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.