Search results
Results From The WOW.Com Content Network
Most test statistics have the form t = Z/s, where Z and s are functions of the data. Z may be sensitive to the alternative hypothesis (i.e., its magnitude tends to be larger when the alternative hypothesis is true), whereas s is a scaling parameter that allows the distribution of t to be determined. As an example, in the one-sample t-test
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 ...
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 informative descriptive statistics, such as the sample range, do not make good test statistics since it is difficult to determine their sampling distribution. Two widely ...
For example, the test statistic might follow a Student's t distribution with known degrees of freedom, or a normal distribution with known mean and variance. 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.
In statistics, the t distribution was first derived as a posterior distribution in 1876 by Helmert [19] [20] [21] and Lüroth. [22] [23] [24] As such, Student's t-distribution is an example of Stigler's Law of Eponymy. The t distribution also appeared in a more general form as Pearson type IV distribution in Karl Pearson's 1895 paper. [25]
Unpaired samples are also called independent samples. Paired samples are also called dependent. Finally, there are some statistical tests that perform analysis of relationship between multiple variables like regression. [1] Number of samples: The number of samples of data. Exactness: A test can be exact or be asymptotic delivering approximate ...
The demonstration of the t and chi-squared distributions for one-sample problems above is the simplest example where degrees-of-freedom arise. However, similar geometry and vector decompositions underlie much of the theory of linear models , including linear regression and analysis of variance .
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.