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The following table lists values for t distributions with ν degrees of freedom for a range of one-sided or two-sided critical regions. The first column is ν , the percentages along the top are confidence levels α , {\displaystyle \ \alpha \ ,} and the numbers in the body of the table are the t α , n − 1 {\displaystyle t_{\alpha ,n-1 ...
In Dunnett's test we can use a common table of critical values, but more flexible options are nowadays readily available in many statistics packages. The critical values for any given percentage point depend on: whether a one- or- two-tailed test is performed; the number of groups being compared; the overall number of trials.
Once the t value and degrees of freedom are determined, a p-value can be found using a table of values from Student's t-distribution. If the calculated p -value is below the threshold chosen for statistical significance (usually the 0.10, the 0.05, or 0.01 level), then the null hypothesis is rejected in favor of the alternative hypothesis.
Here, the degrees of freedom arises from the residual sum-of-squares in the numerator, and in turn the n − 1 degrees of freedom of the underlying residual vector {¯}. In the application of these distributions to linear models, the degrees of freedom parameters can take only integer values.
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 ...
However, the central t-distribution can be used as an approximation to the noncentral t-distribution. [7] If T is noncentral t-distributed with ν degrees of freedom and noncentrality parameter μ and F = T 2, then F has a noncentral F-distribution with 1 numerator degree of freedom, ν denominator degrees of freedom, and noncentrality ...
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The simplest application of this equation is in performing Welch's t-test. An improved equation was derived to reduce underestimating the effective degrees of freedom if the pooled sample variances have small degrees of freedom. Examples are jackknife and imputation-based variance estimates [3].