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In probability theory and statistics, the F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and other F-tests.
The null hypothesis is rejected if the F calculated from the data is greater than the critical value of the F-distribution for some desired false-rejection probability (e.g. 0.05). Since F is a monotone function of the likelihood ratio statistic, the F-test is a likelihood ratio test.
F-ratio or f-ratio may refer to: The F-ratio used in statistics, which relates the variances of independent samples; see F-distribution; f-ratio (oceanography), which relates recycled and total primary production in the surface ocean; f-number, f-ratio, or focal ratio, the ratio of the focal length of an optical system to the diameter of its ...
Definition Named after Field of application Activity coefficient = chemistry (Proportion of "active" molecules or atoms) Arrhenius number = Svante Arrhenius: chemistry (ratio of activation energy to thermal energy) [1]
In the following quote, an "apertal ratio" of "1 ⁄ 24" is calculated as the ratio of 6 inches (150 mm) to 1 ⁄ 4 inch (6.4 mm), corresponding to an f /24 f-stop: In every lens there is, corresponding to a given apertal ratio (that is, the ratio of the diameter of the stop to the focal length), a certain distance of a near object from it ...
A reformulation of the definition of would be the ratio of the average number of differences between pairs of chromosomes sampled within diploid individuals with the average number obtained when sampling chromosomes randomly from the population (excluding the grouping per individual). One can modify this definition and consider a grouping per ...
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]
Diagram of new and regenerated production with nitrification confined to the aphotic zone. This was used to frame the f-ratio and its link to export production. Bio-available nitrogen occurs in the ocean in several forms, including simple ionic forms such as nitrate (NO 3 −), nitrite (NO 2 −) and ammonium (NH 4 +), and more complex organic forms such as urea ((NH 2) 2 CO).