--- title: "mlab-builtins-stats-contingency — Mova code model" description: "Mova code model of mlab/src/builtins/stats.rs: components with their labels, obernants and the model text." url: "https://groupants.elamur.ai/free/en/mova/mlab/src/builtins/stats.rs.groupant/contingency.groupant/" --- Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants** This page as HTML: # mlab-builtins-stats-contingency The groupant beside mlab/src/builtins/stats.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks. ## Facts - **kind:** groupant_fragment - **status:** partial source bound model - **source:** [`mlab/src/builtins/stats.rs`](https://github.com/ElamurAI/mova-free/blob/main/mlab/src/builtins/stats.rs) - **source SHA-256:** `bdc3772b09d9113e…` - **covers:** chi2_ind takes rectangular nonempty counts, computes marginals and rejects <=0 totals; Eij=ri*cj/N, statistic sum(O-E)^2/E, df=(r-1)(c-1)+fault. crosstab categorizes using table groups, counting missing category as group. (bytes 25404–29854) - **part of:** [mlab-builtins-stats](https://md.groupants.elamur.ai/free/en/mova/mlab/src/builtins/stats.rs.groupant/) - **repository folder:** [`mlab/src/builtins/stats.rs.groupant/contingency.groupant`](https://github.com/ElamurAI/mova-free/tree/main/mlab/src/builtins/stats.rs.groupant/contingency.groupant) - **repository commit:** `855da7bd4a7b` > **Implementation material.** A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised. ## Components | component | label | where | |---|---|---| | **approximant** | partial | [approximant](#approximant) | | **ast** | partial | `../syntax.json` | | **cost** | symbolic source derived | [invariant](#invariant) | | **descriptant** | present | [descriptant](#descriptant) | | **invariant** | partial | [invariant](#invariant) | | **tests** | partial bounded parent evidence | [tests](#tests) | ## Obernants The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views. | id | type | label | where | |---|---|---|---| | `behavior_complement` | behavior_complement | partial source derived model | [behavior_complement](#behavior-complement) | | `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) | | `marginal_transport` | marginal_transport | partial source derived model | [marginal_transport](#marginal-transport) | | `category_missing` | category_missing | partial source derived model | [category_missing](#category-missing) | | `branch_relation` | branch_relation | partial source derived model | [branch_relation](#branch-relation) | | `resource_cost` | resource_cost | partial source derived model | [resource_cost](#resource-cost) | ## Model text ### descriptant #### mlab-builtins-stats-contingency chi2_ind takes rectangular nonempty counts, computes marginals and rejects <=0 totals; Eij=ri*cj/N, statistic sum(O-E)^2/E, df=(r-1)(c-1)+fault. crosstab categorizes using table groups, counting missing category as group. Epoch 2026-10-31: isolated source-bound fragment over bytes [25404,29854); includes no claim beyond this relation. Source hash bdc3772b09d9113e108afa29e391fee97a5372caf9052bb1689996c41c94116f. ### approximant #### contingency: forward relation chi2_ind takes rectangular nonempty counts, computes marginals and rejects <=0 totals; Eij=ri*cj/N, statistic sum(O-E)^2/E, df=(r-1)(c-1)+fault. crosstab categorizes using table groups, counting missing category as group. Domain: Finite, well-shaped bounded observations unless branch explicitly describes NaN/Inf. Direct public chi2/OLS helpers assume dimensions not checked at every index; wrappers add validation. Executable surrogate gap: no measured cheaper implementation with a useful scoped metric is supplied. Categorical/error/effect relations are exact obligations, not percent losses. Future numeric caps only1/2/5/10%. ### invariant #### contingency: invariant and cost Expected row/column sums reproduce observed marginals under finite arithmetic up to rounding. NaN categories group, unlike missing join keys; wrapper chi2test requires>=2x2 before options. Scope-specific cost: O(r*c) time and expected matrix storage, plus category sorting O(n log n); invalid marginals fail before matrix fill. ### models ### behavior_complement Positive marginals do not ensure nonnegative cells; direct core does not validate that. crosstab degenerate category dimensions returns chi2=0,p=1. ### reverse_reconstruction Expected table admits many observed tables with same marginals; chi2 scalar further collapses dimensional arrangement. Category indices admit all value relabelings preserving sort order. ### marginal_transport Expected row/column sums reproduce observed marginals under finite arithmetic up to rounding. ### category_missing NaN categories group, unlike missing join keys; wrapper chi2test requires>=2x2 before options. ### branch_relation chi2_ind takes rectangular nonempty counts, computes marginals and rejects <=0 totals; Eij=ri*cj/N, statistic sum(O-E)^2/E, df=(r-1)(c-1)+fault. crosstab categorizes using table groups, counting missing category as group. ### resource_cost O(r*c) time and expected matrix storage, plus category sorting O(n log n); invalid marginals fail before matrix fill. ### tests #### Evidence boundary See ../tests.md for the actual selected source test and mutant. These tests sample the file, not every fragment branch. Positive marginals do not ensure nonnegative cells; direct core does not validate that. crosstab degenerate category dimensions returns chi2=0,p=1. Other branches here are source-derived and unexecuted unless the parent test explicitly calls them.