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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 ...
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 ...
A number of statistics can be shown to have t distributions for samples of moderate size under null hypotheses that are of interest, so that the t distribution forms the basis for significance tests. For example, the distribution of Spearman's rank correlation coefficient ρ , in the null case (zero correlation) is well approximated by the t ...
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 and ...
One-sided normal tolerance intervals have an exact solution in terms of the sample mean and sample variance based on the noncentral t-distribution. [8] This enables the calculation of a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls.
The studentized bootstrap, also called bootstrap-t, is computed analogously to the standard confidence interval, but replaces the quantiles from the normal or student approximation by the quantiles from the bootstrap distribution of the Student's t-test (see Davison and Hinkley 1997, equ. 5.7 p. 194 and Efron and Tibshirani 1993 equ 12.22, p. 160):
a) The expression inside the square root has to be positive, or else the resulting interval will be imaginary. b) When g is very close to 1, the confidence interval is infinite. c) When g is greater than 1, the overall divisor outside the square brackets is negative and the confidence interval is exclusive.
The prediction interval is conventionally written as: [, +]. For example, to calculate the 95% prediction interval for a normal distribution with a mean (μ) of 5 and a standard deviation (σ) of 1, then z is approximately 2. Therefore, the lower limit of the prediction interval is approximately 5 ‒ (2⋅1) = 3, and the upper limit is ...