biosppy.stats¶

This module provides statistical functions and related tools.

copyright:

2015-2026 by Instituto de Telecomunicacoes

license:

BSD 3-clause, see LICENSE for more details.

Functions

`diff_stats`([signal, stats_only])	Compute statistical features from the first signal differences, second signal differences and absolute signal differences.
`histogram`([signal, bins, normalize])	Compute histogram of the input signal.
`linear_regression`([x, y, show])	Plot the linear regression between two signals and get the equation coefficients.
`paired_test`([x, y])	Perform the Student's paired t-test on the arrays x and y.
`pearson_correlation`([x, y])	Compute the Pearson Correlation Coefficient between two signals.
`quartiles`([signal])	Compute quartile features of the signal.
`unpaired_test`([x, y])	Perform the Student's unpaired t-test on the arrays x and y.

biosppy.stats.diff_stats(signal=None, stats_only=True)[source]¶

Compute statistical features from the first signal differences, second signal differences and absolute signal differences.

Parameters:

signal (array) – Input signal.
stats_only (bool, optional) – Whether to output only statistical features. Default is True.

Returns:

{diff} (array) – Difference signal. {diff} can be ‘diff’, ‘diff2’ or ‘abs_diff’.
{diff}_mean (float) – Mean of the difference signal.
{diff}_median (float) – Median of the difference signal.
{diff}_min (float) – Minimum of the difference signal.
{diff}_max (float) – Maximum of the difference signal.
{diff}_max_amp (float) – Maximum amplitude of the difference signal.
{diff}_range (float) – Range of the difference signal.
{diff}_var (float) – Variance of the difference signal.
{diff}_std (float) – Standard deviation of the difference signal.
{diff}_sum (float) – Sum of the difference signal.

biosppy.stats.histogram(signal=None, bins=5, normalize=True)[source]¶

Compute histogram of the input signal.

Parameters:

signal (array) – Input signal.
bins (int, optional) – Number of histogram bins. Default is 5.
normalize (bool, optional) – Whether to normalize the histogram counts. Default is True.

Returns:

hist{bin}_bins (float) – Number of counts of the bin. If normalize is True, the counts are normalized.

biosppy.stats.linear_regression(x=None, y=None, show=True)[source]¶

Plot the linear regression between two signals and get the equation coefficients.

The linear regression uses the least squares method.

Parameters:

x (array) – First input signal.
y (array) – Second input signal.
show (bool) – If True, show the plot.

Returns:

coeffs (array) – Linear regression coefficients: [m, b].

Raises:

ValueError – If the input signals do not have the same length.

biosppy.stats.paired_test(x=None, y=None)[source]¶

Perform the Student’s paired t-test on the arrays x and y. This is a two-sided test for the null hypothesis that 2 related or repeated samples have identical average (expected) values.

Parameters:

x (array) – First input signal.
y (array) – Second input signal.

Returns:

statistic (float) – t-statistic. The t-statistic is used in a t-test to determine if you should support or reject the null hypothesis.
pvalue (float) – Two-sided p-value.

Raises:

ValueError – If the input signals do not have the same length.

biosppy.stats.pearson_correlation(x=None, y=None)[source]¶

Compute the Pearson Correlation Coefficient between two signals.

The coefficient is given by:

$r_{xy} = \frac{E[(X - \mu_X) (Y - \mu_Y)]}{\sigma_X \sigma_Y}$

Parameters:

x (array) – First input signal.
y (array) – Second input signal.

Returns:

r (float) – Pearson correlation coefficient, ranging between -1 and +1.
pvalue (float) – Two-tailed p-value. The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets.

Raises:

ValueError – If the input signals do not have the same length.

biosppy.stats.quartiles(signal=None)[source]¶

Compute quartile features of the signal.

Parameters:

signal (array) – Input signal.

Returns:

q1 (float) – First quartile.
q2 (float) – Second quartile, also known as median.
q3 (float) – Third quartile.
iqr (float) – Interquartile range.
midhinge (float) – Midhinge.
trimean (float) – Trimean.

biosppy.stats.unpaired_test(x=None, y=None)[source]¶

Perform the Student’s unpaired t-test on the arrays x and y. 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.

Parameters:

x (array) – First input signal.
y (array) – Second input signal.

Returns:

statistic (float) – t-statistic. The t-statistic is used in a t-test to determine if you should support or reject the null hypothesis.
pvalue (float) – Two-sided p-value.

Raises:

ValueError – If the input signals do not have the same length.