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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 fixation index (F ST) is a measure of population differentiation due to genetic structure. It is frequently estimated from genetic polymorphism data, such as single-nucleotide polymorphisms (SNP) or microsatellites. Developed as a special case of Wright's F-statistics, it is one of the most commonly used statistics in population genetics ...
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]
The F-test in ANOVA is an example of an omnibus test, which tests the overall significance of the model. A significant F test means that among the tested means, at least two of the means are significantly different, but this result doesn't specify exactly which means are different one from the other.
The following table defines the possible outcomes when testing multiple null hypotheses. Suppose we have a number m of null hypotheses, denoted by: H 1, H 2, ..., H m. Using a statistical test, we reject the null hypothesis if the test is declared significant. We do not reject the null hypothesis if the test is non-significant.
The test involves computing the ratio of the largest group variance, max(s j 2) to the smallest group variance, min(s j 2). The resulting ratio, F max, is then compared to a critical value from a table of the sampling distribution of F max. [2] [3] If the computed ratio is less than the critical value, the groups are assumed to have similar or ...
Developed in 1940 by John W. Mauchly, [3] Mauchly's test of sphericity is a popular test to evaluate whether the sphericity assumption has been violated. The null hypothesis of sphericity and alternative hypothesis of non-sphericity in the above example can be mathematically written in terms of difference scores.
In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or r φ) is a measure of association for two binary variables.. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975.