Chi-square for the goodness of fit

The Chi-square test can be used to test whether the observed data differs significantly from the expected data. Let's take the example of a dice. The dice is rolled 36 times and the probability that each face should turn upwards is 1/6. So, the expected distribution is as follows:

>>> expected = np.array([6,6,6,6,6,6])

The observed distribution is as follows:

>>> observed = observed = np.array([7, 5, 3, 9, 6, 6])

The null hypothesis in the chi-square test is that the observed value is similar to the expected value.

The chi-square can be performed using the chisquare function in the SciPy package:

>>> stats.chisquare(observed,expected)
(3.333333333333333, 0.64874235866759344)

The first value is the chi-square value and the second value is the p-value, which is very high. This means that the null hypothesis is valid and the observed value is similar to the expected value.