsonLee$frequency,
               colour = 'Linear'), se = FALSE, size = 1.5) +
   geom_smooth(aes(weight = PearsonLee$frequency,
               colour = 'Loess'), se = FALSE, size = 1.5) +
   facet_grid(chl ~ par) +
   scale_colour_manual(breaks = c('Linear', 'Loess'),
                       values = c('green', 'red')) +
   theme(legend.position = c(0.14, 0.885),
        legend.background = element_rect(fill = 'white'))

Polio Field Trials Data

Description

The data frame PolioTrials gives the results of the 1954 field trials to test the Salk polio vaccine (named for the developer, Jonas Salk), conducted by the National Foundation for Infantile Paralysis (NFIP). It is adapted from data in the article by Francis et al. (1955). There were actually two clinical trials, corresponding to two statistical designs (Experiment), discussed by Brownlee (1955). The comparison of designs and results represented a milestone in the development of randomized clinical trials.

Usage

data(PolioTrials)

Format

A data frame with 8 observations on the following 6 variables.

Experiment: a factor with levels ObservedControl RandomizedControl
Group: a factor with levels Controls Grade2NotInoculated IncompleteVaccinations NotInoculated Placebo Vaccinated
Population: the size of the population in each group in each experiment
Paralytic: the number of cases of paralytic polio observed in that group
NonParalytic: the number of cases of paralytic polio observed in that group
FalseReports: the number of cases initially reported as polio, but later determined not to be polio in that group

Details

The data frame is in the form of a single table, but actually comprises the results of two separate field trials, given by Experiment. Each should be analyzed separately, because the designs differ markedly.

The original design (Experiment == "ObservedControl") called for vaccination of second-graders at selected schools in selected areas of the country (with the consent of the children's parents, of course). The Vaccinated second-graders formed the treatment group. The first and third-graders at the schools were not given the vaccination, and formed the Controls group.

In the second design (Experiment == "RandomizedControl") children were selected (again in various schools in various areas), all of whose parents consented to vaccination. The sample was randomly divided into treatment (Group == "Vaccinated"), given the real polio vaccination, and control groups (Group == "Placebo"), a placebo dose that looked just like the real vaccine. The experiment was also double blind: neither the parents of a child in the study nor the doctors treating the child knew which group the child belonged to.

In both experiments, NotInnoculated refers to children who did not participate in the experiment. IncompleteVaccinations refers to children who received one or two, but not all three administrations of the vaccine.

Source

Kyle Siegrist, "Virtual Laboratories in Probability and Statistics", https://www.math.uah.edu/stat/data/Polio.html

Thomas Francis, Robert Korn, et al. (1955). "An Evaluation of the 1954 Poliomyelitis Vaccine Trials", American Journal of Public Health, 45, (50 page supplement with a 63 page appendix).

References

K. A. Brownlee (1955). "Statistics of the 1954 Polio Vaccine Trials", Journal of the American Statistical Association, 50, 1005-1013.

Examples

data(PolioTrials)
## maybe str(PolioTrials) ; plot(PolioTrials) ...

Pollen Data Challenge

Description

A synthetic dataset generated by David Coleman at RCA Laboratories in Princeton, N.J and used in the 1986 American Statistical Association JSM meeting as a data challenge for the Statistical Graphics Section.

Usage

data("Pollen")

Format

A data frame with 3848 observations on the following 5 variables, representing ficticious measurements of grains of pollen.

ridge: along X, a numeric vector
nub: along y, a numeric vector
crack: along z, a numeric vector
weight: weight of pollen grain, a numeric vector
density: weight of pollen grain, a numeric vector

Details

The first three variables are the lengths of geometric features observed sampled pollen grains - in the x, y, and z dimensions: a "ridge" along x, a "nub" in the y direction, and a "crack" in along the z dimension. The fourth variable is pollen grain weight, and the fifth is density.

In the description for the data challenge: "the data analyst is advised that there is more than one "feature" to these data. Each feature can be observed through various graphical techniques, but analytic methods, as well, can help "crack" the dataset."

There were several features embedded in this dataset: clusters of points, 5D ellipsoidal voids with no points, and finally, a collection of points which spelled out "EUREKA".

Papers by Becker et al. (1986) and Slomka (1986) describe their work on this problem.

Yihui Xie used this data as an illustration of the animate package, using rgl to zoom in on the magic word. See the video on https://vimeo.com/1982725.

Source

The canonical source for this data is the StatLib – Datasets Archive https://lib.stat.cmu.edu/datasets/pollen.data in the inconvenient form of .sh archive.

It is also available as data(pollen, package="animate").

References

Becker, R.A., Denby, L., McGill, R., and Wilks, A. (1986). Datacryptanalysis: A Case Study. Proceedings of the Section on Statistical Graphics, 92-97.

Slomka, M. (1986). The Analysis of a Synthetic Data Set. Proceedings of the Section on Statistical Graphics, 113-116.

Examples

data(Pollen)
pairs(Pollen)

Parent-Duchatelet's time-series data on the number of prostitutes in Paris

Description

A table indicating month by month, for the years 1812-1854, the number of prostitutes on the registers of the administration of the city of Paris.

Usage

data(Prostitutes)

Format

A data frame with 516 observations on the following 5 variables.

Year: a numeric vector
month: a factor with levels Apr Aug Dec Feb Jan Jul Jun Mar May Nov Oct Sep
count: a numeric vector: number of prostitutes
mon: a numeric vector: numeric month
date: a Date

Details

The data table was digitally scanned with OCR, and errors were corrected by comparing the yearly totals recorded in the table to the row sums of the scanned data.

Source

Parent-Duchatelet, A. (1857), De la prostitution dans la ville de Paris, 3rd ed, p. 32, 36

Examples

data(Prostitutes)
## maybe str(Prostitutes) ; plot(Prostitutes) ...

Trial of the Pyx

Description

Stigler (1997, 1999) recounts the history of one of the oldest continuous schemes of sampling inspection carried out by the Royal Mint in London for about eight centuries. The Trial of the Pyx was the final, ceremonial stage in a process designed to ensure that the weight and quality of gold and silver coins from the mint met the standards for coinage.

At regular intervals, coins would be taken from production and deposited into a box called the Pyx. When a Trial of the Pyx was called, the contents of the Pyx would be counted, weighed and assayed for content, and the results would be compared with the standard set for the Royal Mint.

The data frame Pyx gives the results for the year 1848 (Great Britain, 1848) in which 10,000 gold sovereigns were assayed. The coins in each bag were classified according to the deviation from the standard content of gold for each coin, called the Remedy, R = 123 * (12/5760) = .25625, in grains, for a single sovereign.

Usage

data(Pyx)

Format

A frequency data frame with 72 observations on the following 4 variables giving the distribution of 10,000 sovereigns, classified according to the Bags in which they were collected and the Deviation from the standard weight.

Bags: an ordered factor with levels 1 and 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9 < 10
Group: an ordered factor with levels below std < near std < above std
Deviation: an ordered factor with levels Below -R < (-R to -.2) < (-.2 to -.l) < (-.1 to 0) < (0 to .l) < (.1 to .2) < (.2 to R) < Above R
count: number of sovereigns

Details

Bags 1-4 were selected as "near to standard", bags 5-7 as below standard, bags 8-10 as above standard. This classification is reflected in Group.

Source

Stigler, S. M. (1999). Statistics on the Table. Cambridge, MA: Harvard University Press, table 21.1.

References

Great Britain (1848). "Report of the Commissioners Appointed to Inquire into the Constitution, Management and Expense of the Royal Mint." In Vol 28 of House Documents for 1849.

Stigler, S. M. (1997). Eight Centuries of Sampling Inspection: The Trial of the Pyx Journal of the American Statistical Association, 72(359), 493-500

Examples

data(Pyx)
# display as table
xtabs(count ~ Bags+Deviation, data=Pyx)

# grouped histogram
# from: https://github.com/drjohnrussell/30DayChartChallenge/blob/main/2025/Challenge08.R
library(ggplot2)
library(dplyr)
Pyx |> 
  mutate(Bags=forcats::fct_relevel(Bags,"5","6","7")) |>
  group_by(Bags) |> 
  mutate(percent=count/sum(count)*100) |>
  ungroup() |>
  ggplot(aes(x=Deviation, y=percent,
             group=Bags, fill=Group)) +
  geom_col(position=position_dodge()) +
  scale_fill_brewer(palette="Dark2") +
  theme_minimal() +
  theme(legend.position = "top") +
  labs(x="Deviation from the Standard",
       y="Percentage of an individual bag",
       title="Trial of the Pyx (1848)",
       fill="")

Statistics of Deadly Quarrels

Description

The Statistics Of Deadly Quarrels by Lewis Fry Richardson (1960) is one of the earlier attempts at quantification of historical conflict behavior.

The data set contains 779 dyadic deadly quarrels that cover a time period from 1809 to 1949. A quarrel consists of one pair of belligerents, and is identified by its beginning date and magnitude (log 10 of the number of deaths). Neither actor in a quarrel is identified by name.

Because Richardson took a dyad of belligerents as his unit, a given war, such as World War I or World War II comprises multiple observations, for all pairs of belligerents. For example, there are forty-four pairs of belligerents coded for World War I.

For each quarrel, the nominal variables include the type of quarrel, as well as political, cultural, and economic similarities and dissimilarities between the pair of combatants.

Usage

data(Quarrels)

Format

A data frame with 779 observations on the following 84 variables.

ID: V84: Id sequence
year: V1: Begin date of quarrel
international: V2: Nation vs nation
colonial: V3: Nation vs colony
revolution: V4: Revolution or civil war
nat.grp: V5: Nation vs gp in other nation
grp.grpSame: V6: Grp vs grp (same nation)
grp.grpDif: V7: Grp vs grp (between nations)
numGroups: V8: Number groups against which fighting
months: V9: Number months fighting
pairs: V10: Number pairs in whole matrix
monthsPairs: V11: Num mons for all in matrix
logDeaths: V12: Log (killed) matrix
deaths: V13: Total killed for matrix
exchangeGoods: V14: Gp sent goods to other
obstacleGoods: V15: Gp puts obstacles to goods
intermarriageOK: V16: Present intermarriages
intermarriageBan: V17: Intermarriages banned
simBody: V18: Similar body characteristics
difBody: V19: Difference in body characteristics
simDress: V20: Similarity of customs (dress)
difDress: V21: Difference of customs (dress)
eqWealth: V22: Common level of wealth
difWealth: V23: Difference in wealth
simMariagCust: V24: Similar marriage cusomst
difMariagCust: V25: Different marriage customs
simRelig: V26: Similar religion or philosophy of life
difRelig: V27: Religion or philosophy felt different
philanthropy: V28: General philanthropy
restrictMigration: V29: Restricted immigrations
sameLanguage: V30: Common mother tongue
difLanguage: V31: Different languages
simArtSci: V32: Similar science, arts
travel: V33: Travel
ignorance: V34: Ignorant of other/both
simPersLiberty: V35: Personal liberty similar
difPersLiberty: V36: More personal liberty
sameGov: V37: Common government
sameGovYrs: V38: Years since common govt established
prevConflict: V39: Belligerents fought previously
prevConflictYrs: V40: Years since belligerents fought
chronicFighting: V41: Chronic fighting between belligerents
persFriendship: V42: Autocrats personal friends
persResentment: V43: Leaders personal resentment
difLegal: V44: Annoyingly different legal systems
nonintervention: V45: Policy of nonintervention
thirdParty: V46: Led by 3rd group to conflict
supportEnemy: V47: Supported others enemy
attackAlly: V48: Attacked ally of other
rivalsLand: V49: Rivals territory concess
rivalsTrade: V50: Rivals trade
churchPower: V51: Church civil power
noExtension: V52: Policy not extending term
territory: V53: Desired territory
habitation: V54: Wanted habitation
minerals: V55: Desired minerals
StrongHold: V56: Wanted strategic stronghold
taxation: V57: Taxed other
loot: V58: Wanted loot
objectedWar: V59: Objected to war
enjoyFight: V60: Enjoyed fighting
pride: V61: Elated by strong pride
overpopulated: V62: Insufficient land for population
fightForPay: V63: Fought only for pay
joinWinner: V64: Desired to join winners
otherDesiredWar: V65: Quarrel desired by other
propaganda3rd: V66: Issued of propaganda to third parties
protection: V67: Offered protection
sympathy: V68: Sympathized under control
debt: V69: Owed money to others
prevAllies: V70: Had fought as allies
yearsAllies: V71: Years since fought as allies
intermingled: V72: Had intermingled on territory
interbreeding: V73: Interbreeding between groups
propadanda: V74: Issued propaganda to other group
orderedObey: V75: Ordered other to obey
commerceOther: V76: Commercial enterprises
feltStronger: V77: Felt stronger
competeIntellect: V78: Competed successfully intellectual occ
insecureGovt: V79: Government insecure
prepWar: V80: Preparations for war
RegionalError: V81: Regional error measure
CasualtyError: V82: Casualty error measure
Auxiliaries: V83: Auxiliaries in service of nation at war

Details

In the original data set obtained from ICPSR, variables were named V1-V84. These were renamed to make them more meaningful. V84, renamed ID was moved to the first position, but otherwise the order of variables is the same.

In many of the factor variables, 0 is used to indicate "irrelevant to quarrel". This refers to those relations that Richardson found absent or irrelevant to the particular quarrel, and did not subsequently mention.

See the original codebook at http://www.icpsr.umich.edu/cgi-bin/file?comp=none&study=5407&ds=1&file_id=652814 for details not contained here.

Source

http://www.icpsr.umich.edu/icpsrweb/ICPSR/studies/05407

References

Lewis F. Richardson, (1960). The Statistics Of Deadly Quarrels. (Edited by Q. Wright and C. C. Lienau). Pittsburgh: Boxwood Press.

Rummel, Rudolph J. (1967), "Dimensions of Dyadic War, 1820-1952." Journal of Conflict Resolution. 11, (2), 176 - 183.

Examples

data(Quarrels)
str(Quarrels)

Laplace's Saturn data.

Description

With this dataset Laplace (1787) showed that "noticed defects in the then existing tables of the motions of Jupiter and Saturn" were, de facto, due to "a very long, 917-year, periodic inequality in the planets' mean motion, due to their mutual attraction and the coincidence that their times of revolution about the sun are approximately in the ratio 5:2".

Usage

data(Saturn)

Format

A data frame with 24 observations on the following 6 variables.

Equation: an integer vector, id of the Equation
Year: an integer vector, year of the observations
Y: a numeric vector, adjusted measure of the observed longitude of Saturn, in minutes
X1: a numeric vector, the rate of change of the mean annual motion of Saturn
X2: a numeric vector, the rate of change of the eccentricity of Saturn's orbit
X3: a numeric vector, a variable compound of the rate of change of Saturn's aphelion minus rates of change of the mean longitude of Saturn in 1750, multiplied by 2 times the mean eccentricity of Saturn

Details

Stigler (1986, pp. 25-39):

"In 1676 Halley had verified an earlier suspicion of Horrocks that the motions of Jupiter and Saturn were subject to slight, apparently secular, inequalities. When the actual positions of Jupiter and Saturn were compared with the tabulated observations of many centuries, it appeared that the mean motion of Jupiter was accelerating, whereas that of Saturn was retarding. Halley was able to improve the accuracy of the tables by an empirical adjustment, and he speculated that the irregularity was somehow due to the mutual attraction of the planets. But he was unable to provide a mathematical theory that would account for this inequality.

If the observed trends were to continue indefinitely, Jupiter would crash into the sun as Saturn receded into space! The problem posed by the Academy could be (and was) interpreted as requiring the development of an extension of existing theories of attraction to incorporate the mutual attraction of three bodies, in order to see whether such a theory could account for at least the major observed inequalities as, it was hoped, periodic in nature. Thus stability would be restored to the solar system, and Newtonian gravitational theory would have overcome another obstacle.

The problem was an extraordinarily difficult one for the time, and Euler's attempts to grope for a solution are most revealing. Euler's work was, in comparison with Mayer's a year later, a statistical failure. After he had found values for n and u, Euler had the data needed to produce seventy-five equations, all linear in x, y, m, z, a, and k. He might have added them together in six groups and solved for the unknowns, but he attempted no such overall combination of the equations.

Laplace had come quite a bit closer to providing a general method than Mayer had. Indeed, it was Laplace's generalization that enjoyed popularity throughout the first half of the nineteenth century, as a method that provided some of the accuracy expected from least squares, with much less labor. Because the multipliers were all -1, 0, or 1, no multiplication, only addition, was required."

Author(s)

Luiz Fernando Palin Droubi

Source

Stigler, Stephen (1975). "Napoleonic statistics: The work of Laplace", Biometrika, 62, 503-517.

References

Stigler, Stephen M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Cambridge, MA: Harvard University Press, 1986, Table 1.3, p. 34.

Examples

data(Saturn)

# some scatterplots
pairs(Saturn[,2:6])
plot(Y ~ X1, data=Saturn)
plot(Y ~ X2, data=Saturn)

# Fit the LS model
fit <- lm(Y ~ X1 + X2 + X3, data = Saturn)
# Same residuals of Stigler (1975), Table 1, last column.
library(sp)
dd2dms(residuals(fit)/60)

John Snow's Map and Data on the 1854 London Cholera Outbreak

Description

The Snow data consists of the relevant 1854 London streets, the location of 578 deaths from cholera, and the position of 13 water pumps (wells) that can be used to re-create John Snow's map showing deaths from cholera in the area surrounding Broad Street, London in the 1854 outbreak. Another data frame provides boundaries of a tessellation of the map into Thiessen (Voronoi) regions which include all cholera deaths nearer to a given pump than to any other.

The apocryphal story of the significance of Snow's map is that, by closing the Broad Street pump (by removing its handle), Dr. Snow stopped the epidemic, and demonstrated that cholera is a water borne disease. The method of contagion of cholera was not previously understood. Snow's map is the most famous and classical example in the field of medical cartography, even if it didn't happen exactly this way. (the apocryphal part is that the epidemic ended when the pump handle was removed.) At any rate, the map, together with various statistical annotations, is compelling because it points to the Broad Street pump as the source of the outbreak.

Usage

	data(Snow.deaths)
	data(Snow.pumps)
	data(Snow.streets)
	data(Snow.polygons)
	data(Snow.dates)

Format

Snow.deaths: A data frame with 578 observations on the following 3 variables, giving the address of a person who died from cholera. When many points are associated with a single street address, they are "stacked" in a line away from the street so that they are more easily visualized. This is how they are displayed on John Snow's original map. The dates of the deaths are not individually recorded in this data set.

case: Sequential case number, in some arbitrary, randomized order
x: x coordinate
y: y coordinate

Snow.pumps: A data frame with 13 observations on the following 4 variables, giving the locations of water pumps within the boundaries of the map.

pump: pump number
label: pump label: Briddle St Broad St ... Warwick
x: x coordinate
y: y coordinate

Snow.streets: A data frame with 1241 observations on the following 4 variables, giving coordinates used to draw the 528 street segment lines within the boundaries of the map. The map is created by drawing lines connecting the n points in each street segment.

street: street segment number: 1:528
n: number of points in this street line segment
x: x coordinate
y: y coordinate

Snow.polygons: A list of 13 data frames, giving the vertices of Thiessen (Voronoi) polygons containing each pump. Their boundaries define the area that is closest to each pump relative to all other pumps. They are mathematically defined by the perpendicular bisectors of the lines between all pumps. Each data frame contains:

x: x coordinate
y: y coordinate

Snow.deaths2: An alternative version of Snow.deaths correcting some possible duplicate and missing cases, as described in vignette("Snow_deaths-duplicates").

Snow.dates: A data frame of 44 observations and 3 variables from Table 1 of Snow (1855), giving the number of fatal attacks and number of deaths by date from Aug. 19 – Sept. 30, 1854. There are a total of 616 deaths represented in both columns attacks and deaths; of these, the date of the attack is unknown for 45 cases.

Details

The scale of the source map is approx. 1:2000. The (x, y) coordinate units are 100 meters, with an arbitrary origin.

Of the data in the Snow.dates table, Snow says, “The deaths in the above table are compiled from the sources mentioned above in describing the map; but some deaths which were omitted from the map on account of the number of the house not being known, are included in the table.”

One limitation of these data sets is the lack of exact street addresses. Another is the lack of any data that would serve as a population denominator to allow for a comparison of mortality rates in the Broad Street pump area as opposed to others. See Koch (2000), Koch (2004), Koch & Denike (2009) and Tufte (1999), p. 27-37, for further discussion.

Source

Tobler, W. (1994). Snow's Cholera Map, http://www.ncgia.ucsb.edu/pubs/snow/snow.html; data files were obtained from http://ncgia.ucsb.edu/Publications/Software/cholera/, but these sites seem to be down.

The data in these files were first digitized in 1992 by Rusty Dodson of the NCGIA, Santa Barbara, from the map included in the book by John Snow: "Snow on Cholera...", London, Oxford University Press, 1936.

References

Koch, T. (2000). Cartographies of Disease: Maps, Mapping, and Medicine. ESRI Press. ISBN: 9781589481206.

Koch, T. (2004). The Map as Intent: Variations on the Theme of John Snow Cartographica, 39 (4), 1-14.

Koch, T. and Denike, K. (2009). Crediting his critics' concerns: Remaking John Snow's map of Broad Street cholera, 1854. Social Science & Medicine 69, 1246-1251.

Snow, J. (1885). On the Mode of Communication of Cholera. London: John Churchill. Possibly at https://resource.nlm.nih.gov/0050707.

Tufte, E. (1997). Visual Explanations. Cheshire, CT: Graphics Press.

Examples

data(Snow.deaths)
data(Snow.pumps)
data(Snow.streets)
data(Snow.polygons)
data(Snow.deaths)

## Plot deaths over time
require(lubridate)
clr <- ifelse(Snow.dates$date < mdy("09/08/1854"), "red", "darkgreen")
plot(deaths ~ date, data=Snow.dates, 
     type="h", lwd=2, col=clr)
points(deaths ~ date, data=Snow.dates, 
       cex=0.5, pch=16, col=clr)
text( mdy("09/08/1854"), 40, "Pump handle\nremoved Sept. 8", pos=4)


## draw Snow's map and data

SnowMap()

# add polygons
SnowMap(polygons=TRUE, main="Snow's Cholera Map with Pump Polygons")

# zoom in a bit, and show density estimate
SnowMap(xlim=c(7.5,16.5), ylim=c(7,16), polygons=TRUE, density=TRUE,
        main="Snow's Cholera Map, Annotated")


## re-do this the sp way... [thx: Stephane Dray]
library(sp)

# streets
slist <- split(Snow.streets[,c("x","y")],as.factor(Snow.streets[,"street"]))
Ll1 <- lapply(slist,Line)
Lsl1 <- Lines(Ll1,"Street")
Snow.streets.sp <- SpatialLines(list(Lsl1))
plot(Snow.streets.sp, col="gray")
title(main="Snow's Cholera Map of London (sp)")

# deaths
Snow.deaths.sp = SpatialPoints(Snow.deaths[,c("x","y")])
plot(Snow.deaths.sp, add=TRUE, col ='red', pch=15, cex=0.6)

# pumps
spp <- SpatialPoints(Snow.pumps[,c("x","y")])
Snow.pumps.sp <- SpatialPointsDataFrame(spp,Snow.pumps[,c("x","y")])
plot(Snow.pumps.sp, add=TRUE, col='blue', pch=17, cex=1.5)
text(Snow.pumps[,c("x","y")], labels=Snow.pumps$label, pos=1, cex=0.8)

Draw John Snow's Map of Cholera in London

Description

The main function SnowMap draws versions of John Snow's map of cholera deaths in the South London area surrounding the Borad Street pump. during the 1854 outbreak.

It is a wrapper for the various subfunctions also listed here:
Splot sets up the basic plot
Sstreets draws the streets
Sdeaths plots the deaths
Sdeaths plots the pump locations
Sscale draws the scale
Spolygons draws the boundaries of the Voronoi polygons separating the pumps
Sdensity draws and fills contours of the 2D density of deaths

Usage


SnowMap(xlim = c(3, 20), ylim = c(3, 20), 
        axis.labels = FALSE, main = "Snow's Cholera Map of London", 
        scale = TRUE, polygons = FALSE, density=FALSE,
        streets.args = list(col = "grey", lwd = 1), 
        deaths.args = list(col = "red", pch = 15, cex = 0.6), 
        pumps.args = list(col = "blue", pch = 17, cex = 1.5, cex.lab = 0.9), 
        scale.args = list(xs = 3.5, ys = 19.7), 
        polygons.args = list(col=NA, border="brown", lwd=2, lty=1),
        density.args=list(bandwidth=c(0.5,0.5), 
                  col1=rgb(0,1,0,0),
                  col2=rgb(1,0,0,.8))
)

Splot(xlim = c(3, 20), ylim = c(3, 20), 
      xlab = "", ylab = "", 
      axis.labels = FALSE, 
      main = "Snow's Cholera Map of London")

Sdeaths(col = "red", pch = 15, cex = 0.6)

Spumps(col = "blue", pch = 17, cex = 1.5, cex.lab = 0.9)

Sstreets(col = "gray", lwd = 1)

Sscale(xs = 3.5, ys = 19.7)

Spolygons(col=NA, border="brown", lwd=2, lty=1)

Sdensity(bandwidth = c(0.5, 0.5), col1 = rgb(0, 1, 0, 0), col2 = rgb(1, 0, 0, 0.8))

Arguments

xlim

Limit for the horizontal axis. Specify ranges smaller than the defaults to zoom the plot.

ylim

Limit for the vertical axis.

axis.labels

Logical. Show axis tick mark labels?

main

Plot title

scale

Logical; draw a scale (in meters) on the plot

polygons

Logical; Use Spolygons to draw the Snow.polygons on the plot?

density

Logical; Use Sdensity to draw the 2D bivariate density of deaths on the plot?

streets.args

List of arguments passed to Sstreets

deaths.args

List of arguments passed to Sdeaths

pumps.args

List of arguments passed to Spumps

scale.args

List of arguments passed to Sscale

polygons.args

List of arguments passed to Spolygons. Note that col here now refers to the fill colors, passed to polygon. The col argument here can be a vector of up to 13 colors, one for each pump region.

density.args

List of arguments passed to Sdensity

xlab

Label for horizontal axis

ylab

Label for vertical axis

col

Color of points and lines used by various functions

pch

Point character used by by various functions

cex

Character size used by by various functions

cex.lab

Character size for labels used by Spumps

lwd

Line width used by by various functions

border

Color of border lines used by Spolygons

xs

x location of the scale used by Sscale

ys

y location of the scale used by Sscale

lty

Line type used by by various functions

bandwidth

Bandwidth used by bkde2D in Sdensity

col1

Lower level of color range used by colorRampPalette in Sdensity

col2

Upper level of color range used by colorRampPalette in Sdensity

Value

None

Author(s)

Michael Friendly

References

Snow, J. (1885). On the Mode of Communication of Cholera. London: John Churchill

Thomas Coleman, "John Snow Research project", https://www.hilerun.org/econ/papers/snow/index.html gives extensive analyses of Snow's data with R notebooks on Github.

Examples

SnowMap()
SnowMap(axis.labels=TRUE)
SnowMap(deaths.args=list(col="darkgreen"))

SnowMap(polygons=TRUE, main="Snow's Cholera Map with Pump Polygons")

SnowMap(density=TRUE)

John F. W. Herschel's Data on the Orbit of the Twin Stars `\gamma` Virginis

Description

In 1833 J. F. W. Herschel published two papers in the Memoirs of the Royal Astronomical Society detailing his investigations of calculating the orbits of twin stars from observations of their relative position angle and angular distance.

In the process, he invented the scatterplot, and the use of visual smoothing to obtain a reliable curve that surpassed the accuracy of individual observations (Friendly & Denis, 2005). His data on the recordings of the twin stars \gamma Virginis provide an accessible example of his methods.

Usage

	data("Virginis")
	data("Virginis.interp")

Format

Virgins: A data frame with 18 observations on the following 6 variables giving the measurements of position angle and angular distance between the central (brightest) star and its twin, recorded by various observers over more than 100 years.

year: year ("epoch") of the observation, a decimal numeric vector
posangle: recorded position angle between the two stars, a numeric vector
distance: separation distance between the two stars, a numeric vector
weight: a subjective weight attributed to the accuracy of this observation, a numeric vector
notes: Herschel's notes on this observation, a character vector
authority: A simplified version of the notes giving just the attribution of authority of the observation, a character vector

Virgins.interp: A data frame with 14 observations on the following 4 variables, giving the position angles and angular distance that Herschel interpolated from his smoothed curve.

year: year ("epoch") of the observation, a decimal numeric vector
posangle: recorded position angle between the two stars, a numeric vector
distance: separation distance, calculated 1/sqrt(velocity)
velocity: angular velocity, calculated as the instantaneous slopes of tangents to the smoothed curve, a numeric vector

Details

The data in Virginis come from the table on p. 35 of the “Micrometrical Measures” paper.

The weight variable was assigned by the package author, reflecting Herschel's comments and for use in any weighted analysis.

In the notes and authority variables, "H" refers to William Herschel (John's farther, the discoverer of the planet Uranus), "h" refers to John Herschel himself, and "Sigma", rendered \Sigma in the table on p. 35 refers to Joseph Fraunhofer.

The data in Virginis.interp come from Table 1 on p. 190 of the supplementary paper.

Source

Herschel, J. F. W. III. Micrometrical Measures of 364 Double Stars with a 7-feet Equatorial Acromatic Telescope, taken at Slough, in the years 1828, 1829, and 1830 Memoirs of the Royal Astronomical Society, 1833, 5, 13-91.

Herschel, J. F. W. On the Investigation of the Orbits of Revolving Double Stars: Being a Supplement to a Paper Entitled "Micrometrical Measures of 364 Double Stars" Memoirs of the Royal Astronomical Society, 1833, 5, 171-222.

References

Friendly, M. & Denis, D. The early origins and development of the scatterplot. Journal of the History of the Behavioral Sciences, 2005, 41, 103-130.

Examples

data(Virginis)
data(Virginis.interp)

# Herschel's interpolated curve
plot(posangle ~ year, data=Virginis.interp, 
	pch=15, type="b", col="red", cex=0.8, lwd=2,
	xlim=c(1710,1840), ylim=c(80, 170),
	ylab="Position angle (deg.)", xlab="Year",
	cex.lab=1.5)

# The data points, and indication of their uncertainty
points(posangle ~ year, data=Virginis, pch=16)
points(posangle ~ year, data=Virginis, cex=weight/2)

Playfair's Data on Wages and the Price of Wheat

Description

Playfair (1821) used a graph, showing parallel time-series of the price of wheat and the typical weekly wage for a "good mechanic" from 1565 to 1821 to argue that working men had never been as well-off in terms of purchasing power as they had become toward the end of this period.

His graph is a classic in the history of data visualization, but commits the sin of showing two non-commensurable Y variables on different axes. Scatterplots of wages vs. price or plots of ratios (e.g., wages/price) are in some ways better, but both of these ideas were unknown in 1821.

In this version, information on the reigns of British monarchs is provided in a separate data.frame, Wheat.monarch.

Usage

data(Wheat)
data(Wheat.monarchs)

Format

Wheat A data frame with 53 observations on the following 3 variables.

Year: Year, in intervals of 5 from 1565 to 1821: a numeric vector
Wheat: Price of Wheat (Shillings/Quarter bushel): a numeric vector
Wages: Weekly wage (Shillings): a numeric vector

Wheat.monarchs A data frame with 12 observations on the following 4 variables.

name: Reigning monarch, a factor with levels Anne Charles I Charles II Cromwell Elizabeth George I George II George III George IV James I James II W&M
start: Starting year of reign, a numeric vector
end: Starting year of reign, a numeric vector
commonwealth: A binary variable indicating the period of the Commonwealth under Cromwell

Source

Playfair, W. (1821). Letter on our Agricultural Distresses, Their Causes and Remedies. London: W. Sams, 1821

Data values: originally digitized from http://datavis.ca/gallery/images/playfair-wheat1.gif now taken from http://mbostock.github.io/protovis/ex/wheat.js

References

Friendly, M. & Denis, D. (2005). The early origins and development of the scatterplot Journal of the History of the Behavioral Sciences, 41, 103-130.

Examples

data(Wheat)

data(Wheat)

# ------------------------------------
# Playfair's graph, largely reproduced
# ------------------------------------

# convenience function to fill area under a curve down to a minimum value
fillpoly <- function(x,y, low=min(y),  ...) {
    n <- length(x)
    polygon( c(x, x[n], x[1]), c(y, low, low), ...)
}

# For best results, this graph should be viewed with width ~ 2 * height
# Note use of type='s' to plot a step function for Wheat
#   and panel.first to provide a background grid()
#     The curve for Wages is plotted after the polygon below it is filled
with(Wheat, {
    plot(Year, Wheat, type="s", ylim=c(0,105), 
        ylab="Price of the Quarter of Wheat (shillings)", 
        panel.first=grid(col=gray(.9), lty=1))
    fillpoly(Year, Wages, low=0, col="lightskyblue", border=NA)
    lines(Year, Wages, lwd=3, col="red")
    })


# add some annotations
text(1625,10, "Weekly wages of a good mechanic", cex=0.8, srt=3, col="red")

# cartouche
text(1650, 85, "Chart", cex=2, font=2)
text(1650, 70, 
	paste("Shewing at One View", 
        "The Price of the Quarter of Wheat", 
        "& Wages of Labor by the Week", 
        "from the Year 1565 to 1821",
        "by William Playfair",
        sep="\n"), font=3)

# add the time series bars to show reigning monarchs
# distinguish Cromwell visually, as Playfair did
with(Wheat.monarchs, {
	y <- ifelse( !commonwealth & (!seq_along(start) %% 2), 102, 104)
	segments(start, y, end, y, col="black", lwd=7, lend=1)
	segments(start, y, end, y, col=ifelse(commonwealth, "white", NA), lwd=4, lend=1)
	text((start+end)/2, y-2, name, cex=0.5)
	})

# -----------------------------------------
# plot the labor cost of a quarter of wheat
# -----------------------------------------
Wheat1 <- within(na.omit(Wheat), {Labor=Wheat/Wages})
with(Wheat1, {
	plot(Year, Labor, type='b', pch=16, cex=1.5, lwd=1.5, 
	     ylab="Labor cost of a Quarter of Wheat (weeks)",
	     ylim=c(1,12.5));
	lines(lowess(Year, Labor), col="red", lwd=2)
	})
	
# cartouche
text(1740, 10, "Chart", cex=2, font=2)
text(1740, 8.5, 
	paste("Shewing at One View", 
        "The Work Required to Purchase", 
        "One Quarter of Wheat", 
        sep="\n"), cex=1.5, font=3)

with(Wheat.monarchs, {
	y <- ifelse( !commonwealth & (!seq_along(start) %% 2), 12.3, 12.5)
	segments(start, y, end, y, col="black", lwd=7, lend=1)
	segments(start, y, end, y, col=ifelse(commonwealth, "white", NA), lwd=4, lend=1)
	text((start+end)/2, y-0.2, name, cex=0.5)
	})

Student's (1906) Yeast Cell Counts

Description

Counts of the number of yeast cells were made each of 400 regions in a 20 x 20 grid on a microscope slide, comprising a 1 sq. mm. area. This experiment was repeated four times, giving samples A, B, C and D.

Student (1906) used these data to investigate the errors in random sampling. He says "there are two sources of error: (a) the drop taken may not be representative of the bulk of the liquid; (b) the distribution of the cells over the area which is examined is never exactly uniform, so that there is an 'error of random sampling.'"

The data in the paper are provided in the form of discrete frequency distributions for the four samples. Each shows the frequency distribution squares containing a count of 0, 1, 2, ... yeast cells. These are combined here in Yeast. In addition, he gives a table (Table I) showing the actual number of yeast cells counted in the 20 x 20 grid for sample D, given here as YeastD.mat.

Usage

	data(Yeast)
	data(YeastD.mat)

Format

Yeast: A frequency data frame with 36 observations on the following 3 variables, giving the frequencies of

sample: Sample identifier, a factor with levels A B C D
count: The number of yeast cells counted in a square
freq: The number of squares with the given count

YeastD.mat: A 20 x 20 matrix containing the count of yeast cells in each square for sample D.

Details

Student considers the distribution of a total of Nm particles distributed over N unit areas with an average of m particles per unit area. With uniform mixing, for a given particle, the probability of it falling on any one area is p = 1/N, and not falling on that area is q = 1 - 1/N. He derives the probability distribution of 0, 1, 2, 3, ... particles on a single unit area from the binomial expansion of (p + q)^{mN}.

Source

D. J. Hand, F. Daly, D. Lunn, K. McConway and E. Ostrowski (1994). A Handbook of Small Data Sets. London: Chapman & Hall. The data were originally found at: https://www2.stat.duke.edu/courses/Spring98/sta113/Data/Hand/yeast.dat

References

"Student" (1906) On the error of counting with a haemocytometer. Biometrika, 5, 351-360. http://www.medicine.mcgill.ca/epidemiology/hanley/c626/Student_counting.pdf

Examples

data(Yeast)

require(lattice)
# basic bar charts 
# TODO: frequencies should start at 0, not 1.
barchart(count~freq|sample, data=Yeast, ylab="Number of Cells", xlab="Frequency")
barchart(freq~count|sample, data=Yeast, xlab="Number of Cells", ylab="Frequency",
	horizontal=FALSE, origin=0)

# same, using xyplot
xyplot(freq~count|sample, data=Yeast, xlab="Number of Cells", ylab="Frequency",
	horizontal=FALSE, origin=0, type="h", lwd=10)

Darwin's Heights of Cross- and Self-fertilized Zea May Pairs

Description

Darwin (1876) studied the growth of pairs of zea may (aka corn) seedlings, one produced by cross-fertilization and the other produced by self-fertilization, but otherwise grown under identical conditions. His goal was to demonstrate the greater vigour of the cross-fertilized plants. The data recorded are the final height (inches, to the nearest 1/8th) of the plants in each pair.

In the Design of Experiments, Fisher (1935) used these data to illustrate a paired t-test (well, a one-sample test on the mean difference, cross - self). Later in the book (section 21), he used this data to illustrate an early example of a non-parametric permutation test, treating each paired difference as having (randomly) either a positive or negative sign.

Usage

data(ZeaMays)

Format

A data frame with 15 observations on the following 4 variables.

pair: pair number, a numeric vector
pot: pot, a factor with levels 1 2 3 4
cross: height of cross fertilized plant, a numeric vector
self: height of self fertilized plant, a numeric vector
diff: cross - self for each pair

Details

In addition to the standard paired t-test, several types of non-parametric tests can be contemplated:

(a) Permutation test, where the values of, say self are permuted and diff=cross - self is calculated for each permutation. There are 15! permutations, but a reasonably large number of random permutations would suffice. But this doesn't take the paired samples into account.

(b) Permutation test based on assigning each abs(diff) a + or - sign, and calculating the mean(diff). There are 2^{15} such possible values. This is essentially what Fisher proposed. The p-value for the test is the proportion of absolute mean differences under such randomization which exceed the observed mean difference.

(c) Wilcoxon signed rank test: tests the hypothesis that the median signed rank of the diff is zero, or that the distribution of diff is symmetric about 0, vs. a location shifted alternative.

Source

Darwin, C. (1876). The Effect of Cross- and Self-fertilization in the Vegetable Kingdom, 2nd Ed. London: John Murray.

Andrews, D. and Herzberg, A. (1985) Data: a collection of problems from many fields for the student and research worker. New York: Springer. Data retrieved from: https://www.stat.cmu.edu/StatDat/

References

Fisher, R. A. (1935). The Design of Experiments. London: Oliver & Boyd.

Examples

data(ZeaMays)

##################################
## Some preliminary exploration ##
##################################
boxplot(ZeaMays[,c("cross", "self")], ylab="Height (in)", xlab="Fertilization")

# examine large individual diff/ces
largediff <- subset(ZeaMays, abs(diff) > 2*sd(abs(diff)))
with(largediff, segments(1, cross, 2, self, col="red"))

# plot cross vs. self.  NB: unusual trend and some unusual points
with(ZeaMays, plot(self, cross, pch=16, cex=1.5))
abline(lm(cross ~ self, data=ZeaMays), col="red", lwd=2)

# pot effects ?
 anova(lm(diff ~ pot, data=ZeaMays))

##############################
## Tests of mean difference ##
##############################
# Wilcoxon signed rank test
# signed ranks:
with(ZeaMays, sign(diff) * rank(abs(diff)))
wilcox.test(ZeaMays$cross, ZeaMays$self, conf.int=TRUE, exact=FALSE)

# t-tests
with(ZeaMays, t.test(cross, self))
with(ZeaMays, t.test(diff))

mean(ZeaMays$diff)
# complete permutation distribution of diff, for all 2^15 ways of assigning
# one value to cross and the other to self (thx: Bert Gunter)
N <- nrow(ZeaMays)
allmeans <- as.matrix(expand.grid(as.data.frame(
                         matrix(rep(c(-1,1),N), nr =2))))  %*% abs(ZeaMays$diff) / N

# upper-tail p-value
sum(allmeans > mean(ZeaMays$diff)) / 2^N
# two-tailed p-value
sum(abs(allmeans) > mean(ZeaMays$diff)) / 2^N

hist(allmeans, breaks=64, xlab="Mean difference, cross-self",
	main="Histogram of all mean differences")
abline(v=c(1, -1)*mean(ZeaMays$diff), col="red", lwd=2, lty=1:2)

plot(density(allmeans), xlab="Mean difference, cross-self",
	main="Density plot of all mean differences")
abline(v=c(1, -1)*mean(ZeaMays$diff), col="red", lwd=2, lty=1:2)

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