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As an example, in a two dimensional problem, the line that best divides the two groups is perpendicular to . Generally, the data points to be discriminated are projected onto ; then the threshold that best separates the data is chosen from analysis of the one-dimensional distribution. There is no general rule for the threshold.
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 ...
In the majority of cases, the plaintiff lacks direct evidence of discrimination and must prove discriminatory intent indirectly by inference. The Supreme Court analyzes these cases using the McDonnell Douglas burden-shifting formula. The analysis is as follows: [10] (1) The plaintiff must establish a prima facie case of discrimination.
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.
Discrimination can also occur on group variances in the signals (i.e. in how noisy the signal is), even assuming equal averages. For variance-based discrimination to occur, the decision maker needs to be risk averse; such a decision maker will prefer the group with the lower variance. [8]
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:
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 ...
In an example of a death row sentence (McCleskey v. Kemp [nb 2]) concerning racial discrimination, the petitioner, a black man named McCleskey was charged with the murder of a white police officer during a robbery. Expert testimony for McClesky introduced a statistical proof showing that "defendants charged with killing white victims were 4.3 ...