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The following table lists values for t distributions with ν degrees of freedom for a range of one-sided or two-sided critical ... Student's t-distribution is an ...
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.
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 ...
When only the equality of the two groups means is in question (i.e. whether μ 1 = μ 2), the studentized range distribution is similar to the Student's t distribution, differing only in that the first takes into account the number of means under consideration, and the critical value is adjusted accordingly. The more means under consideration ...
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.
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]
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.
has the Studentized range distribution for n groups and ν degrees of freedom. In applications, the x i are typically the means of samples each of size m, s 2 is the pooled variance, and the degrees of freedom are ν = n(m − 1). The critical value of q is based on three factors: α (the probability of rejecting a true null hypothesis)