Compute the expected frequencies from a contingency table.
Given an n-dimensional contingency table of observed frequencies, compute the expected frequencies for the table based on the marginal sums under the assumption that the groups associated with each dimension are independent.
| Parameters: | observed (array_like) -- The table of observed frequencies. (While this function can handle a 1-D array, that case is trivial. Generally observed is at least 2-D.) |
|---|---|
| Returns: | expected -- The expected frequencies, based on the marginal sums of the table. Same shape as observed. |
| Return type: | ndarray of float64 |
Examples
>>> observed = np.array([[10, 10, 20],[20, 20, 20]])
>>> expected_freq(observed)
array([[ 12., 12., 16.],
[ 18., 18., 24.]])