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In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
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 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.
Precision and recall. In statistical analysis of binary classification and information retrieval systems, the F-score or F-measure is a measure of predictive performance. It is calculated from the precision and recall of the test, where the precision is the number of true positive results divided by the number of all samples predicted to be positive, including those not identified correctly ...
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The formula for the distribution then becomes f ( x ) = τ 2 π e − τ ( x − μ ) 2 / 2 . {\displaystyle f(x)={\sqrt {\frac {\tau }{2\pi }}}e^{-\tau (x-\mu )^{2}/2}.} This choice is claimed to have advantages in numerical computations when σ {\textstyle \sigma } is very close to zero, and simplifies formulas in some contexts, such as in ...
The f-number N is given by: = where f is the focal length, and D is the diameter of the entrance pupil (effective aperture).It is customary to write f-numbers preceded by "f /", which forms a mathematical expression of the entrance pupil's diameter in terms of f and N. [1]
The F-test statistic is the ratio, after scaling by the degrees of freedom. If there is no difference between population means this ratio follows an F-distribution with 2 and 3n − 3 degrees of freedom. In some complicated settings, such as unbalanced split-plot designs, the sums-of-squares no longer have scaled chi-squared distributions ...