# Hypothesis Tests¶

## Unpaired k-Sample Transform¶

mgcpy.hypothesis_tests.transforms.k_sample_transform(x, y, is_y_categorical=False)[source]

Transform to represent a k-sample test as an independence test

Parameters
• X (2D numpy.array) --

is interpreted as either:

• a [n*n] distance matrix, a square matrix with zeros on diagonal for n samples OR

• a [n*p] data matrix, a matrix with n samples in p dimensions

• Y (2D numpy.array) --

is interpreted as either:

• a [n*n] distance matrix, a square matrix with zeros on diagonal for n samples OR

• a [n*p] data matrix, a matrix with n samples in p dimensions

• a [n*1] label matrix, categorical data for X, if is_y_categorical is set to True

• is_y_categorical (boolean) -- if set to True, Y has categorical data ans is a labels array for X, else, it is a plain data matrix

Returns

• u

a concatenated data matrix of dimensions [2*n, p]

• v

a label matrix for u, which indicates to which category each data entry in u belongs to

Return type

list

mgcpy.hypothesis_tests.transforms.paired_two_sample_transform(x, y)[source]

Transform to represent a paired two-sample test as an independence test Steps:

• combine x and y to get the joint_distribution

• sample n pairs from the joint_distribution

• compute the eucledian distance between the sampled n pairs, which is randomly_sampled_pairs_distance

• compute the eucledian distance between the actual x and y, which is actual_pairs_distance

• compute the two sample transformed matrices of randomly_sampled_pairs_distance and actual_pairs_distance

Parameters
• X (2D numpy.array) -- is interpreted as either: - a [n*n] distance matrix, a square matrix with zeros on diagonal for n samples OR - a [n*p] data matrix, a matrix with n samples in p dimensions

• Y (2D numpy.array) -- is interpreted as either: - a [n*n] distance matrix, a square matrix with zeros on diagonal for n samples OR - a [n*p] data matrix, a matrix with n samples in p dimensions

Returns

• u

a data matrix of dimensions [2*n, p]

• v

a label matrix for u, which indicates to which category each data entry in u belongs to

Return type

list

mgcpy.hypothesis_tests.transforms.paired_two_sample_test_dcorr(x, y, which_test='biased', compute_distance_matrix=None, is_fast=False)[source]

Compute paired two sample test's DCorr test_statistic

Parameters
• X (2D numpy.array) --

is interpreted as either:

• a [n*n] distance matrix, a square matrix with zeros on diagonal for n samples OR

• a [n*p] data matrix, a matrix with n samples in p dimensions

• Y (2D numpy.array) --

is interpreted as either:

• a [n*n] distance matrix, a square matrix with zeros on diagonal for n samples OR

• a [n*p] data matrix, a matrix with n samples in p dimensions

Returns

paired two sample DCorr test_statistic

Return type

float