R Notes for Topic 24: Goodness-of-Fit Tests
To do chi-squared tests in R, you use the chisq.test
function. A typical form of chi-squared test (and the kind that matches
the form we see in this book) looks like the following:
chisq.test(vector-of-observations, p=vector-of-probabilities)
For example, for the first chi-squared test of birthdays, we might
write
chisq.test(c(17,26,22,23,19,15,25), p=c(1/7,1/7,1/7,1/7,1/7,1/7,1/7))
Similarly, for the second test (Activity 24-2), we might write
chisq.test(c(17,26,22,23,19,15,25), p=c(1/6,1/6,1/6,1/6,1/6,1/12,1/12))
Similarly, for the third test (Activity 24-3), we might write
chisq.test(c(170,260,220,230,190,150,250), p=c(1/7,1/7,1/7,1/7,1/7,1/7,1/7))
By the time you hit 24-4 d, you should know what to do.
We'll start by creating vectors of counts and probabilities.
(Just so you know, cld stands for
“country population leading digit”.)
cpld = c(55,36,22,23,15,14,12,12,5)
benford = c(.301,.176,.125,.097,.079,.067,.058,.051,.046)
Those vectors make many things easier. To compute proportions, we
just divide each value in cpld by the total population.
cpld/194
Similarly, to compute expected values, we multiply the Benford
probabilities by 194.
benford*194
Calculating the test statistic and p-value:
chisq.test(cpld, p=benford)
