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From the t-test, the difference between the group means is 6-2=4. From the regression, the slope is also 4 indicating that a 1-unit change in drug dose (from 0 to 1) gives a 4-unit change in mean word recall (from 2 to 6). The t-test p-value for the difference in means, and the regression p-value for the slope, are both 0.00805. The methods ...
Where ( ) is the inverse standardized Student t CDF, and ( ) is the standardized Student t PDF. [ 2 ] In probability theory and statistics , Student's t distribution (or simply the t distribution ) t ν {\displaystyle \ t_{\nu }\ } is a continuous probability distribution that generalizes the standard normal distribution .
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.
To design a test, Šidák correction may be applied, as in the case of finitely many t-test. However, when N ( n ) → ∞ as n → ∞ {\displaystyle N(n)\rightarrow \infty {\text{ as }}n\rightarrow \infty } , the Šidák correction for t-test may not achieve the level we want, that is, the true level of the test may not converges to the ...
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 ...
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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.
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