Edgeworth's Data on Death Rates in British Counties

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)
#> Anova Table (Type II tests)
#> 
#> Response: Freq
#>           Sum Sq Df F value    Pr(>F)    
#> County     960.8  5  8.3234 5.005e-05 ***
#> year      3390.3  6 24.4761 2.665e-10 ***
#> Residuals  692.6 30                      
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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

library(vcd)
#> Loading required package: grid
library(MASS)
#> 
#> Attaching package: 'MASS'
#> The following object is masked from 'package:dplyr':
#> 
#>     select
structable( ~ County + year, data=EdgeworthDeaths)
#>           year 1876 1877 1878 1879 1880 1881 1882
#> County                                           
#> Berks           175  172  187  186  181  153  169
#> Herts           174  165  185  184  176  166  163
#> Bucks           182  171  186  195  179  162  177
#> Oxford          179  182  194  183  180  169  167
#> Bedford         196  174  203  195  198  171  181
#> Cambridge       173  177  190  191  187  165  171
loglm( Freq ~ County + year, data=EdgeworthDeaths)
#> Call:
#> loglm(formula = Freq ~ County + year, data = EdgeworthDeaths)
#> 
#> Statistics:
#>                       X^2 df P(> X^2)
#> Likelihood Ratio 3.853131 30        1
#> Pearson          3.850641 30        1

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