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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.
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.
2.7 Student's t-distribution. ... Toggle the table of contents. ... the skewed generalized "t" distribution is a family of continuous probability distributions.
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.
Toggle the table of contents. List of probability distributions. 12 languages. ... The multivariate t-distribution, a generalization of the Student's t-distribution.
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
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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).