Significancewith

Significancewith is a term used in some statistics discussions to describe a measure of joint significance when two or more predictors are considered together in a model. It is not a single standardized statistic with a universal definition, but rather a descriptive concept for evaluating the combined evidence against a null hypothesis that neither predictor contributes to the outcome.

In practical terms, significancewith may be operationalized by applying established methods to assess joint significance. This can include combining individual p-values for the predictors using techniques such as Fisher’s method or Stouffer’s method, with adjustments for correlation between the predictors; or conducting a likelihood ratio test comparing a model that includes both predictors to a baseline model that excludes them. The choice of method often depends on the study design and the degree of interaction or correlation present among the variables.

Applications of the idea include feature selection, model improvement, and exploratory data analysis, particularly in fields where multiple factors may jointly influence an outcome, such as epidemiology, economics, and social sciences. It is important to distinguish the concept of significancewith from interaction effects or causal inference, as joint significance does not by itself imply causation and can be sensitive to model specification and multiple testing issues.

Etymology reflects the intent: to express “the significance with respect to multiple factors.” The term is informal and not widely standardized in formal statistical literature. See also p-values, joint significance, Fisher’s method, and likelihood ratio tests.