Wilks

Wilks is a surname of English origin that appears in various English-speaking countries. In addition to being a family name, the name has been associated with statistical concepts named after researchers who bore it, and it may be found in other cultural or geographic contexts as well.

In statistics, two well-known uses of the name Wilks are Wilks’ lambda and Wilks’ theorem. Wilks’ lambda is a multivariate test statistic used in MANOVA and discriminant analysis to assess whether multiple group means on a set of dependent variables are equal. It ranges from 0 to 1, with smaller values indicating greater differences among groups; under certain assumptions, Wilks’ lambda can be related to an F distribution for hypothesis testing.

Wilks’ theorem is a foundational result for likelihood-ratio tests. It states that, under regularity conditions and when the null hypothesis is true, the statistic −2 log L, where L is the likelihood under the null versus the alternative, converges in distribution to a chi-square distribution with degrees of freedom equal to the number of constrained parameters, in the limit of large sample sizes. This asymptotic result underpins significance testing in many statistical models.

Beyond statistics, the name Wilks may appear in other contexts as a surname, and occasionally in toponymy or organizational names derived from individuals bearing the name. The term does not refer to a single, universally defined concept outside its statistical usages. See also: Wilks (surname).