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In probability theory and statistics, Student's t distribution (or simply the t distribution) is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped.
Student's t-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis.
Multivariate normal distribution, which is the limiting case of the multivariate Student's t-distribution when . Chi distribution , the pdf of the scaling factor in the construction the Student's t-distribution and also the 2-norm (or Euclidean norm ) of a multivariate normally distributed vector (centered at zero).
The noncentral t-distribution generalizes Student's t-distribution using a noncentrality parameter.Whereas the central probability distribution describes how a test statistic t is distributed when the difference tested is null, the noncentral distribution describes how t is distributed when the null is false.
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 ...
Student's t distribution, the distribution of the ratio of a standard normal variable and the square root of a scaled chi squared variable; useful for inference regarding the mean of normally distributed samples with unknown variance (see Student's t-test) F-distribution, the distribution of the ratio of two scaled chi squared variables; useful ...
Student's T Distribution; Earliest known uses of some of the words of mathematics: S under the heading of "Student's t-distribution", describes briefly how Student's z became t. O'Connor, John J.; Robertson, Edmund F., "William Sealy Gosset", MacTutor History of Mathematics Archive, University of St Andrews
In statistics, particularly in hypothesis testing, the Hotelling's T-squared distribution (T 2), proposed by Harold Hotelling, [1] is a multivariate probability distribution that is tightly related to the F-distribution and is most notable for arising as the distribution of a set of sample statistics that are natural generalizations of the statistics underlying the Student's t-distribution.