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Glejser test for heteroscedasticity, developed in 1969 by Herbert Glejser, is a statistical test, which regresses the residuals on the explanatory variable that is thought to be related to the heteroscedastic variance. [1]
For the statistic t, with ν degrees of freedom, A(t | ν) is the probability that t would be less than the observed value if the two means were the same (provided that the smaller mean is subtracted from the larger, so that t ≥ 0). It can be easily calculated from the cumulative distribution function F ν (t) of the t distribution:
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 ...
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 phrase "T distribution" may refer to Student's t-distribution in univariate probability theory, Hotelling's T-square distribution in multivariate statistics.
Flowchart of four phases (enrollment, allocation, intervention, follow-up, and data analysis) of a parallel randomized trial of two groups (in a controlled trial, one of the interventions serves as the control), modified from the CONSORT (Consolidated Standards of Reporting Trials) 2010 Statement [1]
T 1 ≤ T 2 if T 1 (a, b) ≤ T 2 (a, b) for all a, b in [0, 1]. As functions, pointwise larger t-norms are sometimes called stronger than those pointwise smaller. In the semantics of fuzzy logic, however, the larger a t-norm, the weaker (in terms of logical strength) conjunction it represents.
The T-schema is often expressed in natural language, but it can be formalized in many-sorted predicate logic or modal logic; such a formalisation is called a "T-theory." [ citation needed ] T-theories form the basis of much fundamental work in philosophical logic , where they are applied in several important controversies in analytic philosophy .