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In mathematics, the ratio test is a test (or "criterion") for the convergence of a series =, where each term is a real or complex number and a n is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test.
Statistical tests are used to test the fit between a hypothesis and the data. [1] [2] Choosing the right statistical test is not a trivial task. [1] The choice of the test depends on many properties of the research question. The vast majority of studies can be addressed by 30 of the 100 or so statistical tests in use. [3] [4] [5]
When a professor wants to apply a more precise scale and ranking for students assessments, instead of using the full 1–10 scale (which would make the scale inconsistent with that of other professors), s/he may sometimes have recourse to a plethora of symbols and decimals: the range between 5 and 6 is then expressed, in ascending order, by 5 ...
If the null hypothesis is true, the likelihood ratio test, the Wald test, and the Score test are asymptotically equivalent tests of hypotheses. [8] [9] When testing nested models, the statistics for each test then converge to a Chi-squared distribution with degrees of freedom equal to the difference in degrees of freedom in the two models. If ...
Former countries in Europe after 1815; Ship prefixes; Timeline of country and capital changes This page was last edited on 27 January 2025, at 21:15 (UTC). Text is ...
ISO 3166-1 alpha-2 – two-letter country codes which are also used to create the ISO 3166-2 country subdivision codes and the Internet country code top-level domains. ISO 3166-1 alpha-3 – three-letter country codes which may allow a better visual association between the codes and the country names than the 3166-1 alpha-2 codes.
If r < 1, then the series converges absolutely. If r > 1, then the series diverges. If r = 1, the root test is inconclusive, and the series may converge or diverge. The root test is stronger than the ratio test: whenever the ratio test determines the convergence or divergence of an infinite series, the root test does too, but not conversely. [1]
The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.