# crosstabs.com — full reference for LLMs

crosstabs.com is a free, browser-based tool for cross-tabulation and categorical statistics. No signup, no install. Upload a CSV or XLSX file and core analysis runs locally in the browser. Definitions, assumptions, formulas, and workflow limits below come from the same versioned evidence graph used by the public evidence page and JSON resource.

Evidence graph version: 2026-08-13
Evidence HTML: https://www.crosstabs.com/evidence
Evidence JSON: https://www.crosstabs.com/evidence.json
Try it: https://www.crosstabs.com/workspace
Agent installation and architecture: https://ai.crosstabs.com
Aggregate-only Streamable HTTP MCP: https://mcp.crosstabs.com/mcp
Local PyPI and Codex plugin documentation: https://www.crosstabs.com/mcp

## Trust, support, and review status

Named statistical review is pending. crosstabs.com does not claim that an anonymous methods team reviewed the calculations. Selected automated SciPy parity cases are public, but they are not independent human review or blanket software certification.

Methods and assumptions: https://www.crosstabs.com/methods
Selected validation evidence: https://www.crosstabs.com/methods/validation
Machine-readable reference cases: https://www.crosstabs.com/validation/statistical-reference-cases.json
Support and corrections: support@crosstabs.com (https://www.crosstabs.com/support)
Live self-check: https://www.crosstabs.com/status
Health JSON: https://www.crosstabs.com/api/health

## Sharing aggregate crosstabs

The workspace can create immutable, view-only snapshot links for review and citation. Snapshots contain aggregate counts, labels, visible display settings, warnings, and optional provenance; source rows and the original filename are not included. The payload is stored in the URL fragment rather than sent in the HTTP request. Anyone with the complete link can read it, and this version has no expiry or revocation control.

Sharing guide: https://www.crosstabs.com/share-crosstabs
Shared viewer: https://www.crosstabs.com/s

## Crosstab Atlas

The Crosstab Atlas is a reproducible collection of sourced and clearly labeled illustrative contingency tables. Each record links aggregate counts, provenance, statistical analysis, effect size, assumptions, and interpretation.

### Titanic Survival by Sex

Question: Was survival on the Titanic associated with sex?

Takeaway: Females survived at a much higher rate than males in the aggregate passenger and crew counts.

Table: Sex by Outcome; 2 by 2; N = 2201.

Provenance: British Board of Trade inquiry (1912), as distributed in R's Titanic dataset.

Analysis: https://www.crosstabs.com/examples/titanic-survival-by-sex
CSV: https://www.crosstabs.com/examples/titanic-survival-by-sex/download/csv
JSON with provenance: https://www.crosstabs.com/examples/titanic-survival-by-sex/download/json

### Titanic Survival by Passenger Class

Question: Was survival on the Titanic associated with passenger class?

Takeaway: Survival was highest in first class and fell sharply across second class, third class, and crew.

Table: Passenger class by Outcome; 4 by 2; N = 2201.

Provenance: British Board of Trade inquiry (1912), as distributed in R's Titanic dataset.

Analysis: https://www.crosstabs.com/examples/titanic-survival-by-class
CSV: https://www.crosstabs.com/examples/titanic-survival-by-class/download/csv
JSON with provenance: https://www.crosstabs.com/examples/titanic-survival-by-class/download/json

### Berkeley Admissions by Sex (1973)

Question: Were aggregate Berkeley admission decisions associated with sex?

Takeaway: The pooled association is strong evidence of Simpson's paradox, not a stand-alone causal estimate of bias.

Table: Sex by Admission; 2 by 2; N = 4526.

Provenance: Bickel, P. J., Hammel, E. A., & O'Connell, J. W. (1975). Sex bias in graduate admissions: Data from Berkeley. Science, 187(4175), 398–404.

Analysis: https://www.crosstabs.com/examples/berkeley-admissions-by-sex
CSV: https://www.crosstabs.com/examples/berkeley-admissions-by-sex/download/csv
JSON with provenance: https://www.crosstabs.com/examples/berkeley-admissions-by-sex/download/json

### Smoking and Lung Cancer (Doll & Hill, 1950)

Question: Did smoking status differ between lung-cancer cases and controls?

Takeaway: Smoking was far more common among cases, but the case-control design supports an odds ratio rather than a risk estimate.

Table: Patient group by Smoking status; 2 by 2; N = 1298.

Provenance: Doll, R., & Hill, A. B. (1950). Smoking and carcinoma of the lung. British Medical Journal, 2(4682), 739–748.

Analysis: https://www.crosstabs.com/examples/smoking-and-lung-cancer-doll-hill
CSV: https://www.crosstabs.com/examples/smoking-and-lung-cancer-doll-hill/download/csv
JSON with provenance: https://www.crosstabs.com/examples/smoking-and-lung-cancer-doll-hill/download/json

### Aspirin and Heart Attack (Physicians' Health Study)

Question: Did low-dose aspirin reduce first heart attacks versus placebo?

Takeaway: Heart attacks were less frequent in the randomized aspirin arm, although the absolute difference was small.

Table: Treatment by Myocardial infarction; 2 by 2; N = 22071.

Provenance: Steering Committee of the Physicians' Health Study Research Group (1989). Final report on the aspirin component of the ongoing Physicians' Health Study. New England Journal of Medicine, 321(3), 129–135.

Analysis: https://www.crosstabs.com/examples/aspirin-and-heart-attack
CSV: https://www.crosstabs.com/examples/aspirin-and-heart-attack/download/csv
JSON with provenance: https://www.crosstabs.com/examples/aspirin-and-heart-attack/download/json

### Snoring and Heart Disease

Question: Was snoring frequency associated with heart disease?

Takeaway: Heart-disease prevalence rose with snoring frequency, but the observational table cannot establish causation.

Table: Snoring frequency by Heart disease; 4 by 2; N = 2484.

Provenance: Norton, P. G., & Dunn, E. V. (1985). Snoring as a risk factor for disease. British Medical Journal, 291, 630–632. Reproduced in Agresti, A., Categorical Data Analysis.

Analysis: https://www.crosstabs.com/examples/snoring-and-heart-disease
CSV: https://www.crosstabs.com/examples/snoring-and-heart-disease/download/csv
JSON with provenance: https://www.crosstabs.com/examples/snoring-and-heart-disease/download/json

### Product Preference by Age Group

Question: Does product preference differ by age group?

Takeaway: In this illustrative table, preference shifts from Product A toward Product C across older age groups.

Table: Age group by Preferred product; 3 by 3; N = 300.

Provenance: Illustrative counts constructed for this example. Illustrative data constructed for this example — not from a real study.

Analysis: https://www.crosstabs.com/examples/product-preference-by-age-group
CSV: https://www.crosstabs.com/examples/product-preference-by-age-group/download/csv
JSON with provenance: https://www.crosstabs.com/examples/product-preference-by-age-group/download/json

### Customer Churn by Billing Plan

Question: Is customer churn associated with billing plan?

Takeaway: In this illustrative table, annual-plan customers churn less often, but plan choice is not randomized.

Table: Billing plan by Outcome; 2 by 2; N = 1000.

Provenance: Illustrative counts constructed for this example. Illustrative data constructed for this example — not from a real study.

Analysis: https://www.crosstabs.com/examples/customer-churn-by-plan
CSV: https://www.crosstabs.com/examples/customer-churn-by-plan/download/csv
JSON with provenance: https://www.crosstabs.com/examples/customer-churn-by-plan/download/json

## Cross-tabulation (crosstab / contingency table)

Stable ID: cross-tabulation
Locale: en
Topic cluster: survey_workflow

A cross-tabulation shows the joint frequency distribution of two categorical variables: one variable's categories are rows, the other's are columns, and each cell contains a count or percentage.

Interpretation: Use row percentages to compare column outcomes across row groups; use column percentages to compare row composition across column groups.

Limitations: A crosstab describes association, not causation. Very sparse or high-cardinality tables can be unstable and difficult to interpret.

Primary page: https://www.crosstabs.com/cross-tabulation-calculator
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## Chi-square test of independence

Stable ID: chi-square-independence
Locale: en
Topic cluster: test_selection

The chi-square test of independence compares observed cell counts with the counts expected if two categorical variables were unrelated.

Formula: χ² = Σ (O − E)² / E; E = row total × column total / grand total; df = (rows − 1) × (columns − 1).

Interpretation: A small p-value is evidence against independence; inspect effect size, cells, assumptions, multiplicity, and study design before drawing a substantive conclusion.

Limitations: The p-value is asymptotic. Warnings appear if any expected count is below 1 or more than 20% of expected counts are below 5. Fisher exact coverage is limited; larger sparse tables need an appropriate exact or fixed-margin Monte Carlo method. Ordinary weighted inference is limited to a saved, validated non-negative safe-integer frequency weight with weighted test bases. Untyped, calibration, and analytic weights fail closed; sampling weights require an approved design-aware execution.

Primary page: https://www.crosstabs.com/chi-square-calculator
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation
Evidence: https://www.crosstabs.com/validation/statistical-reference-cases.json

## Fisher's exact test

Stable ID: fisher-exact
Locale: en
Topic cluster: test_selection

For an unweighted 2×2 table of non-negative integer counts, Fisher's exact test computes the two-sided Fisher–Irwin fixed-margin p-value by summing table probabilities no greater than the observed table's probability.

Interpretation: Use it when an exact fixed-margin 2×2 test matches the design and sparse expected counts make an asymptotic approximation questionable.

Limitations: Unavailable for fractional weighted cells, larger tables, or supports above 100,000 feasible fixed-margin tables. It does not solve confounding, dependence, or sampling-design problems.

Primary page: https://www.crosstabs.com/fishers-exact-test
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation
Evidence: https://www.crosstabs.com/validation/statistical-reference-cases.json

## Cramér's V

Stable ID: cramers-v
Locale: en
Topic cluster: association_measure

Cramér's V measures the strength of association between two categorical variables on a 0-to-1 scale derived from Pearson's chi-square statistic.

Formula: V = sqrt(χ² / (n × (min(rows, columns) − 1))).

Interpretation: Larger values indicate stronger association; contextual and degrees-of-freedom-aware interpretation is preferable to universal cutoffs.

Limitations: It does not provide direction or identify the cells driving the association. Weighted results inherit the table's weight-design caveats.

Primary page: https://www.crosstabs.com/cramers-v-calculator
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## Phi coefficient

Stable ID: phi-coefficient
Locale: en
Topic cluster: association_measure

Phi is a signed measure of association for a 2×2 table; its magnitude equals Cramér's V for that table.

Formula: φ = (ad − bc) / sqrt((a+b)(c+d)(a+c)(b+d)).

Interpretation: The sign depends on row and column ordering; the absolute value expresses strength.

Limitations: Signed phi is a 2×2 measure and should not be confused with generalized sqrt(χ²/n) for larger tables.

Primary page: https://www.crosstabs.com/phi-coefficient-calculator
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## Pearson's contingency coefficient

Stable ID: pearson-contingency-coefficient
Locale: en
Topic cluster: association_measure

Pearson's contingency coefficient is a chi-square-derived association measure whose attainable maximum depends on table size.

Formula: C = sqrt(χ² / (χ² + n)).

Limitations: Values from differently sized tables are not directly comparable because the maximum is below 1 and depends on shape.

Primary page: https://www.crosstabs.com/contingency-coefficient-calculator
Evidence: https://www.crosstabs.com/methods

## Odds ratio

Stable ID: odds-ratio
Locale: en
Topic cluster: association_measure

The odds ratio compares the odds of an outcome between two groups in a 2×2 table.

Formula: OR = (a × d) / (b × c) for [[a,b],[c,d]].

Interpretation: OR = 1 means equal odds; values above or below 1 indicate higher or lower odds under the chosen orientation.

Limitations: The displayed 95% interval is the large-sample Woolf log interval, not exact. A zero cell produces an uninformative [0, infinity] interval because no continuity correction is added. An odds ratio is not a risk ratio except as an approximation for rare outcomes.

Primary page: https://www.crosstabs.com/odds-ratio-calculator
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/odds-ratio-vs-risk-ratio

## G-test (likelihood-ratio chi-square)

Stable ID: g-test
Locale: en
Topic cluster: test_selection

The G-test is a likelihood-ratio alternative to Pearson's chi-square statistic for a contingency table.

Formula: G = 2 × Σ O × ln(O / E); df = (rows − 1) × (columns − 1).

Limitations: Its p-value uses the same asymptotic chi-square reference distribution, so switching statistics does not solve sparse-cell concerns.

Primary page: https://www.crosstabs.com/g-test-calculator
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## Goodman and Kruskal's lambda

Stable ID: lambda
Locale: en
Topic cluster: association_measure

Lambda is a proportional-reduction-in-error measure: it asks how much knowing one categorical variable reduces errors when predicting the other.

Interpretation: It ranges from 0 for no error reduction to 1 for complete error reduction.

Limitations: A value of zero can occur even when variables are associated if knowledge does not change the modal prediction.

Primary page: https://www.crosstabs.com/goodman-kruskal-lambda-calculator
Evidence: https://www.crosstabs.com/methods

## Goodman and Kruskal's gamma

Stable ID: gamma
Locale: en
Topic cluster: association_measure

Gamma measures ordinal association from concordant and discordant pairs while ignoring ties.

Formula: γ = (C − D) / (C + D).

Limitations: Ignoring ties can make the magnitude appear stronger when ties are common.

Primary page: https://www.crosstabs.com/goodman-kruskal-gamma-calculator
Evidence: https://www.crosstabs.com/methods

## Kendall's tau-b and tau-c

Stable ID: kendall-tau
Locale: en
Topic cluster: association_measure

Kendall's tau-b measures ordinal association with tie correction and is suited to square tables; tau-c adjusts the scale for rectangular tables.

Formula: tau-c = 2m(C − D) / (n²(m − 1)), where m = min(rows, columns).

Limitations: Category order must be substantively meaningful and specified correctly.

Primary page: https://www.crosstabs.com/kendalls-tau-calculator
Evidence: https://www.crosstabs.com/methods

## Somers' d

Stable ID: somers-d
Locale: en
Topic cluster: association_measure

Somers' d is an asymmetric ordinal association measure that treats one variable as the outcome and accounts for ties on the chosen side.

Interpretation: Choose the direction that matches the research question; reversing outcome and predictor can change the result.

Limitations: It is inappropriate when no defensible dependent-variable direction exists.

Primary page: https://www.crosstabs.com/somers-d-calculator
Evidence: https://www.crosstabs.com/methods

## Theil's U (uncertainty coefficient)

Stable ID: theils-u
Locale: en
Topic cluster: association_measure

Theil's U is an entropy-based, directional measure of how much knowing one variable reduces uncertainty about another.

Interpretation: It ranges from 0 for no uncertainty reduction to 1 when the predictor fully determines the outcome.

Limitations: Direction matters, and sparse category estimates may be unstable.

Primary page: https://www.crosstabs.com/uncertainty-coefficient-calculator
Evidence: https://www.crosstabs.com/methods

## Adjusted standardized residual

Stable ID: adjusted-residuals
Locale: en
Topic cluster: association_measure

An adjusted residual standardizes a cell's observed-minus-expected difference to show which cells contribute most to a table-level association.

Interpretation: An absolute value above 1.96 receives a nominal two-sided 0.05 flag in the workspace.

Limitations: Cellwise flags are nominal and are not adjusted for multiple comparisons.

Primary page: https://www.crosstabs.com/crosstab-guide
Evidence: https://www.crosstabs.com/methods

## McNemar's test for paired binary change

Stable ID: mcnemar-paired-change
Locale: en
Topic cluster: test_selection

McNemar's test evaluates marginal change in paired binary outcomes by comparing the two discordant directions in a paired 2×2 table; concordant pairs do not enter the statistic.

Formula: Uncorrected χ² = (b − c)² / (b + c), df = 1; continuity-corrected χ² = max(|b − c| − 1, 0)² / (b + c); the exact two-sided result uses Binomial(b + c, 0.5).

Interpretation: A small p-value indicates asymmetric movement between the two categories, not the magnitude or cause of that movement.

Limitations: Observations must be paired, binary, and independent across subjects or matched pairs. The public calculator requires non-negative integer counts and does not accept percentages or survey weights. Exact binomial tails are computed for at most 10,000 discordant pairs; larger inputs are explicitly labeled as a continuity-corrected normal approximation. A significant result does not by itself establish a causal intervention effect.

Primary page: https://www.crosstabs.com/mcnemar-test-calculator
Evidence: https://www.crosstabs.com/which-statistical-test
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## How to choose a categorical statistical test

Stable ID: statistical-test-selection
Locale: en
Topic cluster: test_selection

Choose from the design first: independent nominal groups usually imply chi-square or an exact alternative; paired binary data imply McNemar; agreement implies kappa; ordered categories imply an ordinal association measure.

Limitations: No decision tree can repair dependence, confounding, invalid sampling, or a mismatch between the table and the estimand.

Primary page: https://www.crosstabs.com/which-statistical-test
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## Sparse expected cells

Stable ID: sparse-cells
Locale: en
Topic cluster: test_selection

Sparse expected counts make chi-square reference approximations less reliable; inspect the pattern, consider defensible category consolidation, or use a design-appropriate exact or Monte Carlo method.

Limitations: Do not merge categories solely to obtain significance. Fisher's exact test on this site is limited to eligible 2×2 integer-frequency tables.

Primary page: https://www.crosstabs.com/chi-square-expected-count-less-than-5
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## Survey weighting and raking for crosstabs

Stable ID: survey-weights
Locale: en
Topic cluster: survey_workflow

A weighted crosstab multiplies each eligible respondent by a positive finite weight before calculating counts and percentages, while retaining the unweighted base for diagnostics; raking creates calibration weights by iteratively matching trusted population margins.

Limitations: The quick workspace rejects an untyped numeric weight instead of assuming frequency semantics. Saved tab-book projects can assign a supported Taylor-linearized or replicate-weight survey design, with explicit strata, PSU, FPC, lonely-PSU, confidence, and replicate policies plus Rao–Scott or adjusted-Wald association; unsupported or invalid designs fail closed, and independent statistical review remains pending.

Primary page: https://www.crosstabs.com/survey-weighting-raking
Evidence: https://www.crosstabs.com/survey-crosstab-tool
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/capacity
Evidence: https://www.crosstabs.com/local-mode

## Multi-select crosstabs

Stable ID: multi-select
Locale: en
Topic cluster: survey_workflow

A select-all-that-apply question should become auditable option-level binary outcomes and be crossed with an independent grouping variable; report percent of cases to show each option's incidence among included respondents rather than treating combined answer strings as exclusive categories.

Interpretation: Percent-of-cases rows can sum above 100% because one respondent may select multiple options; percent of responses uses a different denominator and answers a different question.

Limitations: An omnibus Pearson chi-square across overlapping option rows is invalid; option-level binary comparisons answer a narrower question. Bonferroni correction covers banner-column pairs within each option but not the complete family across options, tables, or exploratory cuts. All-blank skipped sets are excluded while explicit all-zero answered cases remain in the respondent base. An approved survey design uses respondent-case item estimates and separate selected/not-selected Rao–Scott tests with adjusted-Wald alternatives; response-denominator percentages remain descriptive, and independent statistical review remains pending.

Primary page: https://www.crosstabs.com/multi-select-crosstab
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/local-mode
Evidence: https://www.crosstabs.com/crosstab-significance-letters

## Crosstab significance letters

Stable ID: significance-letters
Locale: en
Topic cluster: survey_workflow

Column significance letters encode pairwise column-proportion tests by labeling a cell with the columns it differs from under the configured threshold and correction policy.

Limitations: Small bases and multiple comparisons can produce misleading flags. Untyped weighting cannot produce ordinary significance letters.

Primary page: https://www.crosstabs.com/crosstab-significance-letters
Evidence: https://www.crosstabs.com/methods

## Tracker wave schema drift

Stable ID: tracker-schema-drift
Locale: en
Topic cluster: tracker_workflow

Treat each imported tracker wave as immutable: fingerprint both schemas, match stable identifiers before labels, classify structural and semantic drift, preview and approve explicit transforms, apply them to a copy, validate bases and distributions, and retain the source, audit record, and guarded inverse before comparing waves.

Interpretation: A successful structural repair does not prove longitudinal comparability; question wording, universe, routing, recall period, concept, and representation must still remain defensibly comparable.

Limitations: Automatic suggestions and label similarity are not evidence of semantic equivalence. Exact reversal is refused after later project changes because restoring the old snapshot would erase subsequent work. The current Workspace UI exposes compatible-wave import, rename mapping, retained waves, and comparison, but not the engine's full approval and reversal interface.

Primary page: https://www.crosstabs.com/tracker-schema-drift
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/local-mode
Evidence: https://www.crosstabs.com/capacity
Evidence: https://www.crosstabs.com/survey-tab-book

## Tab-book project model

Stable ID: tab-book-project
Locale: en
Topic cluster: survey_workflow

A tab-book project keeps row sets, multibanners, filters, weights, tests, table order, waves, coding variables, findings, and the export recipe in one versioned graph rather than as unrelated outputs.

Limitations: A definition-only manifest intentionally omits respondent rows and cannot restore a working analysis.

Primary page: https://www.crosstabs.com/survey-tab-book
Evidence: https://www.crosstabs.com/local-mode
Evidence: https://www.crosstabs.com/data-processing

## Auditable open-end coding

Stable ID: open-end-coding
Locale: en
Topic cluster: ai_governance

Crosstabs provides a browser-local manual workflow for open ends: define or reuse themes, assign responses, attest that review is complete, approve the coding, apply it as project variables, and retain decision history with a guarded undo path.

Limitations: The workflow does not send responses to a model or discover themes automatically. A researcher remains responsible for theme definitions, assignment coverage, approval, interpretation, and any sensitive-content handling. Supplying responses to a separate AI assistant is governed by that assistant's data policy, not the Crosstabs local boundary.

Primary page: https://www.crosstabs.com/open-end-coding
Evidence: https://www.crosstabs.com/privacy
Evidence: https://www.crosstabs.com/data-processing
Evidence: https://www.crosstabs.com/local-mode

## Outcome metrics and key-driver modeling

Stable ID: outcome-modeling
Locale: en
Topic cluster: survey_workflow

The outcome studio fits a regularized logistic model to an explicitly selected binary outcome and drivers, then reports deterministic holdout AUC, accuracy, Brier score, calibration, observed segments, and reviewable actions.

Limitations: Association and prediction do not establish causality. At least 60 complete rows, 25 successes, and 25 other outcomes are required. Synthetic scenarios are labeled modeled estimates rather than observed evidence.

Primary page: https://www.crosstabs.com/key-driver-analysis
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/capacity

## Editable report refresh

Stable ID: editable-report-refresh
Locale: en
Topic cluster: reporting

A compatible Crosstabs PPTX or DOCX can refresh current generated values without replacing the whole edited package: stable anchors identify selected tables, metadata, statistics text, and PowerPoint charts; supported equal-shape content is patched in place while manual regions, unselected objects, and unrelated package parts remain under analyst control.

Interpretation: Preservation is regional, not universal: the existing Office package remains the target, and the refresh audit distinguishes updated anchors, preserved anchors, blocking reasons, and package entries that were not rewritten.

Limitations: Selected generated table text is replaced by current approved Crosstabs values; selected PowerPoint chart series and its embedded workbook are also replaced. Equal-shape table formatting and geometry are supported, but arbitrary structural edits inside generated objects are not. A missing or duplicate stable anchor, changed table shape, incompatible chart, corrupt package, or unanchored third-party file fails atomically before a modified file is returned. The current Workspace Export menu refreshes the open tab-current table; it does not expose arbitrary multi-table selection or automatic schema-changing reflow.

Primary page: https://www.crosstabs.com/editable-pptx-docx-refresh
Evidence: https://www.crosstabs.com/workspace
Evidence: https://www.crosstabs.com/local-mode
Evidence: https://www.crosstabs.com/data-processing
Evidence: https://www.crosstabs.com/methods/validation
Evidence: https://www.crosstabs.com/survey-tab-book

## Local browser analysis

Stable ID: local-mode
Locale: en
Topic cluster: trust

Import, table computation, filters, weights, tests, project state, review, open-end coding, and export run in the browser. Crosstabs does not upload respondent data or operate a hosted project or model service.

Limitations: Browser memory, storage quotas, device performance, and file width can constrain work before row count alone does. A full project package contains rows and is not encrypted.

Primary page: https://www.crosstabs.com/local-mode
Evidence: https://www.crosstabs.com/privacy
Evidence: https://www.crosstabs.com/data-processing
Evidence: https://www.crosstabs.com/capacity

## Multidimensional workload envelope

Stable ID: workload-envelope
Locale: en
Topic cluster: trust

Crosstabs publishes tested workload envelopes across rows, file representation, category shape, output cells, memory, filters, weights, statistical tests, cancellation, and browser execution mode instead of claiming unlimited rows.

Limitations: Published fixtures are evidence for tested dimensions and environments, not a universal device guarantee.

Primary page: https://www.crosstabs.com/capacity
Evidence: https://www.crosstabs.com/capacity
Evidence: https://www.crosstabs.com/methods/validation

## Evidence-linked AI analysis

Stable ID: ai-evidence-governance
Locale: en
Topic cluster: ai_governance

Crosstabs does not run a hosted model. An external agent can use the five-tool public MCP for bounded aggregate calculations and fixed evidence, or the local MCP for device-local private projects. Crosstabs binds results to deterministic evidence and fails closed on invalid inputs; project changes use typed operations, current revisions, local audit history, and guarded undo rather than treating generated prose as authority.

Interpretation: Provider routing and model agreement can improve availability or offer another opinion, but neither validates statistical claims nor grants authority to change a research project.

Limitations: The five-tool public MCP accepts only explicit aggregate frequency matrices and fixed evidence; it has no project storage, respondent rows, identity, prompt, or generated-output custody. Private projects belong in the browser or local MCP, and any file supplied to an external assistant remains subject to that assistant's data boundary. Exact undo is refused after later project changes because restoring the earlier snapshot would overwrite subsequent work. Model providers can still make errors, and independent statistical review and third-party certification evidence remain pending where explicitly disclosed.

Primary page: https://www.crosstabs.com/ai-analysis-governance
Evidence: https://www.crosstabs.com/security
Evidence: https://www.crosstabs.com/privacy
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/open-end-coding
Evidence: https://www.crosstabs.com/survey-tab-book

## Crosstabs Codex plugin and MCP server

Stable ID: codex-plugin
Locale: en
Topic cluster: ai_governance

The published crosstabs 1.4.0 package passed fresh public installation checks: 39 statistical tools plus runtime status on the statistical server, and 35 local project tools including portable Plan → Validate → Run → Review workflows and explicit guided weighting preview/apply. Immutable PyPI artifacts, exact source provenance and the MCP Registry record were verified. The 1.3.0 and 1.2.2 evidence remains historical. Plugin source installation, native-host review and directory approval are separate states; see the exact source binding on the MCP page.

Interpretation: Use the local plugin for confidential end-to-end research projects. Use the remote MCP endpoint for public methodology and deterministic calculations over explicitly supplied aggregate matrices, never respondent rows.

Limitations: The browser worker and local MCP enter the same HeadlessCrosstabsService and share TabBookProject, initial-analysis, deterministic calculation, project revision, audit, replay, and undo orchestration. Browser interaction and local MCP transport remain separate release-tested surfaces. Package publication and source installation do not establish native-host widget review, directory submission, approval or listing. The local plugin does not reproduce browser interaction state or browser-local manual open-end coding. The live remote connector intentionally exposes only public evidence and explicitly supplied aggregate calculations; it has no project or respondent-row custody. Any file supplied to an AI assistant remains subject to that assistant's data boundary and the user's configuration.

Primary page: https://www.crosstabs.com/mcp
Evidence: https://www.crosstabs.com/mcp
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation
Evidence: https://www.crosstabs.com/local-mode
Evidence: https://www.crosstabs.com/privacy

## 卡方独立性检验

Stable ID: zh-chi-square
Locale: zh-CN
Topic cluster: test_selection

卡方独立性检验先按行列边际计算独立假设下的期望频数，再用 χ² = Σ(O − E)² / E 汇总观察值与期望值的差异，用于判断两个相互独立观测的分类变量是否存在统计关联。

Formula: χ² = Σ (O − E)² / E；E = 行合计 × 列合计 / 总样本量。

Interpretation: 较小的 P 值反对独立性原假设；还应报告 Cramér's V、样本基数、期望频数诊断、关键单元格和研究设计，不能把统计关联解释为因果。

Limitations: P 值使用渐近卡方分布；最小期望频数小于 1 或超过 20% 的期望频数小于 5 时，近似可能较差。 观察应相互独立；同一对象前后两次的配对二分类表应使用 McNemar 等配对方法。 输入应是互斥类别的观察频数，百分比不能替代检验所需的样本基数。 本网站的 Fisher 精确结果只覆盖合格的非加权 2×2 非负整数频数表和有界工作量。 设计或校准权重、分层和整群抽样需要设计型方差与 Rao–Scott 等方法。 调整标准化残差是诊断量；跨多个单元格、列对、问题或表格的推断仍需定义检验族并处理多重比较。

Primary page: https://www.crosstabs.com/zh-cn/chi-square-calculator
Evidence: https://www.crosstabs.com/chi-square-calculator
Evidence: https://www.crosstabs.com/zh-cn/which-statistical-test
Evidence: https://www.crosstabs.com/zh-cn/chi-square-expected-count-less-than-5
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## Crosstabs Codex 插件与 MCP 统计服务器

Stable ID: zh-codex-plugin
Locale: zh-CN
Topic cluster: ai_governance

已发布的 crosstabs 1.4.0 通过了公开索引全新安装验证：统计服务器提供 39 个统计工具及运行时状态，项目服务器提供 35 个本地工具，包括可移植的计划 → 验证 → 运行 → 审阅流程和经明确批准的引导式加权预览及应用。PyPI 不可变发布文件、准确源码来源和 MCP Registry 记录均已验证；1.3.0 和 1.2.2 的证据保留为历史记录。插件源码安装、原生宿主审查和目录批准属于不同状态；准确的源码绑定见 MCP 页面。

Interpretation: 机密的端到端研究项目使用本地插件；远程 MCP 只用于公开方法证据和明确提供的汇总矩阵，不接收受访者行。

Limitations: 浏览器 Worker 与本地 MCP 进入同一个 HeadlessCrosstabsService，并共享 TabBookProject、初始分析、确定性计算、项目修订、审计、重放与撤销编排。浏览器交互与本地 MCP 传输仍是分别测试的发布界面。 包发布和源码安装不代表原生宿主组件审查、目录提交、批准或上架。 本地插件不复制浏览器交互状态，也不提供浏览器本地的开放题人工编码。 线上远程连接器只公开方法证据和明确提供的汇总计算，不托管项目或受访者行。 提供给 AI 助手的任何文件仍受该助手的数据边界与用户配置约束。

Primary page: https://www.crosstabs.com/zh-cn/mcp
Evidence: https://www.crosstabs.com/zh-cn/mcp
Evidence: https://www.crosstabs.com/mcp
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation
Evidence: https://www.crosstabs.com/local-mode
Evidence: https://www.crosstabs.com/privacy

## McNemar 配对二分类变化检验

Stable ID: zh-mcnemar-paired-change
Locale: zh-CN
Topic cluster: test_selection

McNemar 检验通过比较配对 2×2 表中两个不一致方向 b 与 c，判断同一对象前后或一一匹配对象的二分类边际比例是否发生不对称变化；一致配对 a 与 d 不进入统计量。

Formula: 未校正 χ² = (b − c)² / (b + c)，df = 1；连续性校正 χ² = max(|b − c| − 1, 0)² / (b + c)；精确双侧结果使用 Binomial(b + c, 0.5)。

Interpretation: 较小的 P 值表示两个变化方向不对称，不表示变化幅度，也不会单独证明变化由干预造成。

Limitations: 对象或匹配对之间应相互独立，且每次结果只有两个互斥类别。 公开计算器只接受非负整数频数，不接受百分比、小数或调查权重。 不一致配对不超过 10,000 对时计算精确二项尾概率；更大输入明确标为连续性校正正态近似。 复杂抽样、失访、混杂和多时点重复测量需要适合完整设计的方法。

Primary page: https://www.crosstabs.com/zh-cn/mcnemar-test-calculator
Evidence: https://www.crosstabs.com/mcnemar-test-calculator
Evidence: https://www.crosstabs.com/zh-cn/which-statistical-test
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## 分类数据统计检验选择

Stable ID: zh-statistical-test-selection
Locale: zh-CN
Topic cluster: test_selection

分类数据检验应从研究设计开始：独立分类变量通常使用 Pearson 卡方或适合的精确方法；合格的稀疏 2×2 整数频数表可用 Fisher；配对二分类结果使用 McNemar；对同一对象的分类一致性使用 Cohen's kappa；有序变量还应报告保留顺序信息的关联指标。

Limitations: P 值和关联不能单独证明因果。 普通交叉表方法不适合连续结局、复杂抽样、聚类或未建模的重复测量结构。 本网站的 Fisher 精确检验只覆盖合格的非加权 2×2 非负整数频数表。

Primary page: https://www.crosstabs.com/zh-cn/which-statistical-test
Evidence: https://www.crosstabs.com/which-statistical-test
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation
Evidence: https://www.crosstabs.com/mcnemar-test-calculator
Evidence: https://www.crosstabs.com/cohens-kappa-calculator

## 期望频数小于 5

Stable ID: zh-sparse-cells
Locale: zh-CN
Topic cluster: test_selection

期望频数过小会削弱卡方渐近近似；应先检查稀疏分布，再考虑有理论依据的类别合并、2×2 Fisher 精确检验或适合设计的精确/蒙特卡洛方法。

Limitations: 不要只为获得显著结果而合并类别。 本网站的 Fisher 精确检验仅适用于合格的 2×2 非加权整数频数表。

Primary page: https://www.crosstabs.com/zh-cn/chi-square-expected-count-less-than-5
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## 调查加权与 Raking（迭代比例拟合）

Stable ID: zh-survey-weights
Locale: zh-CN
Topic cluster: survey_workflow

加权交叉表让每位合格受访者按正数有限权重贡献到单元格；应使用加权百分比表达估计，同时保留未加权样本基数用于样本量和数据质量诊断。Raking 通过迭代调整权重，使指定加权边际接近可信总体目标。

Formula: 加权单元格 = Σ wᵢI(rowᵢ = r, columnᵢ = c)；权重离散诊断 n_eff = (Σwᵢ)² / Σwᵢ²。

Limitations: 快速工作区会拒绝未声明语义的数值权重，不会把它默认为频数权重。 已保存项目可执行受支持的 Taylor 线性化或重复权重设计，并报告分层、PSU、FPC、设计自由度以及 Rao–Scott 或调整 Wald 关联；无效或不受支持的设计会关闭失败。

Primary page: https://www.crosstabs.com/zh-cn/survey-weighting-raking
Evidence: https://www.crosstabs.com/survey-weighting-raking
Evidence: https://www.crosstabs.com/survey-crosstab-tool
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/capacity

## Cramér's V 效应量

Stable ID: zh-cramers-v
Locale: zh-CN
Topic cluster: association_measure

Cramér's V 将卡方统计量转换为 0 到 1 的分类变量关联强度指标。

Formula: V = sqrt(χ² / (n × (min(行数, 列数) − 1)))。

Limitations: 它不表示方向，也不说明哪些单元格推动了关联。

Primary page: https://www.crosstabs.com/zh-cn/cramers-v-calculator
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/methods/validation

## 多选题（可多选）交叉分析

Stable ID: zh-multi-select
Locale: zh-CN
Topic cluster: survey_workflow

“选择所有适用项”应定义或整理为选项级二分类结果，再与独立分组变量交叉；通常报告基于个案的百分比，表示每个 Banner 组中选择该选项的受访者比例，而不是把答案组合当成互斥类别。

Interpretation: 同一受访者可选择多个选项，所以基于个案的各行百分比总和可以超过 100%；基于响应的百分比使用全部选择次数作为不同分母。

Limitations: 不能对相互重叠的所有选项行运行一个普通总体 Pearson 卡方检验。 每个选项内部的 Banner 列对使用 Bonferroni 校正，但不会跨所有选项、表格或探索性切分控制完整推断族。 所有选项均为空的跳题记录默认排除；明确作答且全为 0 的个案仍保留在受访者基数。 设计或校准权重下的普通列比例检验只能视为近似结果。

Primary page: https://www.crosstabs.com/zh-cn/multi-select-crosstab
Evidence: https://www.crosstabs.com/multi-select-crosstab
Evidence: https://www.crosstabs.com/crosstab-significance-letters
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/local-mode

## 交叉表显著性字母（A、B、C）

Stable ID: zh-significance-letters
Locale: zh-CN
Topic cluster: survey_workflow

交叉表中的显著性字母表示同一结果行内的成对列比例检验：每个 Banner 列先分配一个字母，某单元格中的字母标出该单元格所在列的比例显著高于哪些列。

Interpretation: 例如 A 列单元格显示“42% B”，表示 A 列的 42% 在设定阈值和多重比较校正下显著高于 B 列同一行的比例；字母不表示差异大小、总体关联强度或因果关系。

Limitations: Crosstabs 对每行内所有合格 Banner 列对使用合并方差双比例 z 检验和 Bonferroni 校正；校正范围不跨其他行、表格或探索性切分。 检验列合计小于 30 的列不参与字母检验；普通表超过 12 个 Banner 列或 250 个行类别时不生成字母；没有字母不等于两列相同。 所选权重时不生成普通列比例字母；受支持的已保存调查设计也不会回退到普通加权列比例检验。 显著性字母应与百分比、未加权基数、置信阈值、效应量和研究设计一起报告。

Primary page: https://www.crosstabs.com/zh-cn/crosstab-significance-letters
Evidence: https://www.crosstabs.com/crosstab-significance-letters
Evidence: https://www.crosstabs.com/zh-cn/multi-select-crosstab
Evidence: https://www.crosstabs.com/zh-cn/survey-weighting-raking
Evidence: https://www.crosstabs.com/methods

## 调查追踪项目的波次结构漂移

Stable ID: zh-tracker-schema-drift
Locale: zh-CN
Topic cluster: tracker_workflow

把每个导入波次视为不可变源数据：比较结构指纹，优先使用稳定内部 ID，分类记录结构与语义漂移，预览并审批明确转换，只在副本上执行，验证基数与分布，并保留来源、审计记录和受保护的逆操作后再比较波次。

Interpretation: 结构修复成功不等于纵向可比；题目措辞、目标总体、跳转逻辑、回忆期、概念和表示方式仍须由研究人员确认。

Limitations: 自动建议和标签相似不能证明语义等价。 项目在修复后已改变时必须拒绝精确回退，以免覆盖后续工作。 当前工作区支持兼容波次导入、改名映射、保留旧波次与比较，但尚未提供底层引擎完整的审批与回退界面。

Primary page: https://www.crosstabs.com/zh-cn/tracker-schema-drift
Evidence: https://www.crosstabs.com/tracker-schema-drift
Evidence: https://www.crosstabs.com/methods
Evidence: https://www.crosstabs.com/local-mode
Evidence: https://www.crosstabs.com/capacity
Evidence: https://www.crosstabs.com/survey-tab-book

## 交叉表 AI 分析治理

Stable ID: zh-ai-evidence-governance
Locale: zh-CN
Topic cluster: ai_governance

Crosstabs 不运行托管模型。外部智能体可通过五个工具的公开 MCP 使用有界汇总计算与固定证据，或通过本地 MCP 处理只保存在设备上的私有项目。Crosstabs 把结果绑定到确定性证据，并在输入无效时默认拒绝；项目变更使用类型化操作、当前修订、本地审计记录与受保护撤销，而不把模型文字当成授权。

Interpretation: 多模型路由或模型间一致只能改善可用性或提供另一种意见，不能验证统计结论，也不能授予模型修改研究项目的权限。

Limitations: 五个工具的公开 MCP 只接受明确的汇总频数矩阵与固定证据，不托管项目、受访者行、身份、提示词或生成结果。 私有项目应留在浏览器或本地 MCP；交给外部智能体的任何文件仍受该智能体的数据边界约束。 项目后来发生变化时会拒绝精确回退，以免覆盖后续工作。 模型仍可能出错；页面明确披露的独立统计审查与第三方认证证据仍处于待完成状态。

Primary page: https://www.crosstabs.com/zh-cn/ai-analysis-governance
Evidence: https://www.crosstabs.com/ai-analysis-governance
Evidence: https://www.crosstabs.com/security
Evidence: https://www.crosstabs.com/privacy
Evidence: https://www.crosstabs.com/open-end-coding
Evidence: https://www.crosstabs.com/survey-tab-book

## 可编辑 PPTX 与 DOCX 选择性刷新

Stable ID: zh-editable-report-refresh
Locale: zh-CN
Topic cluster: reporting

兼容的 Crosstabs PPTX 或 DOCX 可以通过稳定锚点识别选中表格、元数据、统计文字和 PowerPoint 图表，只在支持的等形生成区域内更新当前值，同时保留人工区域、未选中对象和无关 Office 包部件。

Interpretation: 保留是按区域定义的，而不是任意往返编辑承诺；现有 Office 文件保持为目标，刷新审计分别记录已更新锚点、已保留锚点、阻止原因与未重写部件。

Limitations: 选中生成表格内的文字会替换为当前获批 Crosstabs 值；选中 PowerPoint 图表的序列和嵌入工作簿也会替换。 仅支持等形表格的格式与几何保留，不支持生成对象内任意结构修改。 锚点缺失或重复、表格形状变化、图表不兼容、文件损坏或第三方文件没有锚点时会原子失败，不会返回部分修改的文件。 当前 Workspace Export 菜单刷新打开的 tab-current 表格，尚未提供任意多表选择或结构变化后的自动重排。

Primary page: https://www.crosstabs.com/zh-cn/editable-pptx-docx-refresh
Evidence: https://www.crosstabs.com/editable-pptx-docx-refresh
Evidence: https://www.crosstabs.com/workspace
Evidence: https://www.crosstabs.com/local-mode
Evidence: https://www.crosstabs.com/data-processing
Evidence: https://www.crosstabs.com/methods/validation
Evidence: https://www.crosstabs.com/survey-tab-book