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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.
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.
The binomial ratio distribution is of significance in clinical trials: if the distribution of T is known as above, the probability of a given ratio arising purely by chance can be estimated, i.e. a false positive trial. A number of papers compare the robustness of different approximations for the binomial ratio.
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]
In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.Notionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations, where the test statistic used is the ratio of two sample variances. [1]
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Multinomial test is the statistical test of the null hypothesis that the parameters of a multinomial distribution equal specified values; it is used for categorical data. [ 1 ] Beginning with a sample of N {\displaystyle ~N~} items each of which has been observed to fall into one of k {\displaystyle k} categories.