Statistical Inference - Genometric/GeMSE GitHub Wiki

Covariance and correlation

Covariance

Pearson's product-moment correlation coefficients

Principal component analysis

Statistical hypothesis testing

Student's t-test

Each of the spaces (an array) is considered as a single observation (a vector). So, if want to compare two observations, create two spaces, one for each, then analyze the two newly created spaces.

Single Space Test

  1. t-Statistic: Computes a t statistic given observed values and a comparison constant. This statistic can be used to perform a one sample t-test for the mean.

  2. t-Test: Returns the observed significance level, or p-value, associated with a one-sample, two-tailed t-test comparing the mean of the input array with the constant mu.

  3. t-Test: Performs a two-sided t-test evaluating the null hypothesis that the mean of the population from which sample is drawn equals mu. Returns true iff the null hypothesis can be rejected with confidence 1 - alpha. To perform a 1-sided test, use alpha * 2

Double Space Test

  1. t-Statistic: Computes a 2-sample t statistic, without the hypothesis of equal subpopulation variances.
  2. Paired t-statistic: Computes a paired, 2-sample t-statistic based on the data in the input arrays.
  3. p-value: Returns the observed significance level, or p-value, associated with a paired, two-sample, two-tailed t-test based on the data in the input arrays.
  4. p-value: Computes p-value for 2-sided, 2-sample t-test, under the assumption of equal subpopulation variances.
  5. degrees of freedom: Computes approximate degrees of freedom for 2-sample t-test.
  6. Homoscedasticity: Computes a 2-sample t statistic, under the hypothesis of equal subpopulation variances.
  7. Homoscedasticity with alpha: Performs a two-sided t-test evaluating the null hypothesis that sample1 and sample2 are drawn from populations with the same mean, with significance level alpha, assuming that the subpopulation variances are equal.
  8. t-test with alpha: Performs a two-sided t-test evaluating the null hypothesis that sample1 and sample2 are drawn from populations with the same mean, with significance level alpha.