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StatsTtest

Namespace: STSLIB  ·  Library: Statistics Library

#include <sts/sts_ttest.h>

class STSLIB::StatsTtest

Provides t-test implementations: one-sample, paired, and independent two-sample.

One-sample, paired and independent two-sample Student t-tests with exact p-values via the regularised incomplete beta function.

src/examples/ex_sts_statistics/main.cpp
const StatsTtestResult oneSample = StatsTtest::oneSample(a);        // H0: column mean = 0
const StatsTtestResult paired = StatsTtest::paired(a, b);           // H0: mean(a - b) = 0
const StatsTtestResult independent = StatsTtest::independent(a, b); // pooled variance, df = 10
const StatsTtestResult rightTail = StatsTtest::oneSample(a, 0.0, StatsTailType::Right);

Static Methods​

oneSample(data, mu, tail)​

One-sample t-test.

Each column of data is tested against mu.

Parameters:

  • data : const Eigen::MatrixXd & Matrix of observations (rows = observations, cols = variables).

  • mu : double Hypothesized mean (default 0.0).

  • tail : StatsTailType Tail type for the test.

Returns:

paired(dataA, dataB, tail)​

Paired t-test.

Tests dataA - dataB against 0.

Parameters:

  • dataA : const Eigen::MatrixXd & Matrix of observations for condition A.

  • dataB : const Eigen::MatrixXd & Matrix of observations for condition B (same dimensions as dataA).

  • tail : StatsTailType Tail type for the test.

Returns:

independent(dataA, dataB, tail)​

Independent two-sample t-test.

Parameters:

  • dataA : const Eigen::MatrixXd & Matrix of observations for group A (rows = observations, cols = variables).

  • dataB : const Eigen::MatrixXd & Matrix of observations for group B (same number of columns as dataA).

  • tail : StatsTailType Tail type for the test.

Returns:

permutation(data, nPermutations, tail, seed)​

One-sample sign-flip permutation t-test with max-statistic correction, as mne.stats.permutation_t_test.

Every column is tested against 0; the p-values compare each t with the distribution of the maximum |t| over all columns.

Parameters:

  • data : const Eigen::MatrixXd & Observations (rows = samples, cols = tests).

  • nPermutations : int Number of permutations including the observed data; when it exceeds the number of distinct sign flips, all of them are used (exact test).

  • tail : StatsTailType Tail type for the test.

  • seed : unsigned int Seed for the random subset of sign flips.

Returns:

tCdf(t, df)​

Compute the CDF of the t-distribution using the regularized incomplete beta function.

Parameters:

  • t : double The t-value.

  • df : int Degrees of freedom.

Returns:

  • double — The probability P(T <= t).

regularizedBeta(x, a, b)​

Regularized incomplete beta function I_x(a, b).

Public because it is also used by StatsFtest.

Parameters:

  • x : double Upper integration limit in [0, 1].

  • a : double First shape parameter (positive).

  • b : double Second shape parameter (positive).

Returns:

  • double — I_x(a, b) in [0, 1]; 0 for x at or below 0 and 1 for x at or above 1.

Example​

Used in examples​

ex_sts_statistics​

Statistics library on small literal data sets with known answers.

src/examples/ex_sts_statistics/main.cpp, line 94
const StatsTtestResult oneSample = StatsTtest::oneSample(a);        // H0: column mean = 0
const StatsTtestResult paired = StatsTtest::paired(a, b);           // H0: mean(a - b) = 0
const StatsTtestResult independent = StatsTtest::independent(a, b); // pooled variance, df = 10
const StatsTtestResult rightTail = StatsTtest::oneSample(a, 0.0, StatsTailType::Right);
// scipy.stats.ttest_1samp / ttest_rel / ttest_ind
ok &= expectRow(oneSample.matTstat, {10.285912696499036, 0.24544034683690788, -0.12327841818038444}, 1e-10, "one-sample t = scipy");
ok &= expectRow(oneSample.matPval, {0.00014930867649425364, 0.8158714843641037, 0.9066888237538449}, 1e-10, "one-sample p = scipy");
ok &= expectRow(paired.matTstat, {26.0, 0.0, -0.7254762501100115}, 1e-10, "paired t = scipy");
ok &= expectRow(paired.matPval, {1.5724552146685355e-06, 1.0, 0.5006803901900951}, 1e-10, "paired p = scipy");
ok &= expectRow(independent.matTstat, {5.918268896877812, 0.0, -0.34452048127477725}, 1e-10, "independent t = scipy");
ok &= expectRow(independent.matPval, {0.0001473880425533016, 1.0, 0.7375904333691938}, 1e-10, "independent p = scipy");
ok &= expect(oneSample.degreesOfFreedom == 5 && independent.degreesOfFreedom == 10, "df 5 and 10");
ok &= expect(std::fabs(rightTail.matPval(0, 0) - oneSample.matPval(0, 0) / 2.0) < 1e-12, "right-tailed p is half the two-tailed p");

Authors of this file​