{ "schemaVersion": 1, "generatedAt": "2026-11-07", "generator": "scripts/generate-mr-tool-reference.py", "runtime": { "Python": "3.13.13", "NumPy": "2.5.4", "pandas": "3.1.1", "SciPy": "1.18.1", "statsmodels": "0.15.0", "scikit-learn": "1.9.1", "ipfn": "1.4.4", "stepmix": "3.0.0", "dominance-analysis": "1.1.9", "bokeh": "2.4.3", "plotly": "7.1.0", "cufflinks": "0.17.3" }, "scope": { "claim": "Automated parity evidence for the market research tools against established independent implementations; not certification or independent human review.", "limitations": [ "Each procedure is checked on one or two small simulated datasets; other designs, sizes and edge cases are not covered by these cases.", "Hierarchical Bayes estimation (MaxDiff and CBC), market simulators, NMS purchase-probability curves and bootstrap intervals are not part of this comparison.", "Latent class models are compared at the best of 50 random starts on each side; a different start count or a harder dataset can reach different local maxima.", "TURF, NPS, Van Westendorp and Gabor-Granger are compared with an independent recomputation of the stated formulas, not with a third-party package." ] }, "cases": [ { "id": "rim-weighting-3-variables-unweighted", "procedure": "rim-weighting", "label": "Rim weighting: age × sex × region margins, n = 120", "provenance": { "kind": "package", "implementation": "ipfn", "version": "1.4.4", "method": "ipfn.ipfn on the respondent-level data frame (one dimension per raking variable), convergence_rate=1e-15, rate_tolerance=0; Kish effective n = (Σw)²/Σw², efficiency = n_eff/n, design effect = n/n_eff (NumPy). Each raking factor is the returned weight divided by the base weight and is constant within a cell of the raking variables." }, "input": { "data": { "columns": ["id", "age", "sex", "region"], "rows": [ ["r001", "35-54", "Male", "North"], ["r002", "55+", "Female", "North"], ["r003", "55+", "Male", "North"], ["r004", "35-54", "Male", "West"], ["r005", "55+", "Female", "North"], ["r006", "55+", "Male", "North"], ["r007", "55+", "Male", "North"], ["r008", "35-54", "Female", "North"], ["r009", "35-54", "Female", "North"], ["r010", "18-34", "Female", "West"], ["r011", "55+", "Male", "North"], ["r012", "18-34", "Male", "North"], ["r013", "18-34", "Female", "North"], ["r014", "55+", "Male", "North"], ["r015", "55+", "Male", "North"], ["r016", "35-54", "Male", "North"], ["r017", "55+", "Female", "South"], ["r018", "55+", "Male", "South"], ["r019", "18-34", "Male", "South"], ["r020", "18-34", "Male", "South"], ["r021", "35-54", "Male", "North"], ["r022", "18-34", "Male", "South"], ["r023", "35-54", "Male", "North"], ["r024", "55+", "Male", "North"], ["r025", "18-34", "Male", "West"], ["r026", "18-34", "Female", "West"], ["r027", "18-34", "Male", "North"], ["r028", "18-34", "Male", "North"], ["r029", "35-54", "Female", "North"], ["r030", "55+", "Female", "South"], ["r031", "18-34", "Male", "South"], ["r032", "18-34", "Male", "South"], ["r033", "35-54", "Male", "North"], ["r034", "18-34", "Male", "South"], ["r035", "55+", "Female", "West"], ["r036", "55+", "Female", "South"], ["r037", "18-34", "Male", "South"], ["r038", "55+", "Male", "South"], ["r039", "18-34", "Male", "North"], ["r040", "18-34", "Female", "West"], ["r041", "55+", "Male", "North"], ["r042", "18-34", "Male", "North"], ["r043", "18-34", "Female", "South"], ["r044", "18-34", "Male", "South"], ["r045", "18-34", "Male", "North"], ["r046", "35-54", "Female", "South"], ["r047", "18-34", "Female", "North"], ["r048", "18-34", "Male", "South"], ["r049", "35-54", "Male", "North"], ["r050", "18-34", "Male", "South"], ["r051", "18-34", "Female", "North"], ["r052", "55+", "Male", "North"], ["r053", "35-54", "Male", "South"], ["r054", "18-34", "Female", "West"], ["r055", "35-54", "Female", "South"], ["r056", "35-54", "Female", "South"], ["r057", "18-34", "Male", "North"], ["r058", "18-34", "Male", "South"], ["r059", "35-54", "Male", "South"], ["r060", "18-34", "Male", "West"], ["r061", "18-34", "Male", "West"], ["r062", "55+", "Male", "North"], ["r063", "35-54", "Male", "South"], ["r064", "18-34", "Male", "South"], ["r065", "35-54", "Male", "North"], ["r066", "18-34", "Male", "North"], ["r067", "18-34", "Male", "West"], ["r068", "35-54", "Female", "West"], ["r069", "18-34", "Male", "North"], ["r070", "18-34", "Male", "South"], ["r071", "35-54", "Male", "South"], ["r072", "18-34", "Male", "North"], ["r073", "18-34", "Male", "South"], ["r074", "35-54", "Female", "South"], ["r075", "35-54", "Male", "South"], ["r076", "35-54", "Male", "South"], ["r077", "35-54", "Male", "North"], ["r078", "35-54", "Male", "North"], ["r079", "18-34", "Male", "South"], ["r080", "55+", "Male", "South"], ["r081", "18-34", "Female", "North"], ["r082", "35-54", "Female", "North"], ["r083", "35-54", "Male", "South"], ["r084", "18-34", "Female", "South"], ["r085", "18-34", "Female", "West"], ["r086", "18-34", "Female", "South"], ["r087", "35-54", "Male", "North"], ["r088", "35-54", "Male", "South"], ["r089", "18-34", "Male", "North"], ["r090", "35-54", "Male", "North"], ["r091", "18-34", "Male", "West"], ["r092", "35-54", "Male", "North"], ["r093", "35-54", "Female", "South"], ["r094", "18-34", "Female", "North"], ["r095", "35-54", "Female", "South"], ["r096", "18-34", "Female", "North"], ["r097", "18-34", "Male", "South"], ["r098", "55+", "Male", "South"], ["r099", "18-34", "Female", "West"], ["r100", "18-34", "Male", "West"], ["r101", "35-54", "Female", "West"], ["r102", "18-34", "Male", "North"], ["r103", "18-34", "Female", "North"], ["r104", "55+", "Male", "North"], ["r105", "35-54", "Female", "North"], ["r106", "35-54", "Female", "South"], ["r107", "18-34", "Male", "North"], ["r108", "18-34", "Male", "North"], ["r109", "18-34", "Male", "West"], ["r110", "35-54", "Female", "North"], ["r111", "18-34", "Female", "North"], ["r112", "55+", "Male", "South"], ["r113", "18-34", "Female", "West"], ["r114", "55+", "Female", "North"], ["r115", "55+", "Male", "North"], ["r116", "35-54", "Male", "North"], ["r117", "55+", "Male", "South"], ["r118", "55+", "Male", "North"], ["r119", "18-34", "Male", "North"], ["r120", "18-34", "Male", "North"] ] }, "targets": [ { "variable": "age", "proportions": {"18-34": 0.3, "35-54": 0.35, "55+": 0.35} }, { "variable": "sex", "proportions": {"Female": 0.51, "Male": 0.49} }, { "variable": "region", "proportions": {"North": 0.4, "South": 0.35, "West": 0.25} } ], "baseWeightVariable": null, "tolerance": 1e-13, "maxIterations": 5000 }, "expected": [ {"metric": "Raking factor: 18-34 / Female / North", "value": 0.6140980785381263, "tolerance": 1e-09}, {"metric": "Raking factor: 18-34 / Female / South", "value": 0.7434501382259168, "tolerance": 1e-09}, {"metric": "Raking factor: 18-34 / Female / West", "value": 1.5416082585395396, "tolerance": 1e-09}, {"metric": "Raking factor: 18-34 / Male / North", "value": 0.34122922755398616, "tolerance": 1e-09}, {"metric": "Raking factor: 18-34 / Male / South", "value": 0.4131048854535428, "tolerance": 1e-09}, {"metric": "Raking factor: 18-34 / Male / West", "value": 0.8566087627314295, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Female / North", "value": 1.2539082161611637, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Female / South", "value": 1.5180282583635412, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Female / West", "value": 3.1477630838485298, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Male / North", "value": 0.6967455964734877, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Male / South", "value": 0.8435063194459314, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Male / West", "value": 1.7490834170683727, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Female / North", "value": 2.0586162517038873, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Female / South", "value": 2.492237950860733, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Female / West", "value": 5.167871266337781, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Male / North", "value": 1.1438889941997863, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Male / South", "value": 1.3848348668951875, "tolerance": 1e-09}, {"metric": "Sum of weights", "value": 120.0, "tolerance": 1e-09}, {"metric": "Smallest weight", "value": 0.34122922755398616, "tolerance": 1e-09}, {"metric": "Largest weight", "value": 5.167871266337781, "tolerance": 1e-09}, {"metric": "Effective sample size (Kish)", "value": 80.87353906832968, "tolerance": 1e-09}, {"metric": "Weighting efficiency (%)", "value": 67.39461589027472, "tolerance": 1e-09}, {"metric": "Design effect", "value": 1.4837980553640981, "tolerance": 1e-11} ] }, { "id": "rim-weighting-3-variables-base-weights", "procedure": "rim-weighting", "label": "Rim weighting with base weights: age × sex × region margins, n = 150", "provenance": { "kind": "package", "implementation": "ipfn", "version": "1.4.4", "method": "ipfn.ipfn on the respondent-level data frame (one dimension per raking variable), convergence_rate=1e-15, rate_tolerance=0; Kish effective n = (Σw)²/Σw², efficiency = n_eff/n, design effect = n/n_eff (NumPy). Each raking factor is the returned weight divided by the base weight and is constant within a cell of the raking variables." }, "input": { "data": { "columns": ["id", "age", "sex", "region", "base_weight"], "rows": [ ["r001", "18-34", "Female", "North", 1.816], ["r002", "35-54", "Female", "South", 1.115], ["r003", "18-34", "Male", "South", 1.335], ["r004", "18-34", "Male", "South", 1.96], ["r005", "18-34", "Female", "North", 1.217], ["r006", "18-34", "Female", "South", 0.977], ["r007", "18-34", "Male", "North", 1.593], ["r008", "35-54", "Female", "North", 1.469], ["r009", "18-34", "Male", "North", 0.735], ["r010", "18-34", "Female", "West", 1.102], ["r011", "35-54", "Female", "West", 1.996], ["r012", "35-54", "Male", "South", 1.469], ["r013", "18-34", "Female", "North", 1.246], ["r014", "18-34", "Female", "North", 1.107], ["r015", "18-34", "Female", "South", 1.955], ["r016", "55+", "Male", "South", 1.292], ["r017", "18-34", "Male", "West", 1.915], ["r018", "18-34", "Male", "West", 1.522], ["r019", "18-34", "Male", "North", 0.838], ["r020", "18-34", "Female", "South", 1.338], ["r021", "35-54", "Female", "North", 1.867], ["r022", "18-34", "Male", "North", 0.892], ["r023", "55+", "Male", "South", 0.831], ["r024", "18-34", "Female", "North", 1.342], ["r025", "35-54", "Female", "North", 1.186], ["r026", "55+", "Male", "West", 1.92], ["r027", "35-54", "Male", "North", 1.492], ["r028", "55+", "Male", "South", 1.784], ["r029", "18-34", "Male", "North", 0.881], ["r030", "35-54", "Male", "South", 1.384], ["r031", "18-34", "Male", "North", 1.881], ["r032", "18-34", "Female", "South", 0.856], ["r033", "55+", "Female", "North", 1.716], ["r034", "18-34", "Male", "North", 0.959], ["r035", "18-34", "Male", "North", 0.579], ["r036", "35-54", "Female", "South", 1.102], ["r037", "35-54", "Male", "South", 1.238], ["r038", "18-34", "Female", "South", 0.69], ["r039", "55+", "Male", "North", 1.587], ["r040", "35-54", "Female", "South", 1.281], ["r041", "35-54", "Female", "West", 1.665], ["r042", "35-54", "Female", "North", 0.991], ["r043", "18-34", "Male", "North", 0.849], ["r044", "18-34", "Male", "North", 0.542], ["r045", "18-34", "Male", "West", 0.987], ["r046", "18-34", "Female", "North", 1.466], ["r047", "18-34", "Male", "South", 0.946], ["r048", "18-34", "Female", "North", 1.276], ["r049", "35-54", "Male", "North", 1.424], ["r050", "55+", "Female", "North", 0.996], ["r051", "18-34", "Female", "South", 0.913], ["r052", "18-34", "Female", "North", 1.307], ["r053", "35-54", "Female", "North", 1.804], ["r054", "18-34", "Male", "South", 1.364], ["r055", "18-34", "Male", "North", 1.107], ["r056", "55+", "Female", "South", 1.342], ["r057", "35-54", "Female", "North", 1.951], ["r058", "35-54", "Male", "West", 0.541], ["r059", "18-34", "Female", "West", 0.599], ["r060", "18-34", "Female", "North", 0.752], ["r061", "18-34", "Female", "South", 0.663], ["r062", "18-34", "Male", "South", 0.971], ["r063", "35-54", "Female", "North", 1.226], ["r064", "35-54", "Female", "West", 1.905], ["r065", "35-54", "Male", "South", 1.769], ["r066", "55+", "Female", "South", 1.707], ["r067", "55+", "Female", "South", 0.576], ["r068", "18-34", "Female", "North", 1.385], ["r069", "55+", "Female", "North", 1.485], ["r070", "18-34", "Male", "West", 1.659], ["r071", "35-54", "Male", "South", 0.807], ["r072", "35-54", "Male", "North", 1.274], ["r073", "18-34", "Male", "North", 0.867], ["r074", "35-54", "Male", "South", 0.579], ["r075", "18-34", "Male", "South", 1.75], ["r076", "35-54", "Male", "West", 1.678], ["r077", "35-54", "Male", "North", 0.535], ["r078", "55+", "Female", "South", 1.152], ["r079", "55+", "Female", "North", 1.673], ["r080", "18-34", "Male", "North", 0.873], ["r081", "18-34", "Female", "North", 1.847], ["r082", "35-54", "Female", "South", 0.987], ["r083", "35-54", "Male", "North", 1.04], ["r084", "35-54", "Male", "North", 1.042], ["r085", "18-34", "Female", "North", 0.836], ["r086", "18-34", "Female", "West", 0.97], ["r087", "18-34", "Male", "North", 0.995], ["r088", "35-54", "Female", "South", 0.82], ["r089", "18-34", "Male", "North", 1.671], ["r090", "55+", "Male", "North", 1.724], ["r091", "18-34", "Female", "North", 1.354], ["r092", "35-54", "Male", "South", 1.91], ["r093", "18-34", "Male", "North", 0.864], ["r094", "18-34", "Male", "North", 1.402], ["r095", "55+", "Male", "West", 0.912], ["r096", "35-54", "Male", "South", 1.856], ["r097", "18-34", "Male", "South", 1.832], ["r098", "35-54", "Male", "North", 1.298], ["r099", "55+", "Male", "West", 1.749], ["r100", "35-54", "Male", "West", 1.942], ["r101", "18-34", "Female", "North", 0.88], ["r102", "18-34", "Male", "West", 1.676], ["r103", "18-34", "Male", "North", 1.455], ["r104", "55+", "Male", "South", 0.729], ["r105", "18-34", "Male", "West", 1.405], ["r106", "35-54", "Female", "South", 0.574], ["r107", "35-54", "Female", "South", 1.931], ["r108", "35-54", "Male", "North", 0.852], ["r109", "18-34", "Female", "North", 0.579], ["r110", "55+", "Male", "North", 0.898], ["r111", "18-34", "Female", "North", 0.629], ["r112", "18-34", "Female", "North", 1.8], ["r113", "18-34", "Female", "South", 1.488], ["r114", "18-34", "Female", "North", 1.166], ["r115", "18-34", "Female", "North", 1.889], ["r116", "18-34", "Male", "South", 0.868], ["r117", "35-54", "Male", "North", 1.587], ["r118", "55+", "Female", "North", 0.551], ["r119", "35-54", "Male", "North", 1.154], ["r120", "35-54", "Male", "West", 0.65], ["r121", "55+", "Male", "South", 1.115], ["r122", "55+", "Male", "North", 1.894], ["r123", "35-54", "Female", "North", 1.437], ["r124", "55+", "Female", "North", 1.454], ["r125", "18-34", "Female", "South", 0.73], ["r126", "18-34", "Male", "West", 1.367], ["r127", "18-34", "Male", "South", 1.054], ["r128", "35-54", "Female", "South", 1.461], ["r129", "18-34", "Female", "North", 0.525], ["r130", "18-34", "Male", "South", 1.46], ["r131", "35-54", "Male", "North", 1.094], ["r132", "35-54", "Female", "North", 1.292], ["r133", "55+", "Female", "West", 1.464], ["r134", "18-34", "Male", "North", 1.312], ["r135", "55+", "Male", "North", 0.699], ["r136", "18-34", "Female", "North", 1.858], ["r137", "55+", "Female", "West", 1.419], ["r138", "35-54", "Female", "South", 0.933], ["r139", "35-54", "Female", "West", 1.454], ["r140", "35-54", "Female", "West", 0.658], ["r141", "55+", "Female", "South", 1.947], ["r142", "18-34", "Male", "North", 0.527], ["r143", "35-54", "Male", "North", 0.564], ["r144", "18-34", "Male", "West", 0.561], ["r145", "18-34", "Male", "South", 1.835], ["r146", "35-54", "Male", "South", 1.647], ["r147", "35-54", "Male", "West", 1.634], ["r148", "35-54", "Female", "West", 0.802], ["r149", "18-34", "Female", "West", 1.879], ["r150", "18-34", "Male", "South", 1.666] ] }, "targets": [ { "variable": "age", "proportions": {"18-34": 0.3, "35-54": 0.35, "55+": 0.35} }, { "variable": "sex", "proportions": {"Female": 0.51, "Male": 0.49} }, { "variable": "region", "proportions": {"North": 0.4, "South": 0.35, "West": 0.25} } ], "baseWeightVariable": "base_weight", "tolerance": 1e-13, "maxIterations": 5000 }, "expected": [ {"metric": "Raking factor: 18-34 / Female / North", "value": 0.6039434508081943, "tolerance": 1e-09}, {"metric": "Raking factor: 18-34 / Female / South", "value": 0.7093657266247478, "tolerance": 1e-09}, {"metric": "Raking factor: 18-34 / Female / West", "value": 0.8264632314406358, "tolerance": 1e-09}, {"metric": "Raking factor: 18-34 / Male / North", "value": 0.5367224945005489, "tolerance": 1e-09}, {"metric": "Raking factor: 18-34 / Male / South", "value": 0.6304109131372057, "tolerance": 1e-09}, {"metric": "Raking factor: 18-34 / Male / West", "value": 0.7344750681511716, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Female / North", "value": 0.9454709894397679, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Female / South", "value": 1.1105091288415383, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Female / West", "value": 1.2938247912451142, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Male / North", "value": 0.8402368586842687, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Male / South", "value": 0.9869056929085827, "tolerance": 1e-09}, {"metric": "Raking factor: 35-54 / Male / West", "value": 1.1498176997771117, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Female / North", "value": 1.7658424641919481, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Female / South", "value": 2.0740818052420225, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Female / West", "value": 2.4164578111050043, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Male / North", "value": 1.5692982033463563, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Male / South", "value": 1.8432294593442677, "tolerance": 1e-09}, {"metric": "Raking factor: 55+ / Male / West", "value": 2.1474978534762124, "tolerance": 1e-09}, {"metric": "Sum of weights", "value": 188.375, "tolerance": 1e-09}, {"metric": "Smallest weight", "value": 0.28285275460178916, "tolerance": 1e-09}, {"metric": "Largest weight", "value": 4.123195878674328, "tolerance": 1e-09}, {"metric": "Effective sample size (Kish)", "value": 104.73230093781376, "tolerance": 1e-09}, {"metric": "Weighting efficiency (%)", "value": 69.8215339585425, "tolerance": 1e-09}, {"metric": "Design effect", "value": 1.4322229021690696, "tolerance": 1e-11} ] }, { "id": "maxdiff-sequential-best-worst-7-items", "procedure": "maxdiff", "label": "MaxDiff: 7 items, 40 respondents × 7 tasks of 4 items", "provenance": { "kind": "package", "implementation": "statsmodels", "version": "0.15.0", "method": "statsmodels.discrete.conditional_models.ConditionalLogit (Newton, numerical Hessian) on the sequential best-worst design: each task contributes a best choice among the items shown (+1 dummy) and a worst choice among the remaining items (−1 dummy); the last item is the reference. Utilities are zero-centred. Counts score = (best − worst) / times shown; rescaled score = exp(u)/(exp(u)+a−1), normalised to 100, with a = 4 items per task." }, "input": { "data": { "columns": ["respondent", "task", "item1", "item2", "item3", "item4", "best", "worst"], "rows": [ ["r01", 1, "Screen", "Support", "Battery", "Storage", "Screen", "Storage"], ["r01", 2, "Support", "Price", "Camera", "Design", "Price", "Support"], ["r01", 3, "Price", "Support", "Storage", "Screen", "Price", "Storage"], ["r01", 4, "Screen", "Design", "Storage", "Camera", "Screen", "Camera"], ["r01", 5, "Camera", "Price", "Screen", "Support", "Camera", "Support"], ["r01", 6, "Screen", "Design", "Battery", "Camera", "Battery", "Screen"], ["r01", 7, "Support", "Battery", "Camera", "Screen", "Battery", "Screen"], ["r02", 1, "Screen", "Design", "Camera", "Support", "Camera", "Screen"], ["r02", 2, "Price", "Design", "Storage", "Screen", "Price", "Design"], ["r02", 3, "Price", "Screen", "Support", "Storage", "Price", "Support"], ["r02", 4, "Price", "Screen", "Support", "Camera", "Price", "Screen"], ["r02", 5, "Storage", "Battery", "Support", "Screen", "Screen", "Support"], ["r02", 6, "Storage", "Price", "Design", "Battery", "Price", "Storage"], ["r02", 7, "Camera", "Storage", "Design", "Price", "Design", "Storage"], ["r03", 1, "Price", "Camera", "Battery", "Storage", "Storage", "Battery"], ["r03", 2, "Camera", "Price", "Storage", "Battery", "Storage", "Camera"], ["r03", 3, "Price", "Camera", "Storage", "Battery", "Price", "Storage"], ["r03", 4, "Screen", "Battery", "Design", "Support", "Support", "Screen"], ["r03", 5, "Camera", "Screen", "Battery", "Storage", "Storage", "Screen"], ["r03", 6, "Support", "Price", "Design", "Storage", "Price", "Support"], ["r03", 7, "Camera", "Screen", "Support", "Battery", "Support", "Camera"], ["r04", 1, "Support", "Price", "Camera", "Storage", "Price", "Support"], ["r04", 2, "Design", "Battery", "Screen", "Storage", "Battery", "Storage"], ["r04", 3, "Support", "Storage", "Design", "Screen", "Design", "Storage"], ["r04", 4, "Battery", "Storage", "Camera", "Screen", "Camera", "Storage"], ["r04", 5, "Battery", "Design", "Camera", "Support", "Battery", "Design"], ["r04", 6, "Screen", "Storage", "Design", "Battery", "Battery", "Storage"], ["r04", 7, "Design", "Screen", "Battery", "Price", "Screen", "Design"], ["r05", 1, "Camera", "Support", "Screen", "Storage", "Screen", "Storage"], ["r05", 2, "Price", "Storage", "Support", "Battery", "Price", "Support"], ["r05", 3, "Screen", "Camera", "Price", "Storage", "Price", "Storage"], ["r05", 4, "Storage", "Support", "Design", "Screen", "Screen", "Support"], ["r05", 5, "Battery", "Design", "Storage", "Camera", "Camera", "Design"], ["r05", 6, "Design", "Screen", "Camera", "Price", "Screen", "Design"], ["r05", 7, "Storage", "Design", "Battery", "Screen", "Battery", "Storage"], ["r06", 1, "Design", "Camera", "Battery", "Support", "Battery", "Support"], ["r06", 2, "Battery", "Support", "Camera", "Design", "Camera", "Support"], ["r06", 3, "Support", "Design", "Battery", "Camera", "Battery", "Camera"], ["r06", 4, "Battery", "Screen", "Support", "Camera", "Support", "Camera"], ["r06", 5, "Support", "Camera", "Screen", "Storage", "Screen", "Storage"], ["r06", 6, "Camera", "Support", "Battery", "Price", "Price", "Battery"], ["r06", 7, "Support", "Price", "Battery", "Design", "Design", "Price"], ["r07", 1, "Support", "Camera", "Battery", "Screen", "Screen", "Camera"], ["r07", 2, "Camera", "Storage", "Battery", "Design", "Storage", "Camera"], ["r07", 3, "Battery", "Screen", "Support", "Price", "Screen", "Support"], ["r07", 4, "Battery", "Price", "Design", "Screen", "Battery", "Screen"], ["r07", 5, "Battery", "Storage", "Price", "Support", "Support", "Storage"], ["r07", 6, "Camera", "Battery", "Screen", "Storage", "Screen", "Camera"], ["r07", 7, "Storage", "Design", "Screen", "Price", "Screen", "Storage"], ["r08", 1, "Battery", "Storage", "Camera", "Price", "Battery", "Camera"], ["r08", 2, "Storage", "Screen", "Camera", "Support", "Camera", "Support"], ["r08", 3, "Support", "Price", "Design", "Camera", "Price", "Support"], ["r08", 4, "Design", "Storage", "Price", "Support", "Price", "Support"], ["r08", 5, "Battery", "Design", "Screen", "Support", "Battery", "Support"], ["r08", 6, "Support", "Price", "Design", "Camera", "Price", "Support"], ["r08", 7, "Design", "Storage", "Screen", "Battery", "Battery", "Screen"], ["r09", 1, "Price", "Support", "Camera", "Design", "Support", "Design"], ["r09", 2, "Camera", "Storage", "Support", "Design", "Camera", "Design"], ["r09", 3, "Design", "Screen", "Support", "Camera", "Screen", "Design"], ["r09", 4, "Screen", "Battery", "Support", "Design", "Battery", "Design"], ["r09", 5, "Camera", "Storage", "Screen", "Battery", "Camera", "Storage"], ["r09", 6, "Camera", "Design", "Screen", "Storage", "Camera", "Storage"], ["r09", 7, "Battery", "Support", "Design", "Screen", "Battery", "Design"], ["r10", 1, "Support", "Screen", "Price", "Design", "Price", "Design"], ["r10", 2, "Camera", "Support", "Screen", "Price", "Price", "Support"], ["r10", 3, "Battery", "Screen", "Design", "Storage", "Design", "Storage"], ["r10", 4, "Battery", "Price", "Storage", "Screen", "Battery", "Storage"], ["r10", 5, "Battery", "Storage", "Design", "Screen", "Battery", "Design"], ["r10", 6, "Support", "Camera", "Price", "Battery", "Camera", "Price"], ["r10", 7, "Screen", "Design", "Storage", "Support", "Support", "Design"], ["r11", 1, "Design", "Storage", "Camera", "Screen", "Camera", "Storage"], ["r11", 2, "Camera", "Battery", "Screen", "Price", "Battery", "Camera"], ["r11", 3, "Support", "Price", "Design", "Screen", "Price", "Design"], ["r11", 4, "Battery", "Screen", "Design", "Camera", "Battery", "Design"], ["r11", 5, "Price", "Screen", "Camera", "Support", "Price", "Support"], ["r11", 6, "Storage", "Camera", "Screen", "Price", "Price", "Storage"], ["r11", 7, "Battery", "Design", "Support", "Screen", "Battery", "Support"], ["r12", 1, "Screen", "Support", "Price", "Storage", "Support", "Storage"], ["r12", 2, "Screen", "Storage", "Battery", "Support", "Battery", "Storage"], ["r12", 3, "Price", "Design", "Support", "Storage", "Storage", "Price"], ["r12", 4, "Support", "Screen", "Storage", "Design", "Design", "Support"], ["r12", 5, "Screen", "Support", "Storage", "Price", "Price", "Storage"], ["r12", 6, "Design", "Battery", "Storage", "Support", "Storage", "Design"], ["r12", 7, "Camera", "Price", "Screen", "Design", "Price", "Design"], ["r13", 1, "Camera", "Battery", "Design", "Storage", "Battery", "Design"], ["r13", 2, "Support", "Battery", "Storage", "Screen", "Battery", "Storage"], ["r13", 3, "Storage", "Camera", "Screen", "Support", "Camera", "Support"], ["r13", 4, "Storage", "Design", "Screen", "Battery", "Battery", "Storage"], ["r13", 5, "Price", "Battery", "Storage", "Design", "Battery", "Storage"], ["r13", 6, "Camera", "Screen", "Design", "Price", "Price", "Design"], ["r13", 7, "Support", "Design", "Screen", "Battery", "Battery", "Design"], ["r14", 1, "Camera", "Design", "Battery", "Screen", "Battery", "Screen"], ["r14", 2, "Design", "Camera", "Price", "Screen", "Camera", "Screen"], ["r14", 3, "Price", "Battery", "Design", "Screen", "Battery", "Screen"], ["r14", 4, "Support", "Battery", "Price", "Design", "Price", "Support"], ["r14", 5, "Support", "Battery", "Camera", "Price", "Support", "Price"], ["r14", 6, "Battery", "Storage", "Design", "Price", "Price", "Storage"], ["r14", 7, "Support", "Battery", "Design", "Storage", "Battery", "Design"], ["r15", 1, "Camera", "Support", "Design", "Screen", "Screen", "Camera"], ["r15", 2, "Price", "Screen", "Battery", "Support", "Screen", "Battery"], ["r15", 3, "Price", "Storage", "Screen", "Support", "Price", "Storage"], ["r15", 4, "Storage", "Battery", "Camera", "Price", "Camera", "Storage"], ["r15", 5, "Support", "Screen", "Storage", "Design", "Support", "Design"], ["r15", 6, "Camera", "Screen", "Storage", "Design", "Camera", "Storage"], ["r15", 7, "Support", "Price", "Design", "Camera", "Price", "Design"], ["r16", 1, "Design", "Camera", "Price", "Battery", "Battery", "Design"], ["r16", 2, "Storage", "Screen", "Support", "Battery", "Battery", "Storage"], ["r16", 3, "Screen", "Camera", "Support", "Storage", "Camera", "Storage"], ["r16", 4, "Battery", "Design", "Storage", "Screen", "Battery", "Storage"], ["r16", 5, "Design", "Camera", "Screen", "Support", "Camera", "Design"], ["r16", 6, "Battery", "Storage", "Support", "Screen", "Battery", "Storage"], ["r16", 7, "Price", "Storage", "Design", "Camera", "Camera", "Storage"], ["r17", 1, "Camera", "Support", "Battery", "Screen", "Screen", "Support"], ["r17", 2, "Storage", "Support", "Design", "Camera", "Camera", "Storage"], ["r17", 3, "Price", "Screen", "Support", "Camera", "Screen", "Camera"], ["r17", 4, "Price", "Screen", "Battery", "Storage", "Price", "Storage"], ["r17", 5, "Battery", "Price", "Support", "Camera", "Battery", "Support"], ["r17", 6, "Battery", "Support", "Screen", "Design", "Battery", "Support"], ["r17", 7, "Camera", "Battery", "Storage", "Screen", "Camera", "Storage"], ["r18", 1, "Support", "Design", "Camera", "Price", "Design", "Price"], ["r18", 2, "Design", "Camera", "Battery", "Price", "Battery", "Camera"], ["r18", 3, "Support", "Battery", "Screen", "Design", "Screen", "Support"], ["r18", 4, "Camera", "Design", "Price", "Storage", "Design", "Storage"], ["r18", 5, "Price", "Battery", "Support", "Storage", "Battery", "Support"], ["r18", 6, "Camera", "Design", "Price", "Battery", "Battery", "Camera"], ["r18", 7, "Design", "Screen", "Camera", "Price", "Screen", "Design"], ["r19", 1, "Camera", "Price", "Support", "Battery", "Support", "Camera"], ["r19", 2, "Screen", "Price", "Support", "Battery", "Battery", "Screen"], ["r19", 3, "Screen", "Battery", "Design", "Storage", "Design", "Screen"], ["r19", 4, "Price", "Storage", "Battery", "Screen", "Battery", "Storage"], ["r19", 5, "Design", "Camera", "Battery", "Price", "Price", "Battery"], ["r19", 6, "Screen", "Battery", "Camera", "Support", "Battery", "Camera"], ["r19", 7, "Support", "Camera", "Storage", "Battery", "Battery", "Camera"], ["r20", 1, "Support", "Battery", "Camera", "Price", "Battery", "Support"], ["r20", 2, "Support", "Storage", "Price", "Camera", "Camera", "Storage"], ["r20", 3, "Price", "Screen", "Camera", "Battery", "Price", "Battery"], ["r20", 4, "Battery", "Design", "Support", "Screen", "Design", "Support"], ["r20", 5, "Battery", "Price", "Screen", "Storage", "Price", "Storage"], ["r20", 6, "Support", "Storage", "Screen", "Design", "Storage", "Support"], ["r20", 7, "Support", "Storage", "Screen", "Design", "Design", "Storage"], ["r21", 1, "Camera", "Battery", "Price", "Design", "Battery", "Camera"], ["r21", 2, "Camera", "Support", "Battery", "Screen", "Battery", "Screen"], ["r21", 3, "Storage", "Camera", "Support", "Battery", "Battery", "Storage"], ["r21", 4, "Camera", "Screen", "Battery", "Support", "Battery", "Support"], ["r21", 5, "Storage", "Price", "Support", "Battery", "Battery", "Storage"], ["r21", 6, "Design", "Support", "Battery", "Price", "Design", "Support"], ["r21", 7, "Support", "Price", "Battery", "Screen", "Battery", "Screen"], ["r22", 1, "Battery", "Price", "Camera", "Screen", "Price", "Camera"], ["r22", 2, "Camera", "Design", "Price", "Screen", "Screen", "Camera"], ["r22", 3, "Price", "Camera", "Storage", "Design", "Design", "Storage"], ["r22", 4, "Camera", "Price", "Storage", "Support", "Camera", "Storage"], ["r22", 5, "Price", "Battery", "Camera", "Screen", "Screen", "Price"], ["r22", 6, "Support", "Battery", "Design", "Price", "Design", "Battery"], ["r22", 7, "Storage", "Battery", "Design", "Price", "Design", "Storage"], ["r23", 1, "Support", "Storage", "Camera", "Price", "Camera", "Storage"], ["r23", 2, "Price", "Design", "Screen", "Support", "Price", "Screen"], ["r23", 3, "Storage", "Screen", "Battery", "Design", "Screen", "Storage"], ["r23", 4, "Battery", "Storage", "Screen", "Price", "Battery", "Storage"], ["r23", 5, "Camera", "Design", "Support", "Price", "Price", "Support"], ["r23", 6, "Support", "Battery", "Screen", "Camera", "Support", "Camera"], ["r23", 7, "Design", "Storage", "Battery", "Support", "Battery", "Support"], ["r24", 1, "Screen", "Camera", "Price", "Design", "Price", "Screen"], ["r24", 2, "Support", "Camera", "Design", "Price", "Camera", "Design"], ["r24", 3, "Price", "Battery", "Camera", "Storage", "Camera", "Battery"], ["r24", 4, "Storage", "Camera", "Battery", "Support", "Support", "Camera"], ["r24", 5, "Battery", "Screen", "Price", "Support", "Support", "Screen"], ["r24", 6, "Support", "Camera", "Design", "Battery", "Camera", "Support"], ["r24", 7, "Storage", "Camera", "Design", "Price", "Price", "Storage"], ["r25", 1, "Screen", "Support", "Price", "Camera", "Screen", "Support"], ["r25", 2, "Design", "Price", "Storage", "Battery", "Price", "Storage"], ["r25", 3, "Storage", "Price", "Screen", "Camera", "Screen", "Storage"], ["r25", 4, "Storage", "Price", "Support", "Design", "Price", "Design"], ["r25", 5, "Storage", "Design", "Screen", "Support", "Support", "Screen"], ["r25", 6, "Screen", "Camera", "Support", "Price", "Camera", "Price"], ["r25", 7, "Battery", "Camera", "Screen", "Storage", "Battery", "Screen"], ["r26", 1, "Battery", "Camera", "Design", "Support", "Design", "Support"], ["r26", 2, "Screen", "Design", "Price", "Battery", "Price", "Battery"], ["r26", 3, "Storage", "Support", "Battery", "Camera", "Support", "Storage"], ["r26", 4, "Screen", "Design", "Battery", "Storage", "Design", "Storage"], ["r26", 5, "Screen", "Storage", "Price", "Support", "Price", "Screen"], ["r26", 6, "Storage", "Battery", "Support", "Design", "Battery", "Support"], ["r26", 7, "Battery", "Support", "Price", "Storage", "Battery", "Storage"], ["r27", 1, "Storage", "Price", "Camera", "Support", "Price", "Storage"], ["r27", 2, "Screen", "Battery", "Camera", "Design", "Battery", "Camera"], ["r27", 3, "Support", "Battery", "Camera", "Design", "Battery", "Support"], ["r27", 4, "Screen", "Battery", "Storage", "Design", "Battery", "Storage"], ["r27", 5, "Price", "Storage", "Screen", "Support", "Price", "Storage"], ["r27", 6, "Design", "Screen", "Storage", "Support", "Screen", "Storage"], ["r27", 7, "Screen", "Design", "Camera", "Battery", "Camera", "Screen"], ["r28", 1, "Price", "Design", "Screen", "Storage", "Design", "Screen"], ["r28", 2, "Storage", "Screen", "Battery", "Design", "Battery", "Design"], ["r28", 3, "Design", "Support", "Battery", "Price", "Price", "Support"], ["r28", 4, "Battery", "Storage", "Price", "Support", "Storage", "Battery"], ["r28", 5, "Design", "Support", "Storage", "Screen", "Screen", "Support"], ["r28", 6, "Storage", "Support", "Screen", "Design", "Screen", "Storage"], ["r28", 7, "Camera", "Design", "Screen", "Support", "Design", "Support"], ["r29", 1, "Screen", "Design", "Camera", "Support", "Screen", "Camera"], ["r29", 2, "Design", "Screen", "Support", "Battery", "Screen", "Support"], ["r29", 3, "Screen", "Camera", "Design", "Support", "Design", "Camera"], ["r29", 4, "Design", "Price", "Battery", "Storage", "Price", "Battery"], ["r29", 5, "Design", "Camera", "Storage", "Battery", "Battery", "Design"], ["r29", 6, "Price", "Battery", "Design", "Storage", "Design", "Storage"], ["r29", 7, "Storage", "Battery", "Price", "Screen", "Screen", "Battery"], ["r30", 1, "Battery", "Support", "Storage", "Camera", "Camera", "Support"], ["r30", 2, "Design", "Price", "Camera", "Support", "Price", "Support"], ["r30", 3, "Price", "Screen", "Storage", "Design", "Price", "Storage"], ["r30", 4, "Design", "Screen", "Battery", "Support", "Screen", "Design"], ["r30", 5, "Storage", "Screen", "Battery", "Design", "Screen", "Battery"], ["r30", 6, "Design", "Battery", "Support", "Screen", "Screen", "Battery"], ["r30", 7, "Support", "Storage", "Design", "Battery", "Support", "Storage"], ["r31", 1, "Design", "Camera", "Storage", "Price", "Price", "Design"], ["r31", 2, "Camera", "Design", "Support", "Price", "Price", "Support"], ["r31", 3, "Screen", "Storage", "Battery", "Support", "Support", "Battery"], ["r31", 4, "Battery", "Design", "Support", "Screen", "Support", "Battery"], ["r31", 5, "Camera", "Support", "Storage", "Battery", "Battery", "Storage"], ["r31", 6, "Support", "Battery", "Design", "Storage", "Battery", "Storage"], ["r31", 7, "Battery", "Storage", "Price", "Screen", "Screen", "Storage"], ["r32", 1, "Storage", "Price", "Battery", "Screen", "Price", "Screen"], ["r32", 2, "Camera", "Storage", "Support", "Design", "Support", "Design"], ["r32", 3, "Storage", "Price", "Design", "Support", "Price", "Design"], ["r32", 4, "Support", "Screen", "Camera", "Price", "Support", "Screen"], ["r32", 5, "Battery", "Camera", "Support", "Price", "Price", "Support"], ["r32", 6, "Price", "Screen", "Support", "Design", "Price", "Support"], ["r32", 7, "Design", "Screen", "Support", "Camera", "Camera", "Design"], ["r33", 1, "Screen", "Camera", "Battery", "Support", "Battery", "Support"], ["r33", 2, "Support", "Design", "Price", "Screen", "Price", "Support"], ["r33", 3, "Support", "Storage", "Screen", "Battery", "Screen", "Storage"], ["r33", 4, "Price", "Camera", "Battery", "Support", "Battery", "Price"], ["r33", 5, "Design", "Support", "Camera", "Battery", "Battery", "Support"], ["r33", 6, "Battery", "Camera", "Design", "Support", "Battery", "Design"], ["r33", 7, "Price", "Camera", "Screen", "Design", "Camera", "Screen"], ["r34", 1, "Design", "Screen", "Support", "Camera", "Design", "Camera"], ["r34", 2, "Design", "Battery", "Camera", "Storage", "Battery", "Design"], ["r34", 3, "Screen", "Camera", "Storage", "Support", "Storage", "Support"], ["r34", 4, "Battery", "Support", "Price", "Screen", "Battery", "Support"], ["r34", 5, "Support", "Screen", "Battery", "Price", "Battery", "Price"], ["r34", 6, "Camera", "Design", "Support", "Price", "Design", "Support"], ["r34", 7, "Screen", "Camera", "Design", "Support", "Camera", "Design"], ["r35", 1, "Price", "Storage", "Support", "Screen", "Price", "Storage"], ["r35", 2, "Battery", "Screen", "Storage", "Support", "Battery", "Storage"], ["r35", 3, "Camera", "Support", "Screen", "Battery", "Support", "Battery"], ["r35", 4, "Storage", "Support", "Price", "Battery", "Storage", "Price"], ["r35", 5, "Battery", "Camera", "Price", "Storage", "Price", "Camera"], ["r35", 6, "Storage", "Camera", "Support", "Design", "Support", "Storage"], ["r35", 7, "Camera", "Design", "Support", "Storage", "Camera", "Support"], ["r36", 1, "Screen", "Storage", "Design", "Camera", "Screen", "Design"], ["r36", 2, "Support", "Price", "Screen", "Camera", "Screen", "Support"], ["r36", 3, "Support", "Storage", "Screen", "Design", "Support", "Design"], ["r36", 4, "Design", "Storage", "Price", "Camera", "Camera", "Storage"], ["r36", 5, "Battery", "Camera", "Support", "Storage", "Camera", "Storage"], ["r36", 6, "Storage", "Camera", "Design", "Support", "Camera", "Support"], ["r36", 7, "Support", "Design", "Price", "Battery", "Support", "Design"], ["r37", 1, "Support", "Battery", "Price", "Screen", "Price", "Support"], ["r37", 2, "Screen", "Camera", "Price", "Battery", "Camera", "Battery"], ["r37", 3, "Support", "Design", "Price", "Battery", "Price", "Battery"], ["r37", 4, "Battery", "Design", "Support", "Camera", "Battery", "Design"], ["r37", 5, "Screen", "Support", "Price", "Camera", "Price", "Screen"], ["r37", 6, "Screen", "Camera", "Support", "Battery", "Screen", "Support"], ["r37", 7, "Price", "Camera", "Design", "Storage", "Price", "Storage"], ["r38", 1, "Price", "Screen", "Battery", "Support", "Screen", "Price"], ["r38", 2, "Support", "Screen", "Battery", "Price", "Screen", "Support"], ["r38", 3, "Storage", "Screen", "Battery", "Camera", "Battery", "Camera"], ["r38", 4, "Design", "Screen", "Support", "Price", "Support", "Screen"], ["r38", 5, "Design", "Screen", "Camera", "Price", "Price", "Screen"], ["r38", 6, "Camera", "Screen", "Price", "Battery", "Price", "Camera"], ["r38", 7, "Design", "Storage", "Price", "Camera", "Design", "Storage"], ["r39", 1, "Storage", "Support", "Battery", "Screen", "Support", "Screen"], ["r39", 2, "Screen", "Camera", "Battery", "Price", "Battery", "Screen"], ["r39", 3, "Design", "Storage", "Screen", "Battery", "Battery", "Storage"], ["r39", 4, "Camera", "Support", "Battery", "Price", "Price", "Support"], ["r39", 5, "Battery", "Support", "Screen", "Price", "Price", "Screen"], ["r39", 6, "Storage", "Camera", "Price", "Design", "Price", "Storage"], ["r39", 7, "Camera", "Storage", "Design", "Price", "Design", "Price"], ["r40", 1, "Support", "Camera", "Design", "Screen", "Support", "Screen"], ["r40", 2, "Design", "Screen", "Price", "Battery", "Design", "Battery"], ["r40", 3, "Price", "Camera", "Design", "Storage", "Design", "Storage"], ["r40", 4, "Storage", "Design", "Screen", "Battery", "Design", "Storage"], ["r40", 5, "Camera", "Support", "Design", "Battery", "Support", "Battery"], ["r40", 6, "Price", "Support", "Screen", "Battery", "Battery", "Support"], ["r40", 7, "Camera", "Screen", "Support", "Battery", "Support", "Camera"] ] }, "layout": { "kind": "wide", "respondent": "respondent", "task": "task", "itemColumns": ["item1", "item2", "item3", "item4"], "best": "best", "worst": "worst", "picks": "labels" } }, "expected": [ {"metric": "Counts score: Battery", "value": 0.31736526946107785, "tolerance": 1e-12}, {"metric": "Counts score: Camera", "value": 0.045454545454545456, "tolerance": 1e-12}, {"metric": "Counts score: Design", "value": -0.09316770186335403, "tolerance": 1e-12}, {"metric": "Counts score: Price", "value": 0.35374149659863946, "tolerance": 1e-12}, {"metric": "Counts score: Screen", "value": 0.041176470588235294, "tolerance": 1e-12}, {"metric": "Counts score: Storage", "value": -0.4863013698630137, "tolerance": 1e-12}, {"metric": "Counts score: Support", "value": -0.18857142857142858, "tolerance": 1e-12}, {"metric": "Utility (zero-centred): Battery", "value": 0.7101521189470222, "tolerance": 1e-07}, {"metric": "Utility (zero-centred): Camera", "value": 0.1401855276282129, "tolerance": 1e-07}, {"metric": "Utility (zero-centred): Design", "value": -0.236719513527567, "tolerance": 1e-07}, {"metric": "Utility (zero-centred): Price", "value": 0.8347795484515065, "tolerance": 1e-07}, {"metric": "Utility (zero-centred): Screen", "value": 0.07007156940003945, "tolerance": 1e-07}, {"metric": "Utility (zero-centred): Storage", "value": -1.0990885498826988, "tolerance": 1e-07}, {"metric": "Utility (zero-centred): Support", "value": -0.4193807010165155, "tolerance": 1e-07}, {"metric": "Standard error vs Support: Battery", "value": 0.17964254725821793, "tolerance": 1e-06}, {"metric": "Standard error vs Support: Camera", "value": 0.17879675092399588, "tolerance": 1e-06}, {"metric": "Standard error vs Support: Design", "value": 0.17571180154474192, "tolerance": 1e-06}, {"metric": "Standard error vs Support: Price", "value": 0.18698471838704667, "tolerance": 1e-06}, {"metric": "Standard error vs Support: Screen", "value": 0.1750399250862675, "tolerance": 1e-06}, {"metric": "Standard error vs Support: Storage", "value": 0.1867034783081618, "tolerance": 1e-06}, {"metric": "Probability-rescaled score: Battery", "value": 21.642973538646096, "tolerance": 1e-05}, {"metric": "Probability-rescaled score: Camera", "value": 14.846485316808028, "tolerance": 1e-05}, {"metric": "Probability-rescaled score: Design", "value": 11.155421385914453, "tolerance": 1e-05}, {"metric": "Probability-rescaled score: Price", "value": 23.2676495842361, "tolerance": 1e-05}, {"metric": "Probability-rescaled score: Screen", "value": 14.105954487853817, "tolerance": 1e-05}, {"metric": "Probability-rescaled score: Storage", "value": 5.353709170451597, "tolerance": 1e-05}, {"metric": "Probability-rescaled score: Support", "value": 9.6278065160899, "tolerance": 1e-05}, {"metric": "Log-likelihood", "value": -623.9705151304516, "tolerance": 1e-08}, {"metric": "McFadden pseudo R²", "value": 0.10319925875041625, "tolerance": 1e-10} ] }, { "id": "cbc-categorical-3-attributes", "procedure": "cbc-conjoint", "label": "CBC conjoint: 3 categorical attributes, 50 respondents × 8 tasks × 3 profiles", "provenance": { "kind": "package", "implementation": "statsmodels", "version": "0.15.0", "method": "statsmodels ConditionalLogit (Newton, numerical Hessian) on a treatment-coded design (first level of each attribute = 0); part-worths are zero-centred within each attribute and their standard errors come from the same linear map of the covariance matrix. Importance = part-worth range / sum of ranges. The browser engine estimates an effects-coded design." }, "input": { "data": { "columns": ["respondent", "task", "alternative", "brand", "storage", "colour", "chosen"], "rows": [ ["r01", 1, 1, "Gamma", "256GB", "Black", 1], ["r01", 1, 2, "Alpha", "64GB", "Silver", 0], ["r01", 1, 3, "Beta", "64GB", "Silver", 0], ["r01", 2, 1, "Beta", "128GB", "Silver", 1], ["r01", 2, 2, "Beta", "256GB", "Silver", 0], ["r01", 2, 3, "Gamma", "128GB", "Black", 0], ["r01", 3, 1, "Beta", "64GB", "Black", 1], ["r01", 3, 2, "Gamma", "64GB", "Black", 0], ["r01", 3, 3, "Gamma", "256GB", "Black", 0], ["r01", 4, 1, "Gamma", "256GB", "Black", 0], ["r01", 4, 2, "Gamma", "128GB", "Silver", 1], ["r01", 4, 3, "Alpha", "64GB", "Silver", 0], ["r01", 5, 1, "Alpha", "256GB", "Black", 0], ["r01", 5, 2, "Beta", "128GB", "Black", 0], ["r01", 5, 3, "Gamma", "64GB", "Silver", 1], ["r01", 6, 1, "Beta", "64GB", "Black", 0], ["r01", 6, 2, "Alpha", "256GB", "Black", 1], ["r01", 6, 3, "Beta", "128GB", "Silver", 0], ["r01", 7, 1, 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["r15", 6, 2, "Beta", "64GB", "Black", 1], ["r15", 6, 3, "Gamma", "64GB", "Black", 0], ["r15", 7, 1, "Alpha", "64GB", "Black", 0], ["r15", 7, 2, "Beta", "256GB", "Black", 0], ["r15", 7, 3, "Beta", "256GB", "Silver", 1], ["r15", 8, 1, "Alpha", "128GB", "Silver", 0], ["r15", 8, 2, "Alpha", "64GB", "Silver", 1], ["r15", 8, 3, "Alpha", "64GB", "Black", 0], ["r16", 1, 1, "Alpha", "64GB", "Black", 1], ["r16", 1, 2, "Alpha", "128GB", "Silver", 0], ["r16", 1, 3, "Beta", "128GB", "Silver", 0], ["r16", 2, 1, "Gamma", "256GB", "Black", 1], ["r16", 2, 2, "Beta", "64GB", "Silver", 0], ["r16", 2, 3, "Gamma", "64GB", "Silver", 0], ["r16", 3, 1, "Beta", "128GB", "Silver", 0], ["r16", 3, 2, "Alpha", "128GB", "Silver", 1], ["r16", 3, 3, "Alpha", "64GB", "Black", 0], ["r16", 4, 1, "Beta", "64GB", "Black", 0], ["r16", 4, 2, "Alpha", "256GB", "Black", 1], ["r16", 4, 3, "Beta", "64GB", "Silver", 0], ["r16", 5, 1, "Beta", "64GB", "Black", 1], ["r16", 5, 2, "Gamma", "256GB", "Black", 0], ["r16", 5, 3, "Gamma", "64GB", "Silver", 0], ["r16", 6, 1, "Alpha", "256GB", "Black", 1], ["r16", 6, 2, "Gamma", "64GB", "Black", 0], ["r16", 6, 3, "Alpha", "64GB", "Black", 0], ["r16", 7, 1, "Beta", "64GB", "Silver", 0], ["r16", 7, 2, "Alpha", "256GB", "Black", 1], ["r16", 7, 3, "Beta", "128GB", "Silver", 0], ["r16", 8, 1, "Beta", "256GB", "Black", 0], ["r16", 8, 2, "Alpha", "256GB", "Black", 1], ["r16", 8, 3, "Gamma", "128GB", "Black", 0], ["r17", 1, 1, "Beta", "128GB", "Silver", 1], ["r17", 1, 2, "Alpha", "128GB", "Black", 0], ["r17", 1, 3, "Beta", "256GB", "Silver", 0], ["r17", 2, 1, "Gamma", "128GB", "Silver", 0], ["r17", 2, 2, "Beta", "256GB", "Black", 1], ["r17", 2, 3, "Beta", "64GB", "Black", 0], ["r17", 3, 1, "Alpha", "256GB", "Black", 1], ["r17", 3, 2, "Alpha", "64GB", "Silver", 0], ["r17", 3, 3, "Alpha", "128GB", "Black", 0], ["r17", 4, 1, "Beta", "256GB", "Black", 1], ["r17", 4, 2, "Gamma", "256GB", "Black", 0], ["r17", 4, 3, "Beta", "64GB", "Silver", 0], ["r17", 5, 1, "Gamma", "128GB", 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["r18", 4, 3, "Alpha", "256GB", "Black", 0], ["r18", 5, 1, "Beta", "256GB", "Black", 1], ["r18", 5, 2, "Alpha", "128GB", "Black", 0], ["r18", 5, 3, "Beta", "128GB", "Black", 0], ["r18", 6, 1, "Gamma", "256GB", "Black", 1], ["r18", 6, 2, "Alpha", "128GB", "Silver", 0], ["r18", 6, 3, "Alpha", "64GB", "Black", 0], ["r18", 7, 1, "Gamma", "64GB", "Silver", 0], ["r18", 7, 2, "Gamma", "256GB", "Black", 0], ["r18", 7, 3, "Beta", "64GB", "Silver", 1], ["r18", 8, 1, "Beta", "256GB", "Black", 0], ["r18", 8, 2, "Alpha", "128GB", "Black", 1], ["r18", 8, 3, "Beta", "256GB", "Silver", 0], ["r19", 1, 1, "Alpha", "64GB", "Black", 1], ["r19", 1, 2, "Alpha", "128GB", "Silver", 0], ["r19", 1, 3, "Gamma", "64GB", "Silver", 0], ["r19", 2, 1, "Beta", "256GB", "Silver", 1], ["r19", 2, 2, "Beta", "64GB", "Black", 0], ["r19", 2, 3, "Gamma", "128GB", "Silver", 0], ["r19", 3, 1, "Beta", "128GB", "Silver", 1], ["r19", 3, 2, "Alpha", "128GB", "Silver", 0], ["r19", 3, 3, "Gamma", "64GB", "Silver", 0], ["r19", 4, 1, 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"Silver", 0], ["r50", 8, 2, "Alpha", "128GB", "Black", 0], ["r50", 8, 3, "Gamma", "256GB", "Black", 1] ] }, "layout": { "respondent": "respondent", "task": "task", "alternative": "alternative", "attributes": ["brand", "storage", "colour"], "chosen": "chosen", "linear": [] } }, "expected": [ {"metric": "Part-worth: brand = Alpha", "value": 0.4911023682918021, "tolerance": 1e-07}, {"metric": "Part-worth: brand = Beta", "value": -0.005255825484773158, "tolerance": 1e-07}, {"metric": "Part-worth: brand = Gamma", "value": -0.4858465428070291, "tolerance": 1e-07}, {"metric": "Part-worth: storage = 64GB", "value": -0.6154731442250585, "tolerance": 1e-07}, {"metric": "Part-worth: storage = 128GB", "value": 0.01978923304778679, "tolerance": 1e-07}, {"metric": "Part-worth: storage = 256GB", "value": 0.5956839111772718, "tolerance": 1e-07}, {"metric": "Part-worth: colour = Black", "value": 0.18062104153320743, "tolerance": 1e-07}, {"metric": "Part-worth: colour = Silver", "value": -0.18062104153320743, "tolerance": 1e-07}, {"metric": "Standard error: brand = Alpha", "value": 0.08863237844681918, "tolerance": 1e-06}, {"metric": "Standard error: brand = Beta", "value": 0.08823545732015452, "tolerance": 1e-06}, {"metric": "Standard error: brand = Gamma", "value": 0.10048133293651902, "tolerance": 1e-06}, {"metric": "Standard error: storage = 64GB", "value": 0.09789763449717172, "tolerance": 1e-06}, {"metric": "Standard error: storage = 128GB", "value": 0.09096899608244992, "tolerance": 1e-06}, {"metric": "Standard error: storage = 256GB", "value": 0.08890773209596858, "tolerance": 1e-06}, {"metric": "Standard error: colour = Black", "value": 0.06279964217682002, "tolerance": 1e-06}, {"metric": "Standard error: colour = Silver", "value": 0.06279964217682002, "tolerance": 1e-06}, {"metric": "Importance (%): brand", "value": 38.321519545538024, "tolerance": 1e-06}, {"metric": "Importance (%): storage", "value": 47.5085014620804, "tolerance": 1e-06}, {"metric": "Importance (%): colour", "value": 14.16997899238157, "tolerance": 1e-06}, {"metric": "Log-likelihood", "value": -387.689636968529, "tolerance": 1e-08} ] }, { "id": "cbc-linear-price-none-option", "procedure": "cbc-conjoint", "label": "CBC conjoint: linear price and a none option, 50 respondents × 8 tasks × 3 profiles + none", "provenance": { "kind": "package", "implementation": "statsmodels", "version": "0.15.0", "method": "statsmodels ConditionalLogit (Newton, numerical Hessian) on a treatment-coded design (first level of each attribute = 0, linear attributes as raw values, none alternative as its own constant); part-worths are zero-centred within each attribute and their standard errors come from the same linear map of the covariance matrix. Importance = part-worth range / sum of ranges. 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"alternative": "alternative", "attributes": ["brand", "screen", "price"], "chosen": "chosen", "linear": ["price"] } }, "expected": [ {"metric": "Part-worth: brand = Alpha", "value": 0.3021465726794317, "tolerance": 1e-07}, {"metric": "Part-worth: brand = Beta", "value": -0.15366370359426246, "tolerance": 1e-07}, {"metric": "Part-worth: brand = Gamma", "value": -0.14848286908516933, "tolerance": 1e-07}, {"metric": "Part-worth: screen = Small", "value": -0.48500561990658025, "tolerance": 1e-07}, {"metric": "Part-worth: screen = Medium", "value": 0.28046409100996744, "tolerance": 1e-07}, {"metric": "Part-worth: screen = Large", "value": 0.20454152889661303, "tolerance": 1e-07}, {"metric": "Part-worth: price = 199", "value": 0.6977006647421341, "tolerance": 1e-07}, {"metric": "Part-worth: price = 249", "value": 0.232566888247378, "tolerance": 1e-07}, {"metric": "Part-worth: price = 299", "value": -0.232566888247378, "tolerance": 1e-07}, {"metric": "Part-worth: price = 349", "value": 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"Importance (%): brand", "value": 17.419403477568856, "tolerance": 1e-06}, {"metric": "Importance (%): screen", "value": 29.25345574329886, "tolerance": 1e-06}, {"metric": "Importance (%): price", "value": 53.327140779132286, "tolerance": 1e-06}, {"metric": "Utility per unit: price", "value": -0.00930267552989512, "tolerance": 1e-08}, {"metric": "None utility", "value": -0.5694361312606371, "tolerance": 1e-07}, {"metric": "None standard error", "value": 0.14480230753972945, "tolerance": 1e-06}, {"metric": "Log-likelihood", "value": -491.46664869846927, "tolerance": 1e-08} ] }, { "id": "latent-class-categorical-2-classes", "procedure": "latent-class", "label": "Latent class analysis: 2 classes, 5 three-category indicators, n = 400", "provenance": { "kind": "package", "implementation": "stepmix", "version": "3.0.0", "method": "stepmix.StepMix(n_components=2, measurement='categorical', n_init=50, max_iter=5000, abs_tol=1e-13), best of 50 random starts; log-likelihood = score × n; BIC and AIC from StepMix.bic / StepMix.aic. Classes are ordered by share (largest first) on both sides, so label switching cannot affect the comparison. The browser engine runs 50 starts and stops when the relative log-likelihood gain falls below 10⁻¹⁰, which is why parameter tolerances are wider than for closed-form procedures." }, "input": { "data": { "columns": ["q1", "q2", "q3", "q4", "q5"], "rows": [ ["3", "1", "3", "3", "3"], ["2", "2", "3", "2", "2"], ["1", "3", "1", "2", "1"], ["1", "1", "1", "1", "1"], ["3", "2", "1", "2", "3"], ["1", "1", "2", "3", "3"], ["2", "1", "2", "3", "1"], ["1", "1", "1", "2", "2"], ["1", "1", "1", "1", "1"], ["1", "1", "1", "1", "1"], ["2", "1", "2", "3", "1"], ["3", "3", "3", "3", "3"], ["1", "1", "2", "1", "1"], ["3", "3", "3", "3", "3"], ["3", "1", "1", "2", "3"], ["1", "1", "1", "3", "1"], ["3", "3", "2", "3", "2"], ["1", "1", "1", "1", "1"], ["2", "3", "3", "3", "3"], ["2", "1", "1", "1", "1"], ["2", "3", "3", "3", "3"], ["3", "1", "1", "1", "1"], ["1", "1", "1", "1", "2"], ["1", "1", "1", "2", "1"], ["2", "1", "2", "2", "2"], ["2", "3", "3", "3", "3"], ["1", "1", "1", "2", "1"], ["1", "1", "2", 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"value": 0.23584445318647804, "tolerance": 0.001}, {"metric": "Class 1: P(q2 = 3)", "value": 0.11919953734464195, "tolerance": 0.001}, {"metric": "Class 1: P(q3 = 1)", "value": 0.7684844126086643, "tolerance": 0.001}, {"metric": "Class 1: P(q3 = 2)", "value": 0.1594497515118115, "tolerance": 0.001}, {"metric": "Class 1: P(q3 = 3)", "value": 0.07206583587952359, "tolerance": 0.001}, {"metric": "Class 1: P(q4 = 1)", "value": 0.5379239444092705, "tolerance": 0.001}, {"metric": "Class 1: P(q4 = 2)", "value": 0.3623828392746237, "tolerance": 0.001}, {"metric": "Class 1: P(q4 = 3)", "value": 0.09969321631610531, "tolerance": 0.001}, {"metric": "Class 1: P(q5 = 1)", "value": 0.6730814154893965, "tolerance": 0.001}, {"metric": "Class 1: P(q5 = 2)", "value": 0.22290457594984658, "tolerance": 0.001}, {"metric": "Class 1: P(q5 = 3)", "value": 0.10401400856075571, "tolerance": 0.001}, {"metric": "Class 2: P(q1 = 1)", "value": 0.08654213256874849, "tolerance": 0.001}, {"metric": "Class 2: P(q1 = 2)", "value": 0.3732208674225179, "tolerance": 0.001}, {"metric": "Class 2: P(q1 = 3)", "value": 0.5402370000087329, "tolerance": 0.001}, {"metric": "Class 2: P(q2 = 1)", "value": 0.30152956319394497, "tolerance": 0.001}, {"metric": "Class 2: P(q2 = 2)", "value": 0.21291965014716366, "tolerance": 0.001}, {"metric": "Class 2: P(q2 = 3)", "value": 0.4855507866588905, "tolerance": 0.001}, {"metric": "Class 2: P(q3 = 1)", "value": 0.0793645165258962, "tolerance": 0.001}, {"metric": "Class 2: P(q3 = 2)", "value": 0.4459983395398848, "tolerance": 0.001}, {"metric": "Class 2: P(q3 = 3)", "value": 0.4746371439342181, "tolerance": 0.001}, {"metric": "Class 2: P(q4 = 1)", "value": 0.18293847073251676, "tolerance": 0.001}, {"metric": "Class 2: P(q4 = 2)", "value": 0.1670886775344875, "tolerance": 0.001}, {"metric": "Class 2: P(q4 = 3)", "value": 0.6499728517329951, "tolerance": 0.001}, {"metric": "Class 2: P(q5 = 1)", "value": 0.17507036256223066, "tolerance": 0.001}, {"metric": "Class 2: P(q5 = 2)", "value": 0.28018337543703375, "tolerance": 0.001}, {"metric": "Class 2: P(q5 = 3)", "value": 0.5447462620007351, "tolerance": 0.001} ] }, { "id": "latent-class-categorical-3-classes", "procedure": "latent-class", "label": "Latent class analysis: 3 classes, 5 three-category indicators, n = 400", "provenance": { "kind": "package", "implementation": "stepmix", "version": "3.0.0", "method": "stepmix.StepMix(n_components=3, measurement='categorical', n_init=50, max_iter=5000, abs_tol=1e-13), best of 50 random starts; log-likelihood = score × n; BIC and AIC from StepMix.bic / StepMix.aic. Classes are ordered by share (largest first) on both sides, so label switching cannot affect the comparison. 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P(q5 = 1)", "value": 0.1368174522762035, "tolerance": 0.001}, {"metric": "Class 2: P(q5 = 2)", "value": 0.18241837201530073, "tolerance": 0.001}, {"metric": "Class 2: P(q5 = 3)", "value": 0.6807641757084958, "tolerance": 0.001}, {"metric": "Class 3: P(q1 = 1)", "value": 0.27674860126376555, "tolerance": 0.001}, {"metric": "Class 3: P(q1 = 2)", "value": 0.6299684433320636, "tolerance": 0.001}, {"metric": "Class 3: P(q1 = 3)", "value": 0.09328295540417095, "tolerance": 0.001}, {"metric": "Class 3: P(q2 = 1)", "value": 0.6688644133050176, "tolerance": 0.001}, {"metric": "Class 3: P(q2 = 2)", "value": 0.3098010245779313, "tolerance": 0.001}, {"metric": "Class 3: P(q2 = 3)", "value": 0.021334562117051183, "tolerance": 0.001}, {"metric": "Class 3: P(q3 = 1)", "value": 0.04177719846380667, "tolerance": 0.001}, {"metric": "Class 3: P(q3 = 2)", "value": 0.8087211070594162, "tolerance": 0.001}, {"metric": "Class 3: P(q3 = 3)", "value": 0.1495016944767771, "tolerance": 0.001}, {"metric": "Class 3: P(q4 = 1)", "value": 0.0381825861084885, "tolerance": 0.001}, {"metric": "Class 3: P(q4 = 2)", "value": 0.2002416725750934, "tolerance": 0.001}, {"metric": "Class 3: P(q4 = 3)", "value": 0.7615757413164181, "tolerance": 0.001}, {"metric": "Class 3: P(q5 = 1)", "value": 0.33612564444978865, "tolerance": 0.001}, {"metric": "Class 3: P(q5 = 2)", "value": 0.5471294386143626, "tolerance": 0.001}, {"metric": "Class 3: P(q5 = 3)", "value": 0.11674491693584883, "tolerance": 0.001} ] }, { "id": "key-driver-dominance-relative-weights-5-drivers", "procedure": "relative-importance", "label": "Key driver analysis: 5 rating drivers, n = 250", "provenance": { "kind": "package", "implementation": "dominance-analysis", "version": "1.1.9", "method": "dominance_analysis.Dominance(objective=1).incremental_rsquare(): general dominance from scikit-learn LinearRegression R² over all 31 driver subsets (equal to the LMG / Shapley decomposition). Johnson's (2000) relative weights recomputed from the SVD of the standardized data matrix (orthogonal counterparts P·Q′, least squares in NumPy). Standardized betas and R² from statsmodels OLS on z-scored variables." }, "input": { "data": { "columns": ["quality", "price", "service", "speed", "support", "satisfaction"], "rows": [ [6.0, 9.0, 6.0, 2.0, 6.0, 8.09], [7.0, 7.0, 7.0, 6.0, 5.0, 9.14], [5.0, 5.0, 2.0, 4.0, 7.0, 4.9], [5.0, 10.0, 5.0, 4.0, 8.0, 6.23], [3.0, 4.0, 2.0, 2.0, 4.0, 3.59], [4.0, 3.0, 5.0, 5.0, 8.0, 6.31], [5.0, 9.0, 5.0, 5.0, 6.0, 11.27], [7.0, 7.0, 7.0, 6.0, 6.0, 3.79], [5.0, 4.0, 8.0, 4.0, 8.0, 7.67], [5.0, 5.0, 4.0, 4.0, 9.0, 3.67], [7.0, 6.0, 5.0, 5.0, 1.0, 8.67], [6.0, 8.0, 6.0, 7.0, 9.0, 9.07], [7.0, 5.0, 2.0, 6.0, 4.0, 6.94], [5.0, 2.0, 5.0, 3.0, 4.0, 2.79], [6.0, 8.0, 6.0, 4.0, 4.0, 10.58], [7.0, 6.0, 4.0, 5.0, 3.0, 6.08], [7.0, 7.0, 3.0, 6.0, 4.0, 5.29], [7.0, 4.0, 3.0, 6.0, 8.0, 7.72], [6.0, 4.0, 6.0, 2.0, 7.0, 6.47], [6.0, 8.0, 4.0, 2.0, 8.0, 7.96], [6.0, 3.0, 5.0, 5.0, 7.0, 5.3], [8.0, 8.0, 6.0, 9.0, 7.0, 10.22], [7.0, 7.0, 7.0, 6.0, 1.0, 9.21], [7.0, 7.0, 7.0, 4.0, 5.0, 4.68], [5.0, 6.0, 5.0, 6.0, 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[3.0, 4.0, 5.0, 6.0, 3.0, 5.71], [7.0, 4.0, 10.0, 6.0, 6.0, 9.41], [4.0, 4.0, 5.0, 5.0, 8.0, 8.81], [5.0, 6.0, 6.0, 5.0, 8.0, 9.19], [6.0, 3.0, 10.0, 7.0, 3.0, 8.09], [5.0, 6.0, 2.0, 3.0, 9.0, 6.09], [5.0, 4.0, 5.0, 5.0, 4.0, 10.03], [8.0, 7.0, 4.0, 4.0, 5.0, 4.64], [7.0, 6.0, 6.0, 9.0, 5.0, 5.54], [4.0, 7.0, 3.0, 5.0, 6.0, 5.53], [4.0, 7.0, 4.0, 6.0, 2.0, 4.76], [7.0, 7.0, 8.0, 7.0, 6.0, 10.67], [4.0, 3.0, 5.0, 1.0, 3.0, 4.27], [5.0, 5.0, 8.0, 4.0, 6.0, 7.57], [7.0, 5.0, 7.0, 6.0, 4.0, 6.88], [7.0, 6.0, 9.0, 7.0, 5.0, 9.87], [5.0, 3.0, 4.0, 6.0, 5.0, 7.46], [5.0, 8.0, 8.0, 3.0, 7.0, 7.68], [9.0, 4.0, 7.0, 9.0, 8.0, 10.56], [7.0, 4.0, 6.0, 3.0, 2.0, 8.61], [9.0, 7.0, 7.0, 7.0, 5.0, 8.97], [3.0, 7.0, 6.0, 8.0, 7.0, 5.34], [3.0, 4.0, 7.0, 7.0, 7.0, 5.88], [4.0, 2.0, 1.0, 3.0, 4.0, 2.89], [2.0, 6.0, 5.0, 6.0, 4.0, 5.56], [4.0, 7.0, 4.0, 3.0, 2.0, 4.94], [5.0, 9.0, 3.0, 6.0, 5.0, 9.64], [5.0, 6.0, 6.0, 6.0, 4.0, 7.76], [4.0, 4.0, 2.0, 3.0, 5.0, 3.57], [4.0, 6.0, 6.0, 6.0, 6.0, 8.66], [8.0, 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5.0, 6.0, 7.39], [9.0, 10.0, 7.0, 3.0, 5.0, 8.33], [6.0, 7.0, 5.0, 5.0, 6.0, 6.41], [8.0, 6.0, 6.0, 7.0, 5.0, 9.99], [3.0, 3.0, 4.0, 4.0, 5.0, 3.66], [7.0, 4.0, 6.0, 4.0, 7.0, 7.48], [4.0, 6.0, 5.0, 5.0, 3.0, 5.99], [6.0, 4.0, 4.0, 7.0, 6.0, 7.68], [7.0, 10.0, 6.0, 5.0, 2.0, 9.35], [3.0, 4.0, 2.0, 8.0, 6.0, 3.78], [5.0, 6.0, 4.0, 5.0, 6.0, 5.3], [7.0, 5.0, 8.0, 7.0, 8.0, 7.89], [10.0, 7.0, 6.0, 8.0, 7.0, 11.56], [6.0, 7.0, 6.0, 5.0, 6.0, 8.32], [8.0, 8.0, 8.0, 5.0, 5.0, 10.17], [10.0, 5.0, 7.0, 8.0, 8.0, 8.44], [5.0, 6.0, 8.0, 7.0, 6.0, 8.59], [6.0, 6.0, 9.0, 4.0, 5.0, 5.39], [7.0, 9.0, 8.0, 7.0, 4.0, 10.62], [5.0, 6.0, 5.0, 5.0, 4.0, 5.6], [9.0, 6.0, 6.0, 6.0, 8.0, 10.03], [6.0, 4.0, 4.0, 6.0, 5.0, 6.5], [5.0, 7.0, 4.0, 8.0, 5.0, 6.17], [4.0, 5.0, 7.0, 5.0, 5.0, 6.16], [6.0, 4.0, 4.0, 4.0, 7.0, 5.59], [5.0, 5.0, 4.0, 4.0, 5.0, 5.99], [8.0, 6.0, 7.0, 7.0, 8.0, 9.62], [3.0, 4.0, 5.0, 4.0, 7.0, 5.36], [7.0, 7.0, 6.0, 6.0, 5.0, 7.6], [2.0, 3.0, 2.0, 4.0, 2.0, 6.06], [3.0, 8.0, 3.0, 6.0, 5.0, 5.44], [4.0, 9.0, 3.0, 3.0, 2.0, 6.89], [2.0, 4.0, 8.0, 2.0, 2.0, 7.54], [4.0, 8.0, 10.0, 3.0, 4.0, 10.4], [4.0, 4.0, 8.0, 3.0, 8.0, 6.41], [6.0, 6.0, 2.0, 7.0, 8.0, 6.51], [4.0, 5.0, 3.0, 2.0, 4.0, 7.92], [5.0, 6.0, 3.0, 1.0, 4.0, 9.0], [10.0, 9.0, 8.0, 10.0, 7.0, 10.82], [3.0, 6.0, 5.0, 7.0, 6.0, 5.72], [4.0, 7.0, 3.0, 5.0, 5.0, 3.35], [7.0, 7.0, 4.0, 7.0, 7.0, 6.59], [4.0, 8.0, 8.0, 7.0, 4.0, 7.69], [7.0, 9.0, 8.0, 7.0, 4.0, 11.62], [8.0, 9.0, 7.0, 5.0, 3.0, 7.59], [6.0, 7.0, 5.0, 3.0, 5.0, 5.49], [5.0, 4.0, 1.0, 7.0, 4.0, 3.87], [7.0, 5.0, 6.0, 7.0, 8.0, 9.27], [9.0, 6.0, 7.0, 7.0, 6.0, 9.42], [4.0, 5.0, 8.0, 2.0, 4.0, 5.86], [7.0, 6.0, 6.0, 7.0, 6.0, 8.52], [4.0, 7.0, 6.0, 5.0, 1.0, 6.15], [6.0, 2.0, 5.0, 8.0, 5.0, 7.0], [5.0, 5.0, 2.0, 4.0, 6.0, 5.44], [4.0, 7.0, 4.0, 3.0, 3.0, 7.07], [4.0, 5.0, 7.0, 7.0, 8.0, 5.69], [3.0, 4.0, 6.0, 2.0, 5.0, 4.82], [6.0, 3.0, 5.0, 7.0, 7.0, 3.61], [5.0, 8.0, 7.0, 5.0, 6.0, 9.08], [4.0, 3.0, 4.0, 5.0, 2.0, 5.17], [7.0, 5.0, 8.0, 5.0, 8.0, 8.01], [6.0, 6.0, 7.0, 5.0, 5.0, 9.49], [8.0, 7.0, 3.0, 5.0, 10.0, 7.53], [6.0, 5.0, 4.0, 5.0, 6.0, 9.63], [4.0, 5.0, 4.0, 9.0, 5.0, 3.82], [5.0, 5.0, 7.0, 4.0, 4.0, 5.21], [3.0, 7.0, 5.0, 6.0, 2.0, 5.48], [6.0, 6.0, 5.0, 5.0, 7.0, 8.28], [1.0, 5.0, 7.0, 2.0, 5.0, 3.98], [5.0, 3.0, 2.0, 6.0, 5.0, 4.73], [5.0, 6.0, 5.0, 5.0, 8.0, 6.83], [10.0, 5.0, 5.0, 6.0, 8.0, 9.7], [3.0, 8.0, 5.0, 6.0, 3.0, 6.43], [9.0, 10.0, 8.0, 6.0, 6.0, 10.16], [10.0, 5.0, 7.0, 5.0, 1.0, 11.8], [1.0, 4.0, 3.0, 1.0, 5.0, 3.64], [5.0, 6.0, 8.0, 4.0, 2.0, 9.34], [8.0, 8.0, 4.0, 5.0, 3.0, 7.58], [3.0, 3.0, 6.0, 6.0, 7.0, 5.19], [7.0, 6.0, 6.0, 3.0, 7.0, 6.49], [4.0, 7.0, 6.0, 3.0, 9.0, 7.36], [9.0, 5.0, 9.0, 7.0, 5.0, 10.8], [6.0, 2.0, 4.0, 6.0, 4.0, 7.01], [8.0, 6.0, 7.0, 9.0, 4.0, 10.74], [6.0, 7.0, 3.0, 3.0, 7.0, 7.26], [6.0, 4.0, 6.0, 7.0, 4.0, 6.04], [6.0, 7.0, 5.0, 2.0, 5.0, 6.95], [4.0, 4.0, 7.0, 2.0, 7.0, 6.25], [6.0, 8.0, 3.0, 4.0, 6.0, 5.26], [7.0, 6.0, 5.0, 6.0, 5.0, 6.61], [8.0, 7.0, 6.0, 3.0, 5.0, 9.52], [5.0, 6.0, 8.0, 7.0, 7.0, 6.24], [5.0, 3.0, 4.0, 9.0, 8.0, 6.89], [7.0, 8.0, 5.0, 6.0, 7.0, 9.4], [6.0, 7.0, 4.0, 5.0, 5.0, 8.58], [8.0, 8.0, 7.0, 9.0, 9.0, 8.06], [7.0, 7.0, 5.0, 9.0, 5.0, 8.68], [5.0, 4.0, 8.0, 6.0, 9.0, 8.65], [4.0, 5.0, 3.0, 3.0, 6.0, 4.43], [8.0, 3.0, 5.0, 6.0, 8.0, 5.12], [8.0, 5.0, 8.0, 4.0, 4.0, 9.95], [6.0, 4.0, 4.0, 5.0, 5.0, 6.14], [2.0, 4.0, 4.0, 4.0, 6.0, 4.41], [6.0, 6.0, 5.0, 5.0, 7.0, 7.89], [6.0, 4.0, 5.0, 4.0, 4.0, 3.68] ] }, "outcome": "satisfaction", "drivers": ["quality", "price", "service", "speed", "support"] }, "expected": [ {"metric": "R²", "value": 0.5226215856949203, "tolerance": 1e-12}, {"metric": "Standardized beta: quality", "value": 0.42247802026902787, "tolerance": 1e-10}, {"metric": "Standardized beta: price", "value": 0.27342907650976706, "tolerance": 1e-10}, {"metric": "Standardized beta: service", "value": 0.25392070686317764, "tolerance": 1e-10}, {"metric": "Standardized beta: speed", "value": 0.06889157974718255, "tolerance": 1e-10}, {"metric": "Standardized beta: support", "value": -0.012562591352606772, "tolerance": 1e-10}, {"metric": "General dominance (Shapley R²): quality", "value": 0.23576941664944284, "tolerance": 1e-12}, {"metric": "General dominance (Shapley R²): price", "value": 0.12334489588210151, "tolerance": 1e-12}, {"metric": "General dominance (Shapley R²): service", "value": 0.11968732880399743, "tolerance": 1e-12}, {"metric": "General dominance (Shapley R²): speed", "value": 0.03710532909537996, "tolerance": 1e-12}, {"metric": "General dominance (Shapley R²): support", "value": 0.006714615263998594, "tolerance": 1e-12}, {"metric": "General dominance share (%): quality", "value": 45.11283557795352, "tolerance": 1e-09}, {"metric": "General dominance share (%): price", "value": 23.60118664407863, "tolerance": 1e-09}, {"metric": "General dominance share (%): service", "value": 22.901336661181222, "tolerance": 1e-09}, {"metric": "General dominance share (%): speed", "value": 7.099846257984481, "tolerance": 1e-09}, {"metric": "General dominance share (%): support", "value": 1.284794858802147, "tolerance": 1e-09}, {"metric": "Johnson relative weight: quality", "value": 0.22912558484379392, "tolerance": 1e-12}, {"metric": "Johnson relative weight: price", "value": 0.12628957113597397, "tolerance": 1e-12}, {"metric": "Johnson relative weight: service", "value": 0.12200529478694853, "tolerance": 1e-12}, {"metric": "Johnson relative weight: speed", "value": 0.038141703025974465, "tolerance": 1e-12}, {"metric": "Johnson relative weight: support", "value": 0.0070594319022303014, "tolerance": 1e-12}, {"metric": "Johnson relative weight share (%): quality", "value": 43.84158464085058, "tolerance": 1e-09}, {"metric": "Johnson relative weight share (%): price", "value": 24.164629742196556, "tolerance": 1e-09}, {"metric": "Johnson relative weight share (%): service", "value": 23.344863305774165, "tolerance": 1e-09}, {"metric": "Johnson relative weight share (%): speed", "value": 7.298149190538722, "tolerance": 1e-09}, {"metric": "Johnson relative weight share (%): support", "value": 1.350773120640148, "tolerance": 1e-09} ] }, { "id": "turf-top-two-box-weighted-8-items", "procedure": "turf", "label": "TURF: 8 items rated 1–5, top-two-box reach, weighted, n = 150", "provenance": { "kind": "independent-recomputation", "implementation": "NumPy", "version": "2.5.4", "method": "Exhaustive itertools.combinations search of every portfolio of 1–4 items; reach = weighted share reached by at least one item (rating ≥ 4), frequency = weighted mean number of items reaching a respondent. The best portfolio is named in each metric, so the browser engine must pick the same items." }, "input": { "data": { "columns": ["Apple", "Banana", "Cherry", "Grape", "Lemon", "Mango", "Peach", "Strawberry", "weight"], "rows": [ [3, 5, 2, 5, 5, 1, 3, 3, 1.35], [2, 3, 3, 3, 1, 2, 5, 5, 1.47], [3, 3, 1, 1, 1, 4, 2, 1, 1.25], [4, 1, 4, 3, 1, 4, 5, 4, 1.25], [5, 3, 4, 1, 2, 2, 1, 3, 1.32], [2, 1, 2, 5, 1, 3, 2, 5, 0.77], [1, 3, 4, 1, 2, 4, 3, 2, 0.89], [5, 2, 1, 4, 3, 4, 2, 2, 1.09], [2, 5, 3, 3, 3, 4, 1, 4, 1.21], [1, 4, 4, 3, 1, 1, 1, 4, 1.36], [5, 3, 3, 2, 2, 2, 5, 5, 0.68], [1, 2, 5, 4, 5, 5, 1, 3, 0.66], [5, 1, 5, 3, 1, 5, 3, 3, 1.24], [2, 3, 2, 3, 5, 4, 5, 1, 1.4], [5, 1, 1, 2, 1, 5, 2, 2, 0.91], [4, 1, 3, 5, 2, 3, 3, 3, 0.63], [3, 2, 5, 3, 1, 3, 4, 5, 1.39], [4, 1, 4, 2, 3, 4, 2, 5, 0.97], [3, 5, 2, 4, 3, 2, 2, 4, 1.34], [3, 1, 5, 3, 4, 5, 2, 3, 1.39], [4, 1, 1, 3, 1, 5, 1, 4, 1.59], [5, 2, 3, 3, 1, 5, 3, 3, 1.57], [1, 1, 2, 3, 3, 1, 2, 5, 1.39], [5, 3, 4, 5, 2, 2, 1, 3, 1.51], [4, 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5, 1, 1, 1.54] ] }, "items": ["Apple", "Banana", "Cherry", "Grape", "Lemon", "Mango", "Peach", "Strawberry"], "rule": {"kind": "top-2-box", "scaleMax": 5}, "weightColumn": "weight", "portfolioSizes": [1, 2, 3, 4] }, "expected": [ {"metric": "Best 1-item reach: Apple", "value": 0.4923281382143288, "tolerance": 1e-12}, {"metric": "Best 1-item frequency: Apple", "value": 0.4923281382143288, "tolerance": 1e-12}, {"metric": "Best 2-item reach: Apple + Strawberry", "value": 0.7293705448834118, "tolerance": 1e-12}, {"metric": "Best 2-item frequency: Apple + Strawberry", "value": 0.970399903346623, "tolerance": 1e-12}, {"metric": "Best 3-item reach: Apple + Mango + Strawberry", "value": 0.8662558898151503, "tolerance": 1e-12}, {"metric": "Best 3-item frequency: Apple + Mango + Strawberry", "value": 1.4004470218678262, "tolerance": 1e-12}, { "metric": "Best 4-item reach: Apple + Banana + Mango + Strawberry", "value": 0.9254560831219039, "tolerance": 1e-12 }, { "metric": "Best 4-item frequency: Apple + Banana + Mango + Strawberry", "value": 1.766763320043494, "tolerance": 1e-12 } ] }, { "id": "nps-score-distribution-150", "procedure": "nps", "label": "NPS from a 0–10 score distribution, n = 150", "provenance": { "kind": "independent-recomputation", "implementation": "SciPy", "version": "1.18.1", "method": "NPS computed as the mean of +1 (9–10) / 0 (7–8) / −1 (0–6) codes; its standard error is the population standard deviation of those codes over √n (√n_eff, Kish, for weighted data), with z from scipy.stats.norm.ppf. Adjusted Wald adds ¾ promoter, 1½ passive and ¾ detractor pseudo-respondents (Rocks 2016)." }, "input": { "kind": "score-counts", "scoreCounts": [4, 2, 3, 5, 6, 9, 14, 22, 31, 28, 26], "confidence": 0.95 }, "expected": [ {"metric": "NPS", "value": 7.333333333333333, "tolerance": 1e-10}, {"metric": "Standard error", "value": 6.538546672815955, "tolerance": 1e-10}, {"metric": "95% CI lower (Wald)", "value": -5.481982656620138, "tolerance": 1e-10}, {"metric": "95% CI upper (Wald)", "value": 20.148649323286804, "tolerance": 1e-10}, {"metric": "Adjusted-Wald NPS", "value": 7.189542483660133, "tolerance": 1e-10}, {"metric": "95% CI lower (adjusted Wald)", "value": -5.473098056755068, "tolerance": 1e-10}, {"metric": "95% CI upper (adjusted Wald)", "value": 19.852183024075334, "tolerance": 1e-10} ] }, { "id": "nps-weighted-respondents-220", "procedure": "nps", "label": "NPS from weighted respondent scores, n = 220", "provenance": { "kind": "independent-recomputation", "implementation": "SciPy", "version": "1.18.1", "method": "NPS computed as the mean of +1 (9–10) / 0 (7–8) / −1 (0–6) codes; its standard error is the population standard deviation of those codes over √n (√n_eff, Kish, for weighted data), with z from scipy.stats.norm.ppf. Adjusted Wald adds ¾ promoter, 1½ passive and ¾ detractor pseudo-respondents (Rocks 2016). Weighted shares use the respondent weights." }, "input": { "kind": "weighted-rows", "data": { "columns": ["score", "weight"], "rows": [ [4, 2.47], [8, 1.54], [8, 1.21], [9, 2.18], [8, 2.24], [9, 0.98], [10, 0.68], [5, 1.38], [4, 1.33], [7, 2.39], [4, 1.18], [9, 1.92], [6, 1.13], [9, 2.33], [8, 2.18], [7, 2.09], [9, 1.36], [9, 1.79], [9, 0.43], [7, 1.13], [7, 0.48], [8, 1.03], [10, 1.89], [10, 1.77], [8, 2.22], [10, 0.9], [9, 1.53], [7, 0.67], [6, 0.73], [9, 1.43], [10, 2.48], [5, 1.63], [7, 2.08], [10, 0.56], [9, 1.4], [7, 0.59], [8, 1.56], [8, 1.59], [8, 2.22], [9, 0.92], [6, 0.72], [5, 0.97], [6, 2.43], [6, 1.75], [9, 0.83], [9, 1.55], [8, 1.31], [10, 1.58], [5, 1.92], [7, 2.33], [2, 2.19], [7, 0.54], [5, 1.32], [6, 1.18], [9, 1.24], [10, 0.57], [4, 2.06], [8, 2.25], [7, 2.03], [9, 1.18], [10, 1.59], [8, 1.12], [0, 1.15], [6, 1.08], [10, 1.87], [8, 0.61], [7, 1.25], [6, 1.59], [8, 1.46], [9, 0.41], [9, 2.34], [7, 1.93], [7, 0.87], [9, 1.52], [7, 2.32], [8, 1.61], [8, 1.9], [6, 0.44], [9, 0.65], [9, 1.72], [9, 1.44], [7, 1.5], [4, 1.8], [10, 1.41], [10, 1.73], [8, 2.15], [7, 1.98], [10, 0.81], [10, 0.59], [7, 2.28], [9, 1.55], [8, 1.48], [7, 0.54], [5, 1.54], [4, 1.79], [4, 0.51], [8, 2.46], [10, 1.24], [5, 0.82], [1, 1.72], [10, 0.55], [1, 1.66], [8, 1.98], [7, 1.74], [8, 2.36], [9, 1.92], [4, 0.96], [8, 1.63], [8, 1.97], [0, 0.48], [8, 1.79], [7, 2.3], [7, 0.46], [8, 1.18], [0, 0.47], [7, 0.62], [9, 1.12], [4, 2.19], [9, 1.22], [8, 2.11], [7, 0.97], [8, 1.61], [10, 1.33], [8, 1.91], [8, 2.13], [10, 1.45], [8, 0.77], [9, 1.95], [10, 1.04], [7, 1.89], [0, 1.58], [8, 0.98], [4, 0.8], [7, 0.69], [8, 1.05], [3, 0.5], [6, 2.2], [8, 0.85], [10, 1.42], [8, 1.08], [10, 0.76], [10, 1.03], [9, 2.25], [9, 1.62], [9, 1.86], [9, 0.83], [3, 1.22], [7, 2.3], [10, 2.17], [8, 2.48], [10, 1.55], [8, 2.1], [9, 1.7], [8, 2.36], [4, 0.52], [0, 2.09], [7, 0.75], [7, 1.19], [8, 0.64], [6, 1.47], [9, 2.3], [7, 1.19], [8, 1.5], [8, 2.29], [8, 2.22], [9, 0.77], [7, 2.11], [6, 1.08], [4, 1.06], [10, 0.97], [9, 1.39], [8, 2.09], [5, 1.47], [8, 1.31], [10, 1.68], [8, 0.68], [7, 1.79], [8, 1.69], [9, 0.8], [8, 1.9], [8, 1.7], [9, 2.03], [8, 1.29], [6, 2.1], [9, 2.5], [5, 1.44], [9, 1.74], [7, 1.33], [0, 2.06], [8, 0.63], [8, 1.3], [7, 1.19], [10, 1.18], [10, 1.39], [0, 1.04], [5, 2.43], [7, 1.13], [6, 1.76], [8, 1.39], [1, 1.91], [10, 0.99], [10, 2.02], [8, 1.9], [2, 1.21], [4, 1.33], [7, 2.48], [8, 1.91], [9, 2.16], [3, 1.11], [8, 1.92], [8, 1.03], [9, 1.25], [8, 0.86], [9, 0.88], [7, 1.6], [10, 0.49], [1, 1.9], [6, 0.96], [4, 0.78], [10, 0.65] ] }, "scoreColumn": "score", "weightColumn": "weight", "confidence": 0.95 }, "expected": [ {"metric": "NPS", "value": 7.691350342252642, "tolerance": 1e-10}, {"metric": "Standard error", "value": 5.361729864117147, "tolerance": 1e-10}, {"metric": "95% CI lower (Wald)", "value": -2.817447086249804, "tolerance": 1e-10}, {"metric": "95% CI upper (Wald)", "value": 18.200147770755088, "tolerance": 1e-10}, {"metric": "Adjusted-Wald NPS", "value": 7.5721201256624795, "tolerance": 1e-10}, {"metric": "95% CI lower (adjusted Wald)", "value": -2.8487217676896646, "tolerance": 1e-10}, {"metric": "95% CI upper (adjusted Wald)", "value": 17.992962019014623, "tolerance": 1e-10} ] }, { "id": "nps-two-sample-comparison", "procedure": "nps", "label": "NPS difference between two independent samples (52 vs 130 respondents)", "provenance": { "kind": "independent-recomputation", "implementation": "SciPy", "version": "1.18.1", "method": "NPS computed as the mean of +1 (9–10) / 0 (7–8) / −1 (0–6) codes; its standard error is the population standard deviation of those codes over √n (√n_eff, Kish, for weighted data), with z from scipy.stats.norm.ppf. Adjusted Wald adds ¾ promoter, 1½ passive and ¾ detractor pseudo-respondents (Rocks 2016). Difference B − A with SE √(SE_A² + SE_B²) and a two-sided normal p-value." }, "input": { "kind": "comparison", "a": [10, 30, 12], "b": [64, 45, 21], "confidence": 0.95 }, "expected": [ {"metric": "NPS difference (B − A)", "value": 36.92307692307692, "tolerance": 1e-10}, {"metric": "Standard error of the difference", "value": 11.088566365900446, "tolerance": 1e-10}, {"metric": "z", "value": 3.329833244865878, "tolerance": 1e-10}, {"metric": "Two-sided p-value", "value": 0.0008689800952323978, "tolerance": 1e-12} ] }, { "id": "van-westendorp-psm-80", "procedure": "van-westendorp", "label": "Van Westendorp PSM: 83 respondents (3 out of order), whole-currency answers", "provenance": { "kind": "independent-recomputation", "implementation": "SciPy", "version": "1.18.1", "method": "Cumulative curves on the grid of distinct answers (too cheap and cheap: share answering ≥ p; expensive and too expensive: share answering ≤ p), joined by straight lines (numpy.interp); each intersection is the first crossing, solved with scipy.optimize.brentq, or the midpoint of an exact tie run. Respondents whose answers are out of order are excluded." }, "input": { "data": { "columns": ["too_cheap", "cheap", "expensive", "too_expensive"], "rows": [ [13, 15, 19, 25], [14, 16, 26, 33], [15, 21, 31, 39], [18, 24, 35, 40], [15, 16, 30, 38], [18, 22, 28, 39], [23, 28, 36, 43], [12, 17, 27, 35], [14, 19, 31, 41], [10, 13, 27, 30], [21, 22, 25, 30], [10, 19, 29, 33], [21, 26, 36, 52], [15, 23, 30, 41], [14, 21, 31, 40], [14, 17, 25, 37], [17, 22, 30, 41], [13, 17, 26, 32], [24, 30, 39, 52], [19, 20, 32, 38], [15, 18, 25, 37], [15, 19, 27, 38], [10, 18, 28, 37], [10, 12, 18, 26], [15, 22, 24, 38], [20, 24, 40, 46], [8, 15, 24, 35], [13, 14, 21, 27], [11, 15, 23, 29], [20, 24, 30, 39], [16, 20, 23, 29], [11, 17, 26, 30], [19, 24, 31, 41], [19, 27, 37, 47], [12, 14, 20, 25], [23, 26, 27, 36], [15, 20, 28, 35], [9, 17, 29, 32], [18, 19, 28, 39], [17, 20, 31, 42], [7, 15, 24, 34], [16, 21, 28, 37], [17, 22, 29, 32], [16, 19, 27, 39], [14, 21, 33, 40], [12, 17, 24, 33], [13, 20, 27, 32], [6, 11, 25, 28], [12, 15, 28, 39], [10, 14, 21, 24], [10, 13, 17, 27], [10, 14, 25, 32], [12, 18, 26, 38], [10, 16, 26, 32], [10, 14, 22, 28], [16, 20, 33, 43], [12, 14, 25, 33], [13, 20, 30, 40], [12, 17, 22, 29], [12, 17, 25, 31], [13, 15, 26, 34], [15, 16, 24, 35], [16, 20, 29, 41], [14, 21, 29, 35], [15, 22, 25, 32], [10, 17, 23, 34], [17, 22, 29, 40], [24, 27, 33, 43], [16, 19, 30, 39], [12, 19, 24, 29], [13, 17, 24, 33], [12, 16, 29, 38], [17, 24, 34, 43], [10, 18, 29, 37], [19, 21, 30, 37], [13, 19, 31, 39], [17, 23, 35, 47], [13, 16, 24, 33], [18, 20, 31, 39], [16, 19, 23, 36], [20, 15, 30, 40], [10, 18, 45, 35], [12, 25, 22, 50] ] }, "columns": {"tooCheap": "too_cheap", "cheap": "cheap", "expensive": "expensive", "tooExpensive": "too_expensive"} }, "expected": [ {"metric": "Respondents in base", "value": 80.0, "tolerance": 0}, {"metric": "Point of marginal cheapness (PMC)", "value": 17.0, "tolerance": 1e-09}, {"metric": "Optimal price point (OPP)", "value": 24.25, "tolerance": 1e-09}, {"metric": "Indifference price point (IPP)", "value": 23.1, "tolerance": 1e-09}, {"metric": "Point of marginal expensiveness (PME)", "value": 30.5, "tolerance": 1e-09} ] }, { "id": "gabor-granger-ladder-120", "procedure": "gabor-granger", "label": "Gabor-Granger: 5 prices, 1–5 intent, top-two-box, partly adaptive ladders, n = 120", "provenance": { "kind": "independent-recomputation", "implementation": "NumPy", "version": "2.5.4", "method": "Would buy = rating ≥ 4. Blank prices are filled from each respondent's own ladder (blank below a price they would buy at → buy; blank above a price they would not → not buy; conflicting → left blank). Demand = share buying among respondents with an answer at that price; revenue = price × demand; arc elasticity = [(d₂ − d₁)/mean(d)] / [(p₂ − p₁)/mean(p)]." }, "input": { "data": { "columns": ["p499", "p599", "p699", "p799", "p899"], "rows": [ ["", "", 5, 3, ""], [5, 4, 3, 3, 2], [5, 5, 5, 5, 3], [5, 5, 4, 2, 1], [2, "", "", "", ""], [5, 5, 5, 3, 3], [5, 5, 3, 2, 1], ["", "", 5, 2, 1], [5, 5, 5, 3, ""], [5, 5, 4, 2, 1], [3, 2, 1, 1, 1], [5, 5, 5, 4, 3], [5, 5, 4, 2, ""], [5, 5, 3, 2, 1], [3, 2, 1, 1, 1], [2, 1, 1, 1, 1], [5, 4, 5, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 1, 1], [5, 3, 1, 1, 1], [5, 4, 2, "", ""], [5, 3, 3, 1, 1], [2, 1, 1, 1, 1], [4, 4, 3, 2, 1], [5, 5, 2, "", ""], [5, 4, 4, 2, 1], [5, 2, 2, 1, 1], [5, 5, 4, 2, 2], [5, 3, "", "", ""], [4, 2, 2, 1, 1], [3, 3, 2, 1, 1], [4, 1, 1, 1, 1], [5, 5, 4, 3, ""], [5, 5, 3, 3, 1], [5, 4, 3, 1, 2], ["", 5, 2, 1, 1], [5, 5, 4, 4, 2], [4, 4, 3, 2, 1], [4, 2, 1, 1, 1], [3, 1, 1, 1, 1], [5, 4, 2, "", ""], [5, 4, 2, 2, 1], [5, 3, 3, 1, 1], [5, 4, 2, 2, 1], [4, 4, 4, 2, ""], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1], [4, 2, 1, 1, 1], [5, 5, 4, 3, ""], [5, 3, 2, 1, 1], [5, 4, 3, 3, 1], [4, 2, 1, 1, 1], [5, 4, 2, "", ""], [3, 1, 1, 1, 1], [5, 5, 5, 2, 1], [4, 2, 1, 1, 1], [2, "", "", "", ""], [5, 4, 3, 3, 1], [5, 5, 5, 4, 2], [3, 1, 1, 1, 1], [4, 3, "", "", ""], [5, 4, 5, 2, 2], [5, 4, 3, 2, 1], [4, 3, 2, 2, 1], [2, "", "", "", ""], [3, 2, 1, 1, 1], [4, 3, 2, 1, 1], [3, 2, 1, 1, 1], [5, 3, "", "", ""], [3, 2, 1, 1, 1], [4, 3, 1, 1, 1], [4, 3, 2, 1, 1], [5, 5, 4, 3, ""], [2, 1, 1, 1, 1], [5, 5, 4, 2, 1], [5, 3, 4, 3, 1], [4, 3, "", "", ""], ["", 4, 2, 1, 1], [4, 4, 1, 1, 1], [5, 5, 5, 4, 3], [5, 5, 5, 4, 5], [2, 1, 1, 1, 1], [5, 4, 2, 1, 1], [5, 4, 3, 1, 1], ["", 5, 3, "", ""], [3, 1, 1, 1, 1], [1, 1, 1, 1, 1], [4, 3, 3, 1, 1], [5, 4, 2, "", ""], [5, 5, 3, 2, 2], [5, 3, 3, 2, 1], [5, 2, 2, 1, 1], [5, 5, 4, 4, 1], [5, 5, 4, 3, 2], [3, 3, 2, 1, 1], [4, 2, 1, 1, 1], [5, 5, 4, 4, 4], [4, 3, 3, 1, 1], ["", "", 5, 3, 1], [5, 5, 2, 2, 1], [4, 4, 2, "", ""], [5, 5, 5, 4, 4], [5, 5, 5, 5, 4], [4, 4, 2, 1, 1], [5, 4, 2, "", ""], [4, 3, 1, 1, 1], [3, 3, 2, 1, 1], [3, 1, 1, 1, 1], [3, "", "", "", ""], [5, 4, 3, 1, 1], [3, 2, 1, 1, 1], [5, 5, 3, 3, 1], [5, 3, "", "", ""], [5, 4, 3, 2, 1], [4, 4, 2, 1, 1], [5, 4, 2, 1, 1], [5, 5, 3, "", ""], [5, 5, 2, 2, 1], [5, 5, 5, 3, 2], ["", "", 5, 3, 1] ] }, "prices": [ {"column": "p499", "price": 4.99}, {"column": "p599", "price": 5.99}, {"column": "p699", "price": 6.99}, {"column": "p799", "price": 7.99}, {"column": "p899", "price": 8.99} ], "rule": {"kind": "top-2-box", "scaleMax": 5} }, "expected": [ {"metric": "Inferred cells", "value": 67.0, "tolerance": 0}, {"metric": "Demand at 4.99", "value": 0.8083333333333333, "tolerance": 1e-12}, {"metric": "Demand at 5.99", "value": 0.5833333333333334, "tolerance": 1e-12}, {"metric": "Demand at 6.99", "value": 0.275, "tolerance": 1e-12}, {"metric": "Demand at 7.99", "value": 0.09166666666666666, "tolerance": 1e-12}, {"metric": "Demand at 8.99", "value": 0.03333333333333333, "tolerance": 1e-12}, {"metric": "Revenue per respondent at 4.99", "value": 4.0335833333333335, "tolerance": 1e-12}, {"metric": "Revenue per respondent at 5.99", "value": 3.494166666666667, "tolerance": 1e-12}, {"metric": "Revenue per respondent at 6.99", "value": 1.9222500000000002, "tolerance": 1e-12}, {"metric": "Revenue per respondent at 7.99", "value": 0.7324166666666666, "tolerance": 1e-12}, {"metric": "Revenue per respondent at 8.99", "value": 0.2996666666666667, "tolerance": 1e-12}, {"metric": "Revenue-maximising price", "value": 4.99, "tolerance": 0}, {"metric": "Arc elasticity 4.99→5.99", "value": -1.7752095808383235, "tolerance": 1e-10}, {"metric": "Arc elasticity 5.99→6.99", "value": -4.662718446601942, "tolerance": 1e-10}, {"metric": "Arc elasticity 6.99→7.99", "value": -7.49, "tolerance": 1e-10}, {"metric": "Arc elasticity 7.99→8.99", "value": -7.9239999999999995, "tolerance": 1e-10} ] } ] }