Chi-Squared test in Python

Question

I've used the following code in R to determine how well observed values (20, 20, 0 and 0 for example) fit expected values/ratios (25% for each of the four cases, for example):

> chisq.test(c(20,20,0,0), p=c(0.25, 0.25, 0.25, 0.25))      Chi-squared test for given probabilities  data:  c(20, 20, 0, 0)  X-squared = 40, df = 3, p-value = 1.066e-08 

How can I replicate this in Python? I've tried using the chisquare function from scipy but the results I obtained were very different; I'm not sure if this is even the correct function to use. I've searched through the scipy documentation, but it's quite daunting as it runs to 1000+ pages; the numpy documentation is almost 50% more than that.

Answer 1

scipy.stats.chisquare expects observed and expected absolute frequencies, not ratios. You can obtain what you want with

>>> observed = np.array([20., 20., 0., 0.]) >>> expected = np.array([.25, .25, .25, .25]) * np.sum(observed) >>> chisquare(observed, expected) (40.0, 1.065509033425585e-08) 

Although in the case that the expected values are uniformly distributed over the classes, you can leave out the computation of the expected values:

>>> chisquare(observed) (40.0, 1.065509033425585e-08) 

The first returned value is the χ² statistic, the second the p-value of the test.

Answer 2

Just wanted to point out that while the answer appears to be correct syntactically, you should not be using a Chi-squared distribution with your example because you have observed frequencies that are too small for an accurate Chi-square test.

"This test is invalid when the observed or expected frequencies in each category are too small. A typical rule is that all of the observed and expected frequencies should be at least 5." see: http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chisquare.html#scipy.stats.chisquare