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[27] [29] [30] The nonparametric counterpart to the paired samples t-test is the Wilcoxon signed-rank test for paired samples. For a discussion on choosing between the t-test and nonparametric alternatives, see Lumley, et al. (2002). [19] One-way analysis of variance (ANOVA) generalizes the two-sample t-test when the data belong to more than ...
The table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4] The parameters used are:
Likewise, the one-sample t-test statistic, (¯) = (¯) / follows a Student's t distribution with n − 1 degrees of freedom when the hypothesized mean is correct. Again, the degrees-of-freedom arises from the residual vector in the denominator.
For a one sample t-test 16 is to be replaced with 8. Other values provide an appropriate approximation when the desired power or significance level are different. [5] However, a full power analysis should always be performed to confirm and refine this estimate.
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 one-sample version serves a purpose similar to that of the one-sample Student's t-test. [2] For two matched samples, it is a paired difference test like the paired Student's t-test (also known as the "t-test for matched pairs" or "t-test for dependent samples").
The Student's t distribution plays a role in a number of widely used statistical analyses, including Student's t test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis.
the value of T can be compared with its expected value under the null hypothesis of 50, and since the sample size is large, a normal distribution can be used as an approximation to the sampling distribution either for T or for the revised test statistic T−50. Using one of these sampling distributions, it is possible to compute either a one ...