Ignorable

Ignorable is an adjective describing something that may be disregarded without affecting the outcome or interpretation in a given context. In ordinary use, an ignorable detail is one judged irrelevant to a task or conclusion, whereas non-ignorable items warrant attention.

In mathematics and physics, the term has more technical senses. In asymptotic analysis, certain terms are called ignorable because their contribution vanishes in a limit or is of higher order relative to leading terms, allowing simpler approximations. In perturbation theory, ignorable terms can be neglected to obtain an approximate solution. In Lagrangian mechanics, an ignorable (or cyclic) coordinate is one that does not appear in the Lagrangian; its associated momentum is conserved, and the coordinate can be removed from the equations of motion to reduce a system’s complexity.

In statistics and data analysis, an ignorable missing-data mechanism is one that can be ignored in likelihood-based inference under certain conditions, such as missing at random with distinct parameters, enabling standard analyses without modeling the missingness in full detail. Conversely, non-ignorable (or non-missing-at-random) mechanisms require explicit treatment to avoid biased conclusions.

Usage and limitations: whether a term or factor is ignorable depends on the model, the assumptions it imposes, and the required accuracy. If the underlying assumptions fail, what was considered ignorable may actually influence results, leading to bias or error.

See also: negligible, insignificant, nonessential, cyclic coordinate, missing-data mechanism.