The R Book

Frequency Distributions

Here are data on the numbers of bankruptcies in 80 districts. The question is whether there is any evidence that some districts show greater than expected numbers of cases. What would we expect? Of course we should expect some variation, but how much, exactly? Well that depends on our model of the process. Perhaps the simplest model is that absolutely nothing is going on, and that every singly bankruptcy case is absolutely independent of every other. That leads to the prediction that the numbers of cases per district will follow a Poisson process, a distribution in which the variance is equal to the mean (see p. 250). Let's see what the data show.

case.book<-read.table("c:\\temp\\cases.txt",header=T)
attach(case.book)
names(case.book)

[1] "cases"

First we need to count the numbers of districts with no cases, one case, two cases, and so on. The R function that does this is called table:

frequencies<-table(cases)
frequencies

cases
 0   1    2    3    4    5    6    7    8    9    10
34  14   10    7    4    5    2    1    1    1     1

There were no cases at all in 34 districts, but one district had 10 cases. A good way to proceed is to compare our distribution (called frequencies) with the distribution that would be observed if the data really did come from a Poisson distribution as postulated by our model. We can use the R function dpois to compute the probability density of each of the 11 frequencies from 0 to 10 (we multiply the probability produced by dpois by the total sample of 80 to obtain the predicted ...