# Chi Squared Results in R and Python

Based on this answer, Python requires expected values in a chi square test to be absolute frequencies. Consider the following in Python:

import numpy
import scipy.stats
# chisquare function requires (observed, expected)
scipy.stats.chisquare(numpy.array([0,0,23,0]), numpy.array([1,1,1794,1]))
(1751.2948717948718, 0.0)


results in a p-value of 0 (whatever that means).

The same calculation in R, which requires that the expected values be proprotions:

chisq.test(c(0, 0, 23, 0), p=c(1/1797,1/1797,1794/1797, 1/1797))

Chi-squared test for given probabilities

data:  c(0, 0, 23, 0)
X-squared = 0.0385, df = 3, p-value = 0.998


resulting in a p-value of 0.998.

Which is correct?

These two seem to be testing different things. The Python code looks like it is a two way chi square test (but a p value of 0 makes no sense here), while the R code is one way. I am not sure which you want.

To do the two way test in R use

x1 <- c(0, 0, 23, 0)
x2 <- c(1, 1, 1794, 1)
chisq.test(x1, x2)


Which gives a p value of 0.5.

However, since a lot of the expected values are less than 5, Rcorrectly gives a warning. You can simulate using

chisq.test(x1, x2, simulate = TRUE)


which gives a p of 0.25

Your code also gives a warning, but this

chisq.test(c(0, 0, 23, 0),
p=c(1/1797,1/1797,1794/1797, 1/1797),
simulate = TRUE)


gives a p of 1.

This certainly makes sense.

I don't have Python so I can't say for sure what is going on there.

A two way chi square tests whether two categorical variables are associated with each other; a one way tests whether one categorical variable is distributed equal to a certain set of proportions.

• I'm trying to determine if the frequency of the categories of the two sets of observed values differ from each other. I'm doing two tests: one using one dataset as the expected, then the other way round. – SabreWolfy Oct 26 '13 at 13:09
• More in my question here: stats.stackexchange.com/questions/73829/… – SabreWolfy Oct 26 '13 at 13:24
• Then you want a two way test, and you only need one of them. – Peter Flom Oct 26 '13 at 13:40
• FWIW: I've determined that chisquare in Python is a one-way test that the categorical data has the given frequencies, and is invalid when observed or expected frequencies are below 5 (as is typically the case). In this case, it makes sense to use R rather than Python. – SabreWolfy Oct 26 '13 at 13:55