R Dataset / Package HistData / Jevons


On this Picostat.com statistics page, you will find information about the Jevons data set which pertains to W. Stanley Jevons' data on numerical discrimination. The Jevons data set is found in the HistData R package. You can load the Jevons data set in R by issuing the following command at the console data("Jevons"). This will load the data into a variable called Jevons. If R says the Jevons data set is not found, you can try installing the package by issuing this command install.packages("HistData") and then attempt to reload the data. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the Jevons R data set. The size of this file is about 542 bytes.

W. Stanley Jevons' data on numerical discrimination


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.




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


Actual number: a numeric vector


Estimated number: a numeric vector


Frequency of this combination of (actual, estimated): a numeric vector


actual-estimated: a numeric vector


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


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


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/


# 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", 
}# plot average error
if(require(reshape)) {
unJevons <- untable(Jevons, Jevons$frequency)
mean_error <- function(df) mean(df$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'))

Dataset imported from https://www.r-project.org.

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Attachment Size
dataset-16016.csv 542 bytes
Dataset License
GNU General Public License v2.0
Documentation License
GNU General Public License v2.0