#######################
Paired permutation test
#######################

.. code-links:: clear

Test the null hypothesis that the values for two variables are
interchangeable.

See :doc:`animal_attitudes`.

.. nbplot::

    >>> import random

    >>> def mean(a_list):
    ...     return sum(a_list) / len(a_list)

    >>> def mean_with_swap(list_1, list_2):
    ...     # Make new lists where some are swapped
    ...     new_list_1 = []
    ...     new_list_2 = []
    ...     for i in range(len(list_1)):
    ...         if random.random() >= 0.5:
    ...             # Don't swap
    ...             value_1 = list_1[i]
    ...             value_2 = list_2[i]
    ...         else:
    ...             # Swap
    ...             value_2 = list_1[i]
    ...             value_1 = list_2[i]
    ...         new_list_1.append(value_1)
    ...         new_list_2.append(value_2)
    ...     return mean(new_list_1) - mean(new_list_2)

    >>> def paired_permute(variable_1, variable_2):
    ...     n_samples = 10000
    ...     sampled_means = []
    ...     observed = mean(variable_1) - mean(variable_2)
    ...     for i in range(n_samples):
    ...         one_trial = mean_with_swap(variable_1, variable_2)
    ...         sampled_means.append(one_trial)
    ...     return observed, sampled_means

In action on the animal attitude data:

.. nbplot::

    >>> import pandas as pd
    >>> questions = pd.read_csv('animal_questions.csv')
    >>> trust_uni = list(questions['trust_uni'])
    >>> trust_protectors = list(questions['trust_protectors'])
    >>> observed, samples = paired_permute(trust_uni, trust_protectors)
    >>> observed
    0.017223910840932111

.. mpl-interactive::

.. nbplot::

    >>> import matplotlib.pyplot as plt
    >>> plt.hist(samples)
    (...)