Absodds

Absodds is a term occasionally encountered in probability and statistics to denote the magnitude of the odds associated with a binary event. In standard terminology, the odds of an event with probability p (0 < p < 1) are defined as p/(1−p). Absodds is defined as the absolute value of this quantity, |p/(1−p)|. For valid probabilities, this absolute value coincides with the ordinary odds, but the notation is sometimes used in contexts that allow signed odds or to emphasize magnitude.

Formally, for p in (0,1), absodds(p) = p/(1−p). The inverse relationship is p = absodds/(1 + absodds). As p approaches 0, absodds approaches 0; as p approaches 1, absodds grows without bound. The function is strictly increasing on (0,1).

In applied settings, absodds may appear in expository material or toy models to focus on the strength of association without regard to the direction implied by p being less than or greater than 0.5. It is important to note that absodds is not a standard, widely adopted metric in epidemiology or econometrics, where odds, odds ratios, and log-odds (logits) are used with specific interpretations.

See also: odds, odds ratio, log-odds, probability.