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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 ...
The t-test p-value for the difference in means, and the regression p-value for the slope, are both 0.00805. The methods give identical results. This example shows that, for the special case of a simple linear regression where there is a single x-variable that has values 0 and 1, the t-test gives the same results as the linear regression. The ...
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.
In statistics, the Sobel test is a method of testing the significance of a mediation effect. The test is based on the work of Michael E. Sobel, [1] [2] and is an application of the delta method.
The phrase "T distribution" may refer to Student's t-distribution in univariate probability theory, Hotelling's T-square distribution in multivariate statistics.
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This may be verified by substituting 11 mph in place of 12 mph in the Bumped sample, and 19 mph in place of 20 mph in the Smashed and re-computing the test statistic. From tables with k = 3, and m = 4, the critical S value for α = 0.05 is 36 and thus the result would be declared statistically significant at this level.
where is the number of observations and is number of regression variables; the are independent standard normal random variables; and the are the nonzero eigenvalues of (()), where is the matrix that transforms the residuals into the statistic, i.e. =. [3] A number of computational algorithms for finding percentiles of this distribution are ...