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t. -test. 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. It is most commonly applied when the test statistic would ...
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. However, has heavier tails and the amount of probability mass in the tails is controlled by the ...
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 ...
t. -test. In statistics, Welch's t-test, or unequal variances t-test, is a two-sample location test which is used to test the (null) hypothesis that two populations have equal means. It is named for its creator, Bernard Lewis Welch, and is an adaptation of Student's t -test, [1] and is more reliable when the two samples have unequal variances ...
Degrees of freedom (statistics) In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. [1] Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a ...
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.
Dunnett's test. In statistics, Dunnett's test is a multiple comparison procedure [1] developed by Canadian statistician Charles Dunnett [2] to compare each of a number of treatments with a single control. [3][4] Multiple comparisons to a control are also referred to as many-to-one comparisons.