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Test statistic is a quantity derived from the sample for statistical hypothesis testing. [1] A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or ...
Illustration of the Kolmogorov–Smirnov statistic. The red line is a model CDF, the blue line is an empirical CDF, and the black arrow is the KS statistic.. Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions that can be used to test whether a sample came from a ...
Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, [1] is a single-step multiple comparison procedure and statistical test. It can be used to correctly interpret the statistical significance of the difference between means that have been selected ...
Definition. The p -value is the probability under the null hypothesis of obtaining a real-valued test statistic at least as extreme as the one obtained. Consider an observed test-statistic from unknown distribution . Then the p -value is what the prior probability would be of observing a test-statistic value at least as "extreme" as if null ...
t. -test. 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. It is most commonly applied when the test statistic would ...
F. -test. An f-test pdf with d1 and d2 = 10, at a significance level of 0.05. (Red shaded region indicates the critical region) An F-test is any statistical test used to compare the variances of two samples or the ratio of variances between multiple samples. The test statistic, random variable F, is used to determine if the tested data has an F ...
Likelihood-ratio test. In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods.
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 ...