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Student's t-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's t -distribution under the null hypothesis .
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 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.
Modern significance testing is largely the product of Karl Pearson (p-value, Pearson's chi-squared test), William Sealy Gosset (Student's t-distribution), and Ronald Fisher ("null hypothesis", analysis of variance, "significance test"), while hypothesis testing was developed by Jerzy Neyman and Egon Pearson (son of Karl).
Starting in the 2010s, some journals began questioning whether significance testing, and particularly using a threshold of α =5%, was being relied on too heavily as the primary measure of validity of a hypothesis. [52] Some journals encouraged authors to do more detailed analysis than just a statistical significance test.
To Ziliak, Gosset seems to have gotten his pen name "Student" from his 1906–1907 notebook on counting yeast cells with a haemocytometer, "The Student's Science Notebook" [1] [5] Thus his most noteworthy achievement is now called Student's, rather than Gosset's, t-distribution and test of statistical significance. [2]
In statistics, particularly in hypothesis testing, the Hotelling's T-squared distribution (T 2), proposed by Harold Hotelling, [1] is a multivariate probability distribution that is tightly related to the F-distribution and is most notable for arising as the distribution of a set of sample statistics that are natural generalizations of the statistics underlying the Student's t-distribution.
A test statistic shares some of the same qualities of a descriptive statistic, and many statistics can be used as both test statistics and descriptive statistics. However, a test statistic is specifically intended for use in statistical testing, whereas the main quality of a descriptive statistic is that it is easily interpretable. Some ...