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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 F-distribution, which is the distribution of the ratio of two (normalized) chi-squared-distributed random variables, used in the analysis of variance. It is referred to as the beta prime distribution when it is the ratio of two chi-squared variates which are not normalized by dividing them by their numbers of degrees of freedom.
In particular, if d = 1 (for example, if F = Q and D ⊗ R ≅ M 2 (R)), fixing a sufficiently small arithmetic subgroup of D ×, one gets a Shimura curve, and curves arising from this construction are already compact (i.e. projective). Some examples of Shimura curves with explicitly known equations are given by the Hurwitz curves of low genus:
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 formula for the one-way ANOVA F-test statistic is =, or =. The "explained variance", or "between-group variability" is = (¯ ¯) / where ¯ denotes the sample mean in the i-th group, is the number of observations in the i-th group, ¯ denotes the overall mean of the data, and denotes the number of groups.
An FCurve (also written f-curve) is a function curve or the graph of a function.An example of a FCurve is a spline.. In the field of computer animation and especially in animation editors, e.g. Maya, an FCurve is an animation curve with a set of keyframes, which are represented as points, curve segments between keys, and tangents that control how curve segments enter and exit a key.
For example, the ionic strength of the solution can have an effect on the activity coefficients of the analytes. [3] [4] The most common approach for accounting for matrix effects is to build a calibration curve using standard samples with known analyte concentration and which try to approximate the matrix of the sample as much as possible. [2]
Measurements, first and second derivative in a potentiometric titration. In analytical chemistry, potentiometric titration is a technique similar to direct titration of a redox reaction.