{ "title": "Nonparametric comparison workspace", "human_url": "https://happytails.ai/en/calculators/nonparametric-comparison-workspace/", "agent_url": "https://happytails.ai/agents/en/calculators/nonparametric-comparison-workspace/", "language": "en", "markdown_url": "https://happytails.ai/en/calculators/nonparametric-comparison-workspace.md", "content": "Nonparametric comparison workspace\nCompare groups or paired measurements with rank tests: Mann-Whitney U, Wilcoxon signed-rank, Kruskal-Wallis with Dunn comparisons, or Friedman. Get exact p-values for small samples, tie corrections and Hodges-Lehmann estimates with confidence intervals.\nHow can we improve this tool?\nReport a problem or share an idea.\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\nHow to use Nonparametric comparison workspace\nChoose the test that matches your design.\nPaste the CSV and name the group and value columns, the paired columns or the condition columns.\nPick the alternative, the p-value method and the confidence level.\nRun the test, review the ranks and the Hodges-Lehmann interval, and download the report.\nUseful next steps\nMultiple testing correction\nConfidence interval calculator\nSample size calculator\nTwo-sample and paired tests\nMann-Whitney W is the rank sum of the first group minus n1(n1 + 1)/2 (Mann and Whitney 1947, Annals of Mathematical Statistics 18:50), and the signed-rank V is the sum of ranks of positive differences (Wilcoxon 1945, Biometrics Bulletin 1:80), as in R wilcox.test. Automatic mode uses the exact distribution when both groups are under 50 (or under 50 pairs) and there are no ties or zero differences, otherwise the normal approximation with tie and optional continuity correction. Zero differences are dropped. Paired differences and differences from the null value are computed exactly from the decimal values you enter (up to 15 significant digits), so equal differences such as 1.3 - 1.2 and 1.4 - 1.3 count as ties and zeros; R subtracts in binary floating point, which can split such ties. The exact option with ties uses the distribution conditional on the observed ranks, which differs from R, which switches to the normal approximation.\nHodges-Lehmann estimate and interval\nThe estimate is the median of the pairwise differences (two groups) or Walsh averages (paired or one sample) (Hodges and Lehmann 1963, Annals of Mathematical Statistics 34:598). The interval inverts the same test: for exact tests it takes order statistics of those differences (Bauer 1972, JASA 67:687; Hollander, Wolfe and Chicken 2014, Nonparametric Statistical Methods, 3rd ed.), otherwise it takes the difference where the normal statistic crosses the critical value. R finds that point with uniroot to within 0.0001; this tool returns the exact difference. The achieved confidence of exact intervals is reported.\nMore than two groups\nKruskal-Wallis (Kruskal and Wallis 1952, JASA 47:583) uses the chi-square approximation with tie correction and epsilon squared, followed by Dunn z tests (Dunn 1964, Technometrics 6:241) with Holm or Bonferroni adjustment. Friedman (Friedman 1937, JASA 32:675) ranks within each subject, with R's tie correction and Kendall's W.\nLimits\nRank tests compare distributions, not means. The Hodges-Lehmann shift is a fair summary only when the groups have a similar shape. Conventions for ties and continuity corrections differ between programs, so the method used is always labelled.", "content_format": "text/plain", "visibility": "public", "links": [ { "name": "Multiple testing correction", "url": "https://happytails.ai/en/calculators/multiple-testing-correction/" }, { "name": "Confidence interval calculator", "url": "https://happytails.ai/en/calculators/confidence-interval-calculator/" }, { "name": "Sample size calculator", "url": "https://happytails.ai/en/calculators/sample-size-calculator/" } ], "tool": { "id": "nonparametric-comparison-workspace", "category": "calculators", "built": true, "requirements": "Runs locally in your browser in a background worker; nothing is uploaded. CSV up to 1,000,000 characters and 10,000 data rows. Exact Mann-Whitney needs both groups of at most 50 without ties or a total of at most 100 with ties; the exact signed-rank test allows up to 200 nonzero differences. Hodges-Lehmann values are computed when there are at most 1,000,000 pairwise differences or Walsh averages, for example 1,000 x 1,000 values or 1,413 pairs. Kruskal-Wallis and Friedman allow 2 to 20 groups or conditions. Confidence level 0.5 to 0.9999. Setting numbers are plain decimals with a digit before the point, such as 0.95, without exponents. In CSV with two or more columns a blank line between rows is rejected, and in one-column CSV it is a blank cell; blank lines after the last row are ignored. Downloads: a JSON report and CSV tables.", "implementation": { "fields": [ { "key": "test", "label": "Test", "value": "mann-whitney", "type": "select", "values": [ "mann-whitney", "signed-rank", "kruskal-wallis", "friedman" ], "labels": { "mann-whitney": "Mann-Whitney U (two independent groups)", "signed-rank": "Wilcoxon signed-rank (paired or one sample)", "kruskal-wallis": "Kruskal-Wallis with Dunn comparisons (2 to 20 groups)", "friedman": "Friedman (repeated measures, one column per condition)" } }, { "key": "groupColumn", "label": "Group column", "value": "group", "type": "text", "maxLength": 200, "help": "Exact header of the column that names the groups.", "showWhen": { "test": [ "mann-whitney", "kruskal-wallis" ] } }, { "key": "valueColumn", "label": "Value column", "value": "value", "type": "text", "maxLength": 200, "help": "Exact header of the numeric or ordinal score column.", "showWhen": { "test": [ "mann-whitney", "kruskal-wallis" ] } }, { "key": "firstColumn", "label": "First measurement column", "value": "before", "type": "text", "maxLength": 200, "help": "Exact header. Differences are first minus second.", "showWhen": { "test": [ "signed-rank" ] } }, { "key": "secondColumn", "label": "Second measurement column (blank for one sample)", "value": "after", "type": "text", "maxLength": 200, "help": "Leave blank to test the first column against the null value.", "showWhen": { "test": [ "signed-rank" ] } }, { "key": "treatmentColumns", "label": "Condition columns", "value": "", "type": "text", "maxLength": 20000, "help": "Comma-separated exact headers, 2 to 20 conditions, one row per subject.", "showWhen": { "test": [ "friedman" ] } }, { "key": "mu", "label": "Null value", "value": "0", "type": "text", "maxLength": 200, "help": "Location shift under the null hypothesis, for example 0.", "showWhen": { "test": [ "signed-rank" ] } }, { "key": "alternative", "label": "Alternative hypothesis", "value": "two-sided", "type": "select", "values": [ "two-sided", "less", "greater" ], "labels": { "two-sided": "Two-sided", "less": "First group or measurement tends to be smaller", "greater": "First group or measurement tends to be larger" }, "showWhen": { "test": [ "mann-whitney", "signed-rank" ] } }, { "key": "exact", "label": "p-value method", "value": "auto", "type": "select", "values": [ "auto", "exact", "normal" ], "labels": { "auto": "Exact for small samples without ties, otherwise normal", "exact": "Exact (conditional on ties when present)", "normal": "Normal approximation" }, "showWhen": { "test": [ "mann-whitney", "signed-rank" ] } }, { "key": "correct", "label": "Continuity correction for the normal approximation", "value": true, "type": "checkbox", "showWhen": { "test": [ "mann-whitney", "signed-rank" ] } }, { "key": "confidence", "label": "Confidence level for the Hodges-Lehmann interval", "value": "0.95", "type": "text", "maxLength": 200, "help": "A proportion from 0.5 to 0.9999.", "showWhen": { "test": [ "mann-whitney", "signed-rank" ] } }, { "key": "adjust", "label": "p-value adjustment for Dunn comparisons", "value": "Holm", "type": "select", "values": [ "Holm", "Bonferroni" ], "showWhen": { "test": [ "kruskal-wallis" ] } }, { "key": "missing", "label": "Blank cells", "value": "reject", "type": "select", "values": [ "reject", "drop" ], "labels": { "reject": "Stop and show an error", "drop": "Drop incomplete rows" } } ], "registrationFamily": "statistical-comparison-tests", "inputMaxLength": 1000000, "inputErrorCode": "STATISTICAL_COMPARISON_TESTS_TOO_LONG", "note": "Runs on your device in the background. Paste up to 1,000,000 characters of CSV with up to 10,000 rows; exact p-values are used for small samples without ties.", "experience": { "automatic": false, "single": false, "inputMaxLength": 1000000, "inputMode": "text", "label": "CSV data", "placeholder": "group,value", "help": "Paste one row per observation, or paired columns such as before,after. Up to 1,000,000 characters. Review the settings before running.", "action": null }, "mode": "explicit", "interactive": false }, "execution": "Browser interface", "api": null, "browser_agent": { "supported": true, "name": "run_current_tool", "discovery": "WebMCP on the human page in a supporting browser", "verification": "See audit/API-AUDIT.md; availability is not verification" } }, "markdown": "# Nonparametric comparison workspace\n\n- Human page: https://happytails.ai/en/calculators/nonparametric-comparison-workspace/\n- Markdown: https://happytails.ai/en/calculators/nonparametric-comparison-workspace.md\n- Structured JSON: https://happytails.ai/agents/en/calculators/nonparametric-comparison-workspace/index.json\n- Visibility: public\n\n## Tool capabilities\n\n| Property | Value |\n| --- | --- |\n| Tool ID | `nonparametric-comparison-workspace` |\n| Category | calculators |\n| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |\n| Browser execution | Use the visible action or interactive controls. |\n| Browser processing | Browser; see tool notes for network behavior. |\n| HTTP API | Not callable through HTTP. |\n| Browser-agent interface | run_current_tool |\n\n### Implementation notes\n\nRuns on your device in the background. Paste up to 1,000,000 characters of CSV with up to 10,000 rows; exact p-values are used for small samples without ties.\n\n### Inputs and settings\n\nText input: CSV data.\n\nExample or placeholder shown in the interface (not a validated fixture):\n\n```text\ngroup,value\n```\n\nPaste one row per observation, or paired columns such as before,after. Up to 1,000,000 characters. Review the settings before running.\n\n| Setting | Meaning | Control type | Default | Constraints |\n| --- | --- | --- | --- | --- |\n| `test` | Test | select | \"mann-whitney\" | Allowed: mann-whitney, signed-rank, kruskal-wallis, friedman |\n| `groupColumn` | Group column | text | \"group\" | |\n| `valueColumn` | Value column | text | \"value\" | |\n| `firstColumn` | First measurement column | text | \"before\" | |\n| `secondColumn` | Second measurement column (blank for one sample) | text | \"after\" | |\n| `treatmentColumns` | Condition columns | text | \"\" | |\n| `mu` | Null value | text | \"0\" | |\n| `alternative` | Alternative hypothesis | select | \"two-sided\" | Allowed: two-sided, less, greater |\n| `exact` | p-value method | select | \"auto\" | Allowed: auto, exact, normal |\n| `correct` | Continuity correction for the normal approximation | checkbox | true | |\n| `confidence` | Confidence level for the Hodges-Lehmann interval | text | \"0.95\" | |\n| `adjust` | p-value adjustment for Dunn comparisons | select | \"Holm\" | Allowed: Holm, Bonferroni |\n| `missing` | Blank cells | select | \"reject\" | Allowed: reject, drop |\n\n### Browser-agent workflow\n\n1. Open the human page in a browser that supports WebMCP.\n2. Discover the interface exposed by that page; use its actual schema.\n3. Select files on the page first when the tool requires files.\n4. Call `run_current_tool` with valid input and settings.\n5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.\n\nCalls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.\n\n### Planning specification\n\nRuns locally in your browser in a background worker; nothing is uploaded. CSV up to 1,000,000 characters and 10,000 data rows. Exact Mann-Whitney needs both groups of at most 50 without ties or a total of at most 100 with ties; the exact signed-rank test allows up to 200 nonzero differences. Hodges-Lehmann values are computed when there are at most 1,000,000 pairwise differences or Walsh averages, for example 1,000 x 1,000 values or 1,413 pairs. Kruskal-Wallis and Friedman allow 2 to 20 groups or conditions. Confidence level 0.5 to 0.9999. Setting numbers are plain decimals with a digit before the point, such as 0.95, without exponents. In CSV with two or more columns a blank line between rows is rejected, and in one-column CSV it is a blank cell; blank lines after the last row are ignored. Downloads: a JSON report and CSV tables.\n\nThis describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.\n\n### Complete machine-readable capability record\n\n```json\n{\n \"id\": \"nonparametric-comparison-workspace\",\n \"category\": \"calculators\",\n \"built\": true,\n \"requirements\": \"Runs locally in your browser in a background worker; nothing is uploaded. CSV up to 1,000,000 characters and 10,000 data rows. Exact Mann-Whitney needs both groups of at most 50 without ties or a total of at most 100 with ties; the exact signed-rank test allows up to 200 nonzero differences. Hodges-Lehmann values are computed when there are at most 1,000,000 pairwise differences or Walsh averages, for example 1,000 x 1,000 values or 1,413 pairs. Kruskal-Wallis and Friedman allow 2 to 20 groups or conditions. Confidence level 0.5 to 0.9999. Setting numbers are plain decimals with a digit before the point, such as 0.95, without exponents. In CSV with two or more columns a blank line between rows is rejected, and in one-column CSV it is a blank cell; blank lines after the last row are ignored. Downloads: a JSON report and CSV tables.\",\n \"implementation\": {\n \"fields\": [\n {\n \"key\": \"test\",\n \"label\": \"Test\",\n \"value\": \"mann-whitney\",\n \"type\": \"select\",\n \"values\": [\n \"mann-whitney\",\n \"signed-rank\",\n \"kruskal-wallis\",\n \"friedman\"\n ],\n \"labels\": {\n \"mann-whitney\": \"Mann-Whitney U (two independent groups)\",\n \"signed-rank\": \"Wilcoxon signed-rank (paired or one sample)\",\n \"kruskal-wallis\": \"Kruskal-Wallis with Dunn comparisons (2 to 20 groups)\",\n \"friedman\": \"Friedman (repeated measures, one column per condition)\"\n }\n },\n {\n \"key\": \"groupColumn\",\n \"label\": \"Group column\",\n \"value\": \"group\",\n \"type\": \"text\",\n \"maxLength\": 200,\n \"help\": \"Exact header of the column that names the groups.\",\n \"showWhen\": {\n \"test\": [\n \"mann-whitney\",\n \"kruskal-wallis\"\n ]\n }\n },\n {\n \"key\": \"valueColumn\",\n \"label\": \"Value column\",\n \"value\": \"value\",\n \"type\": \"text\",\n \"maxLength\": 200,\n \"help\": \"Exact header of the numeric or ordinal score column.\",\n \"showWhen\": {\n \"test\": [\n \"mann-whitney\",\n \"kruskal-wallis\"\n ]\n }\n },\n {\n \"key\": \"firstColumn\",\n \"label\": \"First measurement column\",\n \"value\": \"before\",\n \"type\": \"text\",\n \"maxLength\": 200,\n \"help\": \"Exact header. Differences are first minus second.\",\n \"showWhen\": {\n \"test\": [\n \"signed-rank\"\n ]\n }\n },\n {\n \"key\": \"secondColumn\",\n \"label\": \"Second measurement column (blank for one sample)\",\n \"value\": \"after\",\n \"type\": \"text\",\n \"maxLength\": 200,\n \"help\": \"Leave blank to test the first column against the null value.\",\n \"showWhen\": {\n \"test\": [\n \"signed-rank\"\n ]\n }\n },\n {\n \"key\": \"treatmentColumns\",\n \"label\": \"Condition columns\",\n \"value\": \"\",\n \"type\": \"text\",\n \"maxLength\": 20000,\n \"help\": \"Comma-separated exact headers, 2 to 20 conditions, one row per subject.\",\n \"showWhen\": {\n \"test\": [\n \"friedman\"\n ]\n }\n },\n {\n \"key\": \"mu\",\n \"label\": \"Null value\",\n \"value\": \"0\",\n \"type\": \"text\",\n \"maxLength\": 200,\n \"help\": \"Location shift under the null hypothesis, for example 0.\",\n \"showWhen\": {\n \"test\": [\n \"signed-rank\"\n ]\n }\n },\n {\n \"key\": \"alternative\",\n \"label\": \"Alternative hypothesis\",\n \"value\": \"two-sided\",\n \"type\": \"select\",\n \"values\": [\n \"two-sided\",\n \"less\",\n \"greater\"\n ],\n \"labels\": {\n \"two-sided\": \"Two-sided\",\n \"less\": \"First group or measurement tends to be smaller\",\n \"greater\": \"First group or measurement tends to be larger\"\n },\n \"showWhen\": {\n \"test\": [\n \"mann-whitney\",\n \"signed-rank\"\n ]\n }\n },\n {\n \"key\": \"exact\",\n \"label\": \"p-value method\",\n \"value\": \"auto\",\n \"type\": \"select\",\n \"values\": [\n \"auto\",\n \"exact\",\n \"normal\"\n ],\n \"labels\": {\n \"auto\": \"Exact for small samples without ties, otherwise normal\",\n \"exact\": \"Exact (conditional on ties when present)\",\n \"normal\": \"Normal approximation\"\n },\n \"showWhen\": {\n \"test\": [\n \"mann-whitney\",\n \"signed-rank\"\n ]\n }\n },\n {\n \"key\": \"correct\",\n \"label\": \"Continuity correction for the normal approximation\",\n \"value\": true,\n \"type\": \"checkbox\",\n \"showWhen\": {\n \"test\": [\n \"mann-whitney\",\n \"signed-rank\"\n ]\n }\n },\n {\n \"key\": \"confidence\",\n \"label\": \"Confidence level for the Hodges-Lehmann interval\",\n \"value\": \"0.95\",\n \"type\": \"text\",\n \"maxLength\": 200,\n \"help\": \"A proportion from 0.5 to 0.9999.\",\n \"showWhen\": {\n \"test\": [\n \"mann-whitney\",\n \"signed-rank\"\n ]\n }\n },\n {\n \"key\": \"adjust\",\n \"label\": \"p-value adjustment for Dunn comparisons\",\n \"value\": \"Holm\",\n \"type\": \"select\",\n \"values\": [\n \"Holm\",\n \"Bonferroni\"\n ],\n \"showWhen\": {\n \"test\": [\n \"kruskal-wallis\"\n ]\n }\n },\n {\n \"key\": \"missing\",\n \"label\": \"Blank cells\",\n \"value\": \"reject\",\n \"type\": \"select\",\n \"values\": [\n \"reject\",\n \"drop\"\n ],\n \"labels\": {\n \"reject\": \"Stop and show an error\",\n \"drop\": \"Drop incomplete rows\"\n }\n }\n ],\n \"registrationFamily\": \"statistical-comparison-tests\",\n \"inputMaxLength\": 1000000,\n \"inputErrorCode\": \"STATISTICAL_COMPARISON_TESTS_TOO_LONG\",\n \"note\": \"Runs on your device in the background. Paste up to 1,000,000 characters of CSV with up to 10,000 rows; exact p-values are used for small samples without ties.\",\n \"experience\": {\n \"automatic\": false,\n \"single\": false,\n \"inputMaxLength\": 1000000,\n \"inputMode\": \"text\",\n \"label\": \"CSV data\",\n \"placeholder\": \"group,value\",\n \"help\": \"Paste one row per observation, or paired columns such as before,after. Up to 1,000,000 characters. Review the settings before running.\",\n \"action\": null\n },\n \"mode\": \"explicit\",\n \"interactive\": false\n },\n \"execution\": \"Browser interface\",\n \"api\": null,\n \"browser_agent\": {\n \"supported\": true,\n \"name\": \"run_current_tool\",\n \"discovery\": \"WebMCP on the human page in a supporting browser\",\n \"verification\": \"See audit/API-AUDIT.md; availability is not verification\"\n }\n}\n```\n\n## Page guide\n\nCompare groups or paired measurements with rank tests: Mann-Whitney U, Wilcoxon signed-rank, Kruskal-Wallis with Dunn comparisons, or Friedman. Get exact p-values for small samples, tie corrections and Hodges-Lehmann estimates with confidence intervals.\n\nHow can we improve this tool?\n\nReport a problem or share an idea.\n\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\n\n### How to use Nonparametric comparison workspace\n\n1. Choose the test that matches your design.\n2. Paste the CSV and name the group and value columns, the paired columns or the condition columns.\n3. Pick the alternative, the p-value method and the confidence level.\n4. Run the test, review the ranks and the Hodges-Lehmann interval, and download the report.\n\n## Useful next steps\n\n- [Multiple testing correction](https://happytails.ai/en/calculators/multiple-testing-correction/) ([Markdown](https://happytails.ai/en/calculators/multiple-testing-correction.md))\n\n- [Confidence interval calculator](https://happytails.ai/en/calculators/confidence-interval-calculator/) ([Markdown](https://happytails.ai/en/calculators/confidence-interval-calculator.md))\n\n- [Sample size calculator](https://happytails.ai/en/calculators/sample-size-calculator/) ([Markdown](https://happytails.ai/en/calculators/sample-size-calculator.md))\n\n## Two-sample and paired tests\n\nMann-Whitney W is the rank sum of the first group minus n1(n1 + 1)/2 (Mann and Whitney 1947, Annals of Mathematical Statistics 18:50), and the signed-rank V is the sum of ranks of positive differences (Wilcoxon 1945, Biometrics Bulletin 1:80), as in R wilcox.test. Automatic mode uses the exact distribution when both groups are under 50 (or under 50 pairs) and there are no ties or zero differences, otherwise the normal approximation with tie and optional continuity correction. Zero differences are dropped. Paired differences and differences from the null value are computed exactly from the decimal values you enter (up to 15 significant digits), so equal differences such as 1.3 - 1.2 and 1.4 - 1.3 count as ties and zeros; R subtracts in binary floating point, which can split such ties. The exact option with ties uses the distribution conditional on the observed ranks, which differs from R, which switches to the normal approximation.\n\n### Hodges-Lehmann estimate and interval\n\nThe estimate is the median of the pairwise differences (two groups) or Walsh averages (paired or one sample) (Hodges and Lehmann 1963, Annals of Mathematical Statistics 34:598). The interval inverts the same test: for exact tests it takes order statistics of those differences (Bauer 1972, JASA 67:687; Hollander, Wolfe and Chicken 2014, Nonparametric Statistical Methods, 3rd ed.), otherwise it takes the difference where the normal statistic crosses the critical value. R finds that point with uniroot to within 0.0001; this tool returns the exact difference. The achieved confidence of exact intervals is reported.\n\n### More than two groups\n\nKruskal-Wallis (Kruskal and Wallis 1952, JASA 47:583) uses the chi-square approximation with tie correction and epsilon squared, followed by Dunn z tests (Dunn 1964, Technometrics 6:241) with Holm or Bonferroni adjustment. Friedman (Friedman 1937, JASA 32:675) ranks within each subject, with R's tie correction and Kendall's W.\n\n### Limits\n\nRank tests compare distributions, not means. The Hodges-Lehmann shift is a fair summary only when the groups have a similar shape. Conventions for ties and continuity corrections differ between programs, so the method used is always labelled.\n" }