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.
A data frame with 42 observations on the following 3 variables.
a factor with levels
an ordered factor with levels
a numeric vector, death rate per 1000 population
Edgeworth's data came from the Registrar General's report for the final year, 1883.
Freq variable represents death rates per 1000 population in the six counties listed.
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.
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
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)