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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 ...
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 ...
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.
The log-t distribution has the probability density function: (, ^, ^) = (+) ^ (+ ( ^ ^)) +,where ^ is the location parameter of the underlying (non-standardized) Student's t-distribution, ^ is the scale parameter of the underlying (non-standardized) Student's t-distribution, and is the number of degrees of freedom of the underlying Student's t-distribution. [1]
For instance, if the variable X has a continuous uniform distribution between 0 and 100 and Y is a dichotomous variable equal to 1 if X ≥ 50 and 0 if X < 50, the Tau-c statistic of X and Y is equal to 1 while Tau-b is equal to 0.707.
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 function T(h, a) gives the probability of the event (X > h and 0 < Y < aX) where X and Y are independent standard normal random variables.. This function can be used to calculate bivariate normal distribution probabilities [2] [3] and, from there, in the calculation of multivariate normal distribution probabilities. [4]
The phrase "T distribution" may refer to Student's t-distribution in univariate probability theory, Hotelling's T-square distribution in multivariate statistics.