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The square root of a quantity strongly related to the discriminant appears in the formulas for the roots of a cubic polynomial. Specifically, this quantity can be −3 times the discriminant, or its product with the square of a rational number; for example, the square of 1/18 in the case of Cardano formula.
The main application of discriminant analysis in medicine is the assessment of severity state of a patient and prognosis of disease outcome. For example, during retrospective analysis, patients are divided into groups according to severity of disease – mild, moderate, and severe form.
For example, if an hypothetical fire department used a 100-pound test, that policy might disproportionately exclude female job applicants from employment. Under the 80% rule mentioned above, unsuccessful female job applicants would have a prima facie case of disparate impact "discrimination" against the department if they passed the 100-pound ...
For two univariate distributions and with the same standard deviation, it is denoted by ′ ('dee-prime'): ′ = | |. In higher dimensions, i.e. with two multivariate distributions with the same variance-covariance matrix , (whose symmetric square-root, the standard deviation matrix, is ), this generalizes to the Mahalanobis distance between the two distributions:
This formula can be obtained by Taylor series expansion: (+) = + ′ ()! ″ ()! () +. The complex-step derivative formula is only valid for calculating first-order derivatives. A generalization of the above for calculating derivatives of any order employs multicomplex numbers , resulting in multicomplex derivatives.
One of the best-known examples of Simpson's paradox comes from a study of gender bias among graduate school admissions to University of California, Berkeley.The admission figures for the fall of 1973 showed that men applying were more likely than women to be admitted, and the difference was so large that it was unlikely to be due to chance.
In that 2020 case, the justices ruled that gay and transgender workers were covered by a prohibition on discrimination “because of … sex” in Title VII of the 1964 Civil Rights Act.
Using Blinder-Oaxaca decomposition one can distinguish between "change of mean" contribution (purple) and "change of effect" contribution. The Oaxaca-Blinder decomposition (/ ˈ b l aɪ n d ər w ɑː ˈ h ɑː k ɑː /), also known as Kitagawa decomposition, is a statistical method that explains the difference in the means of a dependent variable between two groups by decomposing the gap into ...