hotelling_test_ind#

skfda.inference.hotelling.hotelling_test_ind(fd1: FData, fd2: FData, *, n_reps: int | None = None, random_state: int | RandomState | Generator | None = None, return_dist: typing_extensions.Literal[False] = False) → Tuple[float, float][source]#

skfda.inference.hotelling.hotelling_test_ind(fd1: FData, fd2: FData, *, n_reps: int | None = None, random_state: int | RandomState | Generator | None = None, return_dist: typing_extensions.Literal[True]) → Tuple[float, float, ndarray[Any, dtype[float64]]]

Compute Hotelling \(T^2\)-test.

Calculate the \(T^2\)-test for the means of two independent samples of functional data.

This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by default.

The p-value of the test is calculated using a permutation test over the statistic hotelling_t2(). If a maximum number of repetitions of the algorithm is provided then the permutations tested are generated randomly.

This procedure is from Pini, Stamm and Vantinni [1].

Parameters:

fd1 – First sample of data.
fd2 – Second sample of data. The data objects must have the same type.
n_reps – Maximum number of repetitions to compute p-value. Default value is None.
random_state – Random state.
return_dist – Flag to indicate if the function should return a numpy.array with the values of the statistic computed over each permutation.

Returns:

Value of the sample statistic, one tailed p-value and a collection of statistic values from permutations of the sample.

Raises:

TypeError – In case of bad arguments.

Examples

>>> from skfda.inference.hotelling import hotelling_test_ind
>>> from skfda.representation import FDataGrid
>>> from numpy import printoptions

>>> fd1 = FDataGrid([[1, 1, 1], [3, 3, 3]])
>>> fd2 = FDataGrid([[3, 3, 3], [5, 5, 5]])
>>> t2n, pval, dist = hotelling_test_ind(fd1, fd2, return_dist=True)
>>> '%.2f' % t2n
'2.00'
>>> '%.2f' % pval
'0.00'
>>> with printoptions(precision=4):
...     print(dist)
[ 2. 2. 0. 0. 2. 2.]

References