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  2. Student's t-distribution - Wikipedia

    en.wikipedia.org/wiki/Student's_t-distribution

    In statistics, the t distribution was first derived as a posterior distribution in 1876 by Helmert [19] [20] [21] and Lüroth. [22] [23] [24] As such, Student's t-distribution is an example of Stigler's Law of Eponymy. The t distribution also appeared in a more general form as Pearson type IV distribution in Karl Pearson's 1895 paper. [25]

  3. Student's t-test - Wikipedia

    en.wikipedia.org/wiki/Student's_t-test

    Once the t value and degrees of freedom are determined, a p-value can be found using a table of values from Student's t-distribution. If the calculated p-value is below the threshold chosen for statistical significance (usually the 0.10, the 0.05, or 0.01 level), then the null hypothesis is rejected in favor of the alternative hypothesis.

  4. t-statistic - Wikipedia

    en.wikipedia.org/wiki/T-statistic

    Most frequently, t statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals. The key property of the t statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the population parameters, and thus it can be used regardless of what these ...

  5. Noncentral t-distribution - Wikipedia

    en.wikipedia.org/wiki/Noncentral_t-distribution

    Central t-distribution: the central t-distribution can be converted into a location/scale family. This family of distributions is used in data modeling to capture various tail behaviors. The location/scale generalization of the central t-distribution is a different distribution from the noncentral t-distribution

  6. Folded-t and half-t distributions - Wikipedia

    en.wikipedia.org/wiki/Folded-t_and_half-t...

    In statistics, the folded-t and half-t distributions are derived from Student's t-distribution by taking the absolute values of variates. This is analogous to the folded-normal and the half-normal statistical distributions being derived from the normal distribution.

  7. Multivariate t-distribution - Wikipedia

    en.wikipedia.org/wiki/Multivariate_t-distribution

    One common method of construction of a multivariate t-distribution, for the case of dimensions, is based on the observation that if and are independent and distributed as (,) and (i.e. multivariate normal and chi-squared distributions) respectively, the matrix is a p × p matrix, and is a constant vector then the random variable = / / + has the density [1]

  8. Studentized residual - Wikipedia

    en.wikipedia.org/wiki/Studentized_residual

    where t is a random variable distributed as Student's t-distribution with ν − 1 degrees of freedom. In fact, this implies that t i 2 /ν follows the beta distribution B(1/2,(ν − 1)/2). The distribution above is sometimes referred to as the tau distribution; [2] it was first derived by Thompson in 1935. [3]

  9. Degrees of freedom (statistics) - Wikipedia

    en.wikipedia.org/wiki/Degrees_of_freedom...

    Likewise, the one-sample t-test statistic, (¯) = (¯) / follows a Student's t distribution with n − 1 degrees of freedom when the hypothesized mean is correct. Again, the degrees-of-freedom arises from the residual vector in the denominator.