{"schema":"https://www.crosstabs.com/schemas/evidence-graph.v1.json","version":"2026-08-13","generatedFrom":"https://www.crosstabs.com/evidence","reviewStatus":"named_independent_statistical_review_pending","nodes":[{"id":"cross-tabulation","term":"Cross-tabulation (crosstab / contingency table)","path":"/cross-tabulation-calculator","cluster":"survey_workflow","locale":"en","answer":"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."],"evidencePaths":["/methods","/methods/validation"],"url":"https://www.crosstabs.com/cross-tabulation-calculator","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/methods/validation"]},{"id":"chi-square-independence","term":"Chi-square test of independence","path":"/chi-square-calculator","cluster":"test_selection","locale":"en","answer":"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.","Survey weights require design-aware methods unless they are genuine frequency weights."],"evidencePaths":["/methods","/methods/validation","/validation/statistical-reference-cases.json"],"url":"https://www.crosstabs.com/chi-square-calculator","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/methods/validation","https://www.crosstabs.com/validation/statistical-reference-cases.json"]},{"id":"fisher-exact","term":"Fisher's exact test","path":"/fishers-exact-test","cluster":"test_selection","locale":"en","answer":"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."],"evidencePaths":["/methods","/methods/validation","/research/chi-square-vs-fisher"],"url":"https://www.crosstabs.com/fishers-exact-test","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/methods/validation","https://www.crosstabs.com/research/chi-square-vs-fisher"]},{"id":"cramers-v","term":"Cramér's V","path":"/cramers-v-calculator","cluster":"association_measure","locale":"en","answer":"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."],"evidencePaths":["/methods","/methods/validation"],"url":"https://www.crosstabs.com/cramers-v-calculator","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/methods/validation"]},{"id":"phi-coefficient","term":"Phi coefficient","path":"/phi-coefficient-calculator","cluster":"association_measure","locale":"en","answer":"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."],"evidencePaths":["/methods","/methods/validation"],"url":"https://www.crosstabs.com/phi-coefficient-calculator","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/methods/validation"]},{"id":"pearson-contingency-coefficient","term":"Pearson's contingency coefficient","path":"/contingency-coefficient-calculator","cluster":"association_measure","locale":"en","answer":"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."],"evidencePaths":["/methods"],"url":"https://www.crosstabs.com/contingency-coefficient-calculator","evidenceUrls":["https://www.crosstabs.com/methods"]},{"id":"odds-ratio","term":"Odds ratio","path":"/odds-ratio-calculator","cluster":"association_measure","locale":"en","answer":"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."],"evidencePaths":["/methods","/odds-ratio-vs-risk-ratio"],"url":"https://www.crosstabs.com/odds-ratio-calculator","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/odds-ratio-vs-risk-ratio"]},{"id":"g-test","term":"G-test (likelihood-ratio chi-square)","path":"/g-test-calculator","cluster":"test_selection","locale":"en","answer":"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."],"evidencePaths":["/methods","/methods/validation"],"url":"https://www.crosstabs.com/g-test-calculator","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/methods/validation"]},{"id":"lambda","term":"Goodman and Kruskal's lambda","path":"/goodman-kruskal-lambda-calculator","cluster":"association_measure","locale":"en","answer":"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."],"evidencePaths":["/methods"],"url":"https://www.crosstabs.com/goodman-kruskal-lambda-calculator","evidenceUrls":["https://www.crosstabs.com/methods"]},{"id":"gamma","term":"Goodman and Kruskal's gamma","path":"/goodman-kruskal-gamma-calculator","cluster":"association_measure","locale":"en","answer":"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."],"evidencePaths":["/methods"],"url":"https://www.crosstabs.com/goodman-kruskal-gamma-calculator","evidenceUrls":["https://www.crosstabs.com/methods"]},{"id":"kendall-tau","term":"Kendall's tau-b and tau-c","path":"/kendalls-tau-calculator","cluster":"association_measure","locale":"en","answer":"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."],"evidencePaths":["/methods"],"url":"https://www.crosstabs.com/kendalls-tau-calculator","evidenceUrls":["https://www.crosstabs.com/methods"]},{"id":"somers-d","term":"Somers' d","path":"/somers-d-calculator","cluster":"association_measure","locale":"en","answer":"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."],"evidencePaths":["/methods"],"url":"https://www.crosstabs.com/somers-d-calculator","evidenceUrls":["https://www.crosstabs.com/methods"]},{"id":"theils-u","term":"Theil's U (uncertainty coefficient)","path":"/uncertainty-coefficient-calculator","cluster":"association_measure","locale":"en","answer":"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."],"evidencePaths":["/methods"],"url":"https://www.crosstabs.com/uncertainty-coefficient-calculator","evidenceUrls":["https://www.crosstabs.com/methods"]},{"id":"adjusted-residuals","term":"Adjusted standardized residual","path":"/crosstab-guide","cluster":"association_measure","locale":"en","answer":"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."],"evidencePaths":["/methods"],"url":"https://www.crosstabs.com/crosstab-guide","evidenceUrls":["https://www.crosstabs.com/methods"]},{"id":"mcnemar-paired-change","term":"McNemar's test for paired binary change","path":"/mcnemar-test-calculator","cluster":"test_selection","locale":"en","answer":"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."],"evidencePaths":["/which-statistical-test","/methods","/methods/validation"],"url":"https://www.crosstabs.com/mcnemar-test-calculator","evidenceUrls":["https://www.crosstabs.com/which-statistical-test","https://www.crosstabs.com/methods","https://www.crosstabs.com/methods/validation"]},{"id":"statistical-test-selection","term":"How to choose a categorical statistical test","path":"/which-statistical-test","cluster":"test_selection","locale":"en","answer":"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."],"evidencePaths":["/methods","/methods/validation"],"url":"https://www.crosstabs.com/which-statistical-test","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/methods/validation"]},{"id":"sparse-cells","term":"Sparse expected cells","path":"/chi-square-expected-count-less-than-5","cluster":"test_selection","locale":"en","answer":"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."],"evidencePaths":["/methods","/research/chi-square-vs-fisher"],"url":"https://www.crosstabs.com/chi-square-expected-count-less-than-5","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/research/chi-square-vs-fisher"]},{"id":"survey-weights","term":"Survey weighting and raking for crosstabs","path":"/survey-weighting-raking","cluster":"survey_workflow","locale":"en","answer":"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":["Inferential statistics are descriptive or approximate unless weights are genuine frequency weights.","Complex survey variance, strata, clusters, finite-population corrections, replicate weights, and Rao–Scott corrections are not implemented."],"evidencePaths":["/survey-crosstab-tool","/methods","/capacity","/local-mode"],"url":"https://www.crosstabs.com/survey-weighting-raking","evidenceUrls":["https://www.crosstabs.com/survey-crosstab-tool","https://www.crosstabs.com/methods","https://www.crosstabs.com/capacity","https://www.crosstabs.com/local-mode"]},{"id":"multi-select","term":"Multi-select crosstabs","path":"/multi-select-crosstab","cluster":"survey_workflow","locale":"en","answer":"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.","Weighted tests are approximate unless weights are genuine frequency weights."],"evidencePaths":["/methods","/local-mode","/crosstab-significance-letters"],"url":"https://www.crosstabs.com/multi-select-crosstab","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/local-mode","https://www.crosstabs.com/crosstab-significance-letters"]},{"id":"significance-letters","term":"Crosstab significance letters","path":"/crosstab-significance-letters","cluster":"survey_workflow","locale":"en","answer":"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.","Weighting is treated with the disclosed frequency-weight approximation caveat."],"evidencePaths":["/methods"],"url":"https://www.crosstabs.com/crosstab-significance-letters","evidenceUrls":["https://www.crosstabs.com/methods"]},{"id":"tracker-schema-drift","term":"Tracker wave schema drift","path":"/tracker-schema-drift","cluster":"tracker_workflow","locale":"en","answer":"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."],"evidencePaths":["/methods","/local-mode","/capacity","/survey-tab-book"],"url":"https://www.crosstabs.com/tracker-schema-drift","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/local-mode","https://www.crosstabs.com/capacity","https://www.crosstabs.com/survey-tab-book"]},{"id":"tab-book-project","term":"Tab-book project model","path":"/survey-tab-book","cluster":"survey_workflow","locale":"en","answer":"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."],"evidencePaths":["/local-mode","/data-processing"],"url":"https://www.crosstabs.com/survey-tab-book","evidenceUrls":["https://www.crosstabs.com/local-mode","https://www.crosstabs.com/data-processing"]},{"id":"open-end-coding","term":"Auditable AI open-end coding","path":"/open-end-coding","cluster":"ai_governance","locale":"en","answer":"AI-created open-end themes remain proposals until a researcher reviews them; approved themes become variables with assignment evidence, decision history, and a safe undo path inside the same project graph.","limitations":["Hosted theme discovery sends only the disclosed response texts and theme definitions through Vercel AI Gateway.","Model output is not treated as ground truth and requires human approval."],"evidencePaths":["/privacy","/data-processing","/local-mode"],"url":"https://www.crosstabs.com/open-end-coding","evidenceUrls":["https://www.crosstabs.com/privacy","https://www.crosstabs.com/data-processing","https://www.crosstabs.com/local-mode"]},{"id":"outcome-modeling","term":"Outcome metrics and key-driver modeling","path":"/key-driver-analysis","cluster":"survey_workflow","locale":"en","answer":"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."],"evidencePaths":["/methods","/capacity"],"url":"https://www.crosstabs.com/key-driver-analysis","evidenceUrls":["https://www.crosstabs.com/methods","https://www.crosstabs.com/capacity"]},{"id":"editable-report-refresh","term":"Editable report refresh","path":"/editable-pptx-docx-refresh","cluster":"reporting","locale":"en","answer":"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."],"evidencePaths":["/workspace","/local-mode","/data-processing","/methods/validation","/survey-tab-book"],"url":"https://www.crosstabs.com/editable-pptx-docx-refresh","evidenceUrls":["https://www.crosstabs.com/workspace","https://www.crosstabs.com/local-mode","https://www.crosstabs.com/data-processing","https://www.crosstabs.com/methods/validation","https://www.crosstabs.com/survey-tab-book"]},{"id":"local-mode","term":"Local browser analysis","path":"/local-mode","cluster":"trust","locale":"en","answer":"Core import, table computation, filters, weights, tests, project state, review, and export run in the browser; hosted AI actions are optional, disclosed, and bounded to the relevant aggregate context or selected open text.","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."],"evidencePaths":["/privacy","/data-processing","/capacity"],"url":"https://www.crosstabs.com/local-mode","evidenceUrls":["https://www.crosstabs.com/privacy","https://www.crosstabs.com/data-processing","https://www.crosstabs.com/capacity"]},{"id":"workload-envelope","term":"Multidimensional workload envelope","path":"/capacity","cluster":"trust","locale":"en","answer":"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."],"evidencePaths":["/capacity","/methods/validation"],"url":"https://www.crosstabs.com/capacity","evidenceUrls":["https://www.crosstabs.com/capacity","https://www.crosstabs.com/methods/validation"]},{"id":"ai-evidence-governance","term":"Evidence-linked AI analysis","path":"/ai-analysis-governance","cluster":"ai_governance","locale":"en","answer":"Give the model only bounded analytical context; bind factual cell claims to stable evidence IDs; independently resolve each pointer against the computed result; fail closed on a mismatch; keep answers read-only; and express requested project mutations as typed proposals that require human approval, stale-state checks, an audit record, and guarded undo.","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 AI answer activity list is session-level and is not a durable project audit log.","The governed project agent supports a bounded typed operation set, not arbitrary recodes, filters, weights, row edits, or exports.","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."],"evidencePaths":["/security","/privacy","/methods","/open-end-coding","/survey-tab-book"],"url":"https://www.crosstabs.com/ai-analysis-governance","evidenceUrls":["https://www.crosstabs.com/security","https://www.crosstabs.com/privacy","https://www.crosstabs.com/methods","https://www.crosstabs.com/open-end-coding","https://www.crosstabs.com/survey-tab-book"]},{"id":"codex-plugin","term":"Crosstabs Codex plugin and MCP server","path":"/mcp","cluster":"ai_governance","locale":"en","answer":"The official Crosstabs Codex marketplace installs the immutable crosstabs 1.1.4 package over local stdio and exposes two servers: 39 focused statistical tools plus 23 project-workflow tools for import, tab books, weights, waves, coding, schema repair, editable reports, export, and audit history.","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. The candidate hosted lifecycle enters that service through tenant-storage and authorization adapters. Shared orchestration is verified; complete browser-interaction and production-hosting parity are separate release gates.","The local plugin does not reproduce browser interaction state, shared cloud review, comments, or optional connector authorization.","The live remote connector intentionally exposes only public evidence and aggregate calculations. The hosted 23-tool lifecycle remains gated until durable tenant storage and capability-scoped OAuth pass production verification.","Local code_open_ends is the only generative operation and requires explicit Vercel AI Gateway processing approval; any file supplied to an AI assistant also remains subject to that assistant's data boundary and the user's configuration."],"evidencePaths":["/mcp","/methods","/methods/validation","/local-mode","/privacy"],"url":"https://www.crosstabs.com/mcp","evidenceUrls":["https://www.crosstabs.com/mcp","https://www.crosstabs.com/methods","https://www.crosstabs.com/methods/validation","https://www.crosstabs.com/local-mode","https://www.crosstabs.com/privacy"]},{"id":"zh-chi-square","term":"卡方独立性检验","path":"/zh-cn/chi-square-calculator","cluster":"test_selection","locale":"zh-CN","answer":"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。"],"evidencePaths":["/chi-square-calculator","/zh-cn/which-statistical-test","/zh-cn/chi-square-expected-count-less-than-5","/methods","/methods/validation"],"url":"https://www.crosstabs.com/zh-cn/chi-square-calculator","evidenceUrls":["https://www.crosstabs.com/chi-square-calculator","https://www.crosstabs.com/zh-cn/which-statistical-test","https://www.crosstabs.com/zh-cn/chi-square-expected-count-less-than-5","https://www.crosstabs.com/methods","https://www.crosstabs.com/methods/validation"]},{"id":"zh-codex-plugin","term":"Crosstabs Codex 插件与 MCP 统计服务器","path":"/zh-cn/mcp","cluster":"ai_governance","locale":"zh-CN","answer":"官方 Crosstabs Codex 市场插件通过本地 stdio 启动不可变的 crosstabs 1.1.4 包，并提供两个服务器：39 个专项统计工具，以及 23 个覆盖导入、Tab Book、权重、波次、开放题编码、Schema 修复、可编辑报告、导出与审计历史的项目工作流工具。","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；候选托管生命周期通过租户存储与授权适配器进入同一服务。共享编排已经验证，但浏览器交互与生产托管的完整对等仍是独立发布门槛。","本地插件不复制浏览器交互状态、共享云端审核、评论或可选连接器授权。","线上远程连接器目前只公开证据与汇总计算；托管的 23 工具生命周期仍须等待持久化租户存储与能力范围 OAuth 通过生产验证。","本地 code_open_ends 是唯一生成式操作，必须先明确批准 Vercel AI Gateway 外部处理；提供给 AI 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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。"],"evidencePaths":["/tracker-schema-drift","/methods","/local-mode","/capacity","/survey-tab-book"],"url":"https://www.crosstabs.com/zh-cn/tracker-schema-drift","evidenceUrls":["https://www.crosstabs.com/tracker-schema-drift","https://www.crosstabs.com/methods","https://www.crosstabs.com/local-mode","https://www.crosstabs.com/capacity","https://www.crosstabs.com/survey-tab-book"]},{"id":"zh-ai-evidence-governance","term":"交叉表 AI 分析治理","path":"/zh-cn/ai-analysis-governance","cluster":"ai_governance","locale":"zh-CN","answer":"只向模型提供有界且已披露的分析上下文，把每项单元格事实绑定到稳定证据 ID，由应用独立解析引用并在不匹配时默认拒绝模型文字；AI 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