Splits and other stat measurements

import numpy as np
import pandas as pd
import scipy.stats
from math import sqrt


def cramers_v(x, y):
    confusion_matrix = pd.crosstab(x, y)
    chi2 = scipy.stats.chi2_contingency(confusion_matrix)[0]
    n = confusion_matrix.sum().sum()
    phi2 = chi2 / n
    r, k = confusion_matrix.shape
    phi2corr = max(0, phi2 - ((k - 1) * (r - 1)) / (n - 1))
    rcorr = r - ((r - 1) ** 2) / (n - 1)
    kcorr = k - ((k - 1) ** 2) / (n - 1)
    return np.sqrt(phi2corr / min((kcorr - 1), (rcorr - 1)))


def gini(list_of_values):
    '''
    Compute the Gini coefficient.
    :param list_of_values: list/series
    :return: Gini coefficient
    '''
    if isinstance(list_of_values, float):
        return 1
    sorted_list = sorted(list_of_values)
    height, area = 0, 0
    for value in sorted_list:
        height += value
        area += height - value / 2.
    fair_area = height * len(list_of_values) / 2.
    return (fair_area - area) / fair_area


def mean_confidence_interval(data, confidence=0.95):
    '''
    Confidence interval of the mean
    :param data:
    :param confidence:
    :return:
    '''
    a = 1.0 * np.array(data)
    n, se = len(a), scipy.stats.sem(a)
    h = se * scipy.stats.t.ppf((1 + confidence) / 2., n - 1)
    return h


def median_confidence_interval(data, confidence=0.95):
    '''
    Get the confidence interval over the median
    :param data: an array/series
    :param confidence:
    :return:
    '''
    a = 1.0 * np.array(data)
    n = len(a)
    n, se = len(a), sqrt(n * .5 * .5)
    h = se * scipy.stats.t.ppf((1 + confidence) / 2., n - 1)
    return h


def test_diff(a, b):
    '''
    Run the Mann Whitney test
    :param a: first list/series
    :param b: second list/series
    :return: U and p-val
    '''
    a, b = np.array(a), np.array(b)
    if len(a) == 0 or len(b) == 0:
        return 1
    if np.array_equal(a, b):
        return 1

    t, p = scipy.stats.mannwhitneyu(a, b)
    return p  # "U = {}, p = {}".format(t, p)


def crombach_alpha(two_columns_df):
    '''
    Compute the Crombach alpha
    :param two_columns_df: df
    :return: the Crombach Alpha
    '''
    nr_items = len(two_columns_df.columns)
    cov_mtr = two_columns_df.cov()  # variance - covariance matrix

    mean_var_item = sum(np.diagonal(cov_mtr)) / nr_items  # mean variance
    mean_cov_ii = sum(np.sum(cov_mtr)) - sum(
        np.diagonal(cov_mtr))  # sume all the covariance among item, and remove the variance
    mean_cov_ii = mean_cov_ii / (nr_items * nr_items - nr_items)  # average

    return nr_items * mean_cov_ii / (mean_var_item + (nr_items - 1) * mean_cov_ii)


def median_split(two_column_dataset):
    """
Split dataset on the median of the second column
    :param two_column_dataset
    :return: low, high subset
    """

    two_column_dataset = two_column_dataset.sort_values(by=two_column_dataset.columns[1])  # order by scale
    median_position = int(two_column_dataset.shape[0] / 2)  # find median index

    # split
    low = two_column_dataset.iloc[:median_position, ]
    high = two_column_dataset.iloc[median_position:, ]

    return low, high


def low_high_split(two_column_dataset):
    """
Split dataset in three of the second column
    :param two_column_dataset
    :return: low, high subset
    """

    two_column_dataset = two_column_dataset.sort_values(by=two_column_dataset.columns[1])  # order by scale
    low_position = int(two_column_dataset.shape[0] / 3)  # find median index
    high_position = int(2 * two_column_dataset.shape[0]/3)

    # split
    low = two_column_dataset.iloc[:low_position, ]
    high = two_column_dataset.iloc[high_position:, ]

    return low, high


if __name__ == "__main__":
    print("MAIN")