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Another is Hotelling's T 2 statistic follows a T 2 distribution. However, in practice the distribution is rarely used, since tabulated values for T 2 are hard to find. Usually, T 2 is converted instead to an F statistic. For a one-sample multivariate test, the hypothesis is that the mean vector (μ) is equal to a given vector (μ 0).
Select a significance level (α), the maximum acceptable false positive rate. Common values are 5% and 1%. Compute from the observations the observed value t obs of the test statistic T. Decide to either reject the null hypothesis in favor of the alternative or not reject it.
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 ...
[15] [16] But if the p-value of an observed effect is less than (or equal to) the significance level, an investigator may conclude that the effect reflects the characteristics of the whole population, [1] thereby rejecting the null hypothesis. [17] This technique for testing the statistical significance of results was developed in the early ...
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.
This q s test statistic can then be compared to a q value for the chosen significance level α from a table of the studentized range distribution. If the q s value is larger than the critical value q α obtained from the distribution, the two means are said to be significantly different at level α : 0 ≤ α ≤ 1 . {\displaystyle \ \alpha ...
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:
For a given significance level in a two-tailed test for a test statistic, the corresponding one-tailed tests for the same test statistic will be considered either twice as significant (half the p-value) if the data is in the direction specified by the test, or not significant at all (p-value above ) if the data is in the direction opposite of ...