{
  "title": "Effect size calculator",
  "human_url": "https://happytails.ai/en/calculators/effect-size-calculator/",
  "agent_url": "https://happytails.ai/agents/en/calculators/effect-size-calculator/",
  "language": "en",
  "markdown_url": "https://happytails.ai/en/calculators/effect-size-calculator.md",
  "content": "Effect size calculator\nTurn group summaries, paired differences, 2 x 2 counts or a published t, F or r into standardized effect sizes with confidence intervals. Every measure is labelled with the groups and standard deviation it uses.\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 Effect size calculator\nChoose the input type that matches what you have: two groups, paired differences, event counts or a test statistic.\nEnter the summary values and the confidence level.\nCalculate, then read each measure with its interval and the standard deviation it divides by.\nDownload the JSON report or the CSV table of every measure.\nUseful next steps\nConfidence interval calculator\nSample size calculator\nPooled summary statistics\nBox plot comparison\nWhich d is which\nd_s divides the mean difference by the pooled SD of two independent groups (Cohen 1988). Hedges g multiplies it by the exact small-sample correction J. Glass delta uses the SD of group 2 only. For paired data, d_z divides the mean difference by the SD of the differences, d_av by the average of the two SDs (enter both, or leave both blank to skip it) and d_rm adjusts d_z for the correlation (Lakens 2013, Frontiers in Psychology 4:863). These measures are not interchangeable, so report which one you used.\nHow the intervals are found\nIntervals for d_s, d_z and d from a t statistic invert the noncentral t distribution (Steiger and Fouladi 1997), computed accurately even for very large effects; the g interval multiplies those limits by J. A normal-approximation interval from the Hedges and Olkin (1985) variance is also listed. The partial eta squared interval inverts the noncentral F distribution with N = df1 + df2 + 1. Odds and risk ratios use log intervals (Woolf 1955; Katz et al. 1978), the risk difference a Wald interval, and r a Fisher z interval.\nAssumptions and limits\nGroup SDs are sample SDs with n - 1. If any 2 x 2 cell is zero, 0.5 is added to every cell before ratios are computed, and the report says so. Conversions such as d to r or d to a log odds ratio (Chinn 2000, Statistics in Medicine 19:3127) assume roughly normal data. The d to r conversion allows unequal group sizes: r = d / sqrt(d^2 + a) with a = (n1 + n2)^2 / (n1 n2) (Borenstein et al. 2009, Introduction to Meta-Analysis, chapter 7). An effect size describes these data; it does not show importance or cause.",
  "content_format": "text/plain",
  "visibility": "public",
  "links": [
    {
      "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/"
    },
    {
      "name": "Pooled summary statistics",
      "url": "https://happytails.ai/en/calculators/pooled-summary-statistics/"
    },
    {
      "name": "Box plot comparison",
      "url": "https://happytails.ai/en/calculators/box-plot-comparison/"
    }
  ],
  "tool": {
    "id": "effect-size-calculator",
    "category": "calculators",
    "built": true,
    "requirements": "Runs locally in your browser; nothing is uploaded. Group sizes are whole numbers of at least 2 (pairs at least 2, correlation sample size at least 4), means and SDs are plain decimals within plus or minus 1,000,000,000,000, counts are whole numbers up to 1,000,000,000 and the confidence level is from 0.5 to 0.9999. Downloads: a JSON report and a CSV table of measures, estimates, limits and methods.",
    "implementation": {
      "fields": [
        {
          "key": "mode",
          "label": "Input type",
          "value": "independent-means",
          "type": "select",
          "values": [
            "independent-means",
            "paired-means",
            "two-by-two",
            "t-statistic",
            "f-statistic",
            "correlation"
          ],
          "labels": {
            "independent-means": "Two independent groups (n, mean, SD)",
            "paired-means": "Paired measurements (mean and SD of differences)",
            "two-by-two": "2 x 2 event counts",
            "t-statistic": "Two-sample t statistic",
            "f-statistic": "F statistic from an ANOVA",
            "correlation": "Correlation r"
          }
        },
        {
          "key": "confidence",
          "label": "Confidence level",
          "value": "0.95",
          "type": "text",
          "maxLength": 40,
          "help": "A proportion from 0.5 to 0.9999, for example 0.95."
        },
        {
          "key": "n1",
          "label": "Group 1 size",
          "value": "25",
          "type": "text",
          "maxLength": 40,
          "help": "Whole number of at least 2.",
          "showWhen": {
            "mode": [
              "independent-means",
              "t-statistic"
            ]
          }
        },
        {
          "key": "mean1",
          "label": "Group 1 mean",
          "value": "24.5",
          "type": "text",
          "maxLength": 40,
          "help": "Use a decimal point and no thousands separators.",
          "showWhen": {
            "mode": [
              "independent-means"
            ]
          }
        },
        {
          "key": "sd1",
          "label": "Group 1 standard deviation",
          "value": "4.2",
          "type": "text",
          "maxLength": 40,
          "help": "Sample SD with n - 1, greater than zero.",
          "showWhen": {
            "mode": [
              "independent-means"
            ]
          }
        },
        {
          "key": "n2",
          "label": "Group 2 size",
          "value": "30",
          "type": "text",
          "maxLength": 40,
          "help": "Whole number of at least 2. Group 2 is the comparison group for Glass delta.",
          "showWhen": {
            "mode": [
              "independent-means",
              "t-statistic"
            ]
          }
        },
        {
          "key": "mean2",
          "label": "Group 2 mean",
          "value": "21.9",
          "type": "text",
          "maxLength": 40,
          "help": "Use a decimal point and no thousands separators.",
          "showWhen": {
            "mode": [
              "independent-means"
            ]
          }
        },
        {
          "key": "sd2",
          "label": "Group 2 standard deviation",
          "value": "5.1",
          "type": "text",
          "maxLength": 40,
          "help": "Sample SD with n - 1, greater than zero.",
          "showWhen": {
            "mode": [
              "independent-means"
            ]
          }
        },
        {
          "key": "pairs",
          "label": "Number of pairs",
          "value": "18",
          "type": "text",
          "maxLength": 40,
          "help": "Whole number of at least 2.",
          "showWhen": {
            "mode": [
              "paired-means"
            ]
          }
        },
        {
          "key": "meanDifference",
          "label": "Mean of the differences",
          "value": "1.7",
          "type": "text",
          "maxLength": 40,
          "help": "First measurement minus second.",
          "showWhen": {
            "mode": [
              "paired-means"
            ]
          }
        },
        {
          "key": "sdDifference",
          "label": "SD of the differences",
          "value": "2.9",
          "type": "text",
          "maxLength": 40,
          "help": "Greater than zero.",
          "showWhen": {
            "mode": [
              "paired-means"
            ]
          }
        },
        {
          "key": "sdFirst",
          "label": "SD of the first measurement (optional)",
          "value": "",
          "type": "text",
          "maxLength": 40,
          "help": "Enter both measurement SDs for d_av, or leave both blank to skip it.",
          "showWhen": {
            "mode": [
              "paired-means"
            ]
          }
        },
        {
          "key": "sdSecond",
          "label": "SD of the second measurement (optional)",
          "value": "",
          "type": "text",
          "maxLength": 40,
          "help": "Enter both measurement SDs for d_av, or leave both blank to skip it.",
          "showWhen": {
            "mode": [
              "paired-means"
            ]
          }
        },
        {
          "key": "correlation",
          "label": "Correlation between measurements (optional)",
          "value": "",
          "type": "text",
          "maxLength": 40,
          "help": "Between -1 and 1; leave blank to skip d_rm.",
          "showWhen": {
            "mode": [
              "paired-means"
            ]
          }
        },
        {
          "key": "a",
          "label": "Group 1 events",
          "value": "15",
          "type": "text",
          "maxLength": 40,
          "help": "Whole number of zero or more.",
          "showWhen": {
            "mode": [
              "two-by-two"
            ]
          }
        },
        {
          "key": "b",
          "label": "Group 1 non-events",
          "value": "85",
          "type": "text",
          "maxLength": 40,
          "help": "Whole number of zero or more.",
          "showWhen": {
            "mode": [
              "two-by-two"
            ]
          }
        },
        {
          "key": "c",
          "label": "Group 2 events",
          "value": "30",
          "type": "text",
          "maxLength": 40,
          "help": "Whole number of zero or more.",
          "showWhen": {
            "mode": [
              "two-by-two"
            ]
          }
        },
        {
          "key": "d",
          "label": "Group 2 non-events",
          "value": "70",
          "type": "text",
          "maxLength": 40,
          "help": "Whole number of zero or more.",
          "showWhen": {
            "mode": [
              "two-by-two"
            ]
          }
        },
        {
          "key": "t",
          "label": "t statistic",
          "value": "2.5",
          "type": "text",
          "maxLength": 40,
          "help": "From a pooled-variance two-sample t test.",
          "showWhen": {
            "mode": [
              "t-statistic"
            ]
          }
        },
        {
          "key": "f",
          "label": "F statistic",
          "value": "5.2",
          "type": "text",
          "maxLength": 40,
          "help": "Zero or more.",
          "showWhen": {
            "mode": [
              "f-statistic"
            ]
          }
        },
        {
          "key": "df1",
          "label": "Effect degrees of freedom",
          "value": "2",
          "type": "text",
          "maxLength": 40,
          "help": "Whole number of at least 1.",
          "showWhen": {
            "mode": [
              "f-statistic"
            ]
          }
        },
        {
          "key": "df2",
          "label": "Error degrees of freedom",
          "value": "45",
          "type": "text",
          "maxLength": 40,
          "help": "Whole number of at least 1.",
          "showWhen": {
            "mode": [
              "f-statistic"
            ]
          }
        },
        {
          "key": "r",
          "label": "Correlation r",
          "value": "0.42",
          "type": "text",
          "maxLength": 40,
          "help": "Strictly between -1 and 1.",
          "showWhen": {
            "mode": [
              "correlation"
            ]
          }
        },
        {
          "key": "sampleSize",
          "label": "Sample size",
          "value": "50",
          "type": "text",
          "maxLength": 40,
          "help": "Whole number of at least 4.",
          "showWhen": {
            "mode": [
              "correlation"
            ]
          }
        }
      ],
      "registrationFamily": "statistical-analysis-reference",
      "input": false,
      "note": "Runs on your device. Enter summaries for one input type; intervals use the noncentral t or F distribution where noted, and the JSON report and CSV hold every measure.",
      "experience": {
        "automatic": false,
        "single": false,
        "inputMaxLength": 1000000,
        "inputMode": "text",
        "label": "Summary values",
        "placeholder": "Enter values in the form fields",
        "help": "This calculator reads the form fields below; there is no text box. 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": "# Effect size calculator\n\n- Human page: https://happytails.ai/en/calculators/effect-size-calculator/\n- Markdown: https://happytails.ai/en/calculators/effect-size-calculator.md\n- Structured JSON: https://happytails.ai/agents/en/calculators/effect-size-calculator/index.json\n- Visibility: public\n\n## Tool capabilities\n\n| Property | Value |\n| --- | --- |\n| Tool ID | `effect-size-calculator` |\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. Enter summaries for one input type; intervals use the noncentral t or F distribution where noted, and the JSON report and CSV hold every measure.\n\n### Inputs and settings\n\nNo free-text input is required. Use the file inputs and/or settings below.\n\n| Setting | Meaning | Control type | Default | Constraints |\n| --- | --- | --- | --- | --- |\n| `mode` | Input type | select | \"independent-means\" | Allowed: independent-means, paired-means, two-by-two, t-statistic, f-statistic, correlation |\n| `confidence` | Confidence level | text | \"0.95\" |  |\n| `n1` | Group 1 size | text | \"25\" |  |\n| `mean1` | Group 1 mean | text | \"24.5\" |  |\n| `sd1` | Group 1 standard deviation | text | \"4.2\" |  |\n| `n2` | Group 2 size | text | \"30\" |  |\n| `mean2` | Group 2 mean | text | \"21.9\" |  |\n| `sd2` | Group 2 standard deviation | text | \"5.1\" |  |\n| `pairs` | Number of pairs | text | \"18\" |  |\n| `meanDifference` | Mean of the differences | text | \"1.7\" |  |\n| `sdDifference` | SD of the differences | text | \"2.9\" |  |\n| `sdFirst` | SD of the first measurement (optional) | text | \"\" |  |\n| `sdSecond` | SD of the second measurement (optional) | text | \"\" |  |\n| `correlation` | Correlation between measurements (optional) | text | \"\" |  |\n| `a` | Group 1 events | text | \"15\" |  |\n| `b` | Group 1 non-events | text | \"85\" |  |\n| `c` | Group 2 events | text | \"30\" |  |\n| `d` | Group 2 non-events | text | \"70\" |  |\n| `t` | t statistic | text | \"2.5\" |  |\n| `f` | F statistic | text | \"5.2\" |  |\n| `df1` | Effect degrees of freedom | text | \"2\" |  |\n| `df2` | Error degrees of freedom | text | \"45\" |  |\n| `r` | Correlation r | text | \"0.42\" |  |\n| `sampleSize` | Sample size | text | \"50\" |  |\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; nothing is uploaded. Group sizes are whole numbers of at least 2 (pairs at least 2, correlation sample size at least 4), means and SDs are plain decimals within plus or minus 1,000,000,000,000, counts are whole numbers up to 1,000,000,000 and the confidence level is from 0.5 to 0.9999. Downloads: a JSON report and a CSV table of measures, estimates, limits and methods.\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\": \"effect-size-calculator\",\n  \"category\": \"calculators\",\n  \"built\": true,\n  \"requirements\": \"Runs locally in your browser; nothing is uploaded. Group sizes are whole numbers of at least 2 (pairs at least 2, correlation sample size at least 4), means and SDs are plain decimals within plus or minus 1,000,000,000,000, counts are whole numbers up to 1,000,000,000 and the confidence level is from 0.5 to 0.9999. Downloads: a JSON report and a CSV table of measures, estimates, limits and methods.\",\n  \"implementation\": {\n    \"fields\": [\n      {\n        \"key\": \"mode\",\n        \"label\": \"Input type\",\n        \"value\": \"independent-means\",\n        \"type\": \"select\",\n        \"values\": [\n          \"independent-means\",\n          \"paired-means\",\n          \"two-by-two\",\n          \"t-statistic\",\n          \"f-statistic\",\n          \"correlation\"\n        ],\n        \"labels\": {\n          \"independent-means\": \"Two independent groups (n, mean, SD)\",\n          \"paired-means\": \"Paired measurements (mean and SD of differences)\",\n          \"two-by-two\": \"2 x 2 event counts\",\n          \"t-statistic\": \"Two-sample t statistic\",\n          \"f-statistic\": \"F statistic from an ANOVA\",\n          \"correlation\": \"Correlation r\"\n        }\n      },\n      {\n        \"key\": \"confidence\",\n        \"label\": \"Confidence level\",\n        \"value\": \"0.95\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"A proportion from 0.5 to 0.9999, for example 0.95.\"\n      },\n      {\n        \"key\": \"n1\",\n        \"label\": \"Group 1 size\",\n        \"value\": \"25\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Whole number of at least 2.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"independent-means\",\n            \"t-statistic\"\n          ]\n        }\n      },\n      {\n        \"key\": \"mean1\",\n        \"label\": \"Group 1 mean\",\n        \"value\": \"24.5\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Use a decimal point and no thousands separators.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"independent-means\"\n          ]\n        }\n      },\n      {\n        \"key\": \"sd1\",\n        \"label\": \"Group 1 standard deviation\",\n        \"value\": \"4.2\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Sample SD with n - 1, greater than zero.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"independent-means\"\n          ]\n        }\n      },\n      {\n        \"key\": \"n2\",\n        \"label\": \"Group 2 size\",\n        \"value\": \"30\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Whole number of at least 2. Group 2 is the comparison group for Glass delta.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"independent-means\",\n            \"t-statistic\"\n          ]\n        }\n      },\n      {\n        \"key\": \"mean2\",\n        \"label\": \"Group 2 mean\",\n        \"value\": \"21.9\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Use a decimal point and no thousands separators.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"independent-means\"\n          ]\n        }\n      },\n      {\n        \"key\": \"sd2\",\n        \"label\": \"Group 2 standard deviation\",\n        \"value\": \"5.1\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Sample SD with n - 1, greater than zero.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"independent-means\"\n          ]\n        }\n      },\n      {\n        \"key\": \"pairs\",\n        \"label\": \"Number of pairs\",\n        \"value\": \"18\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Whole number of at least 2.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"paired-means\"\n          ]\n        }\n      },\n      {\n        \"key\": \"meanDifference\",\n        \"label\": \"Mean of the differences\",\n        \"value\": \"1.7\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"First measurement minus second.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"paired-means\"\n          ]\n        }\n      },\n      {\n        \"key\": \"sdDifference\",\n        \"label\": \"SD of the differences\",\n        \"value\": \"2.9\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Greater than zero.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"paired-means\"\n          ]\n        }\n      },\n      {\n        \"key\": \"sdFirst\",\n        \"label\": \"SD of the first measurement (optional)\",\n        \"value\": \"\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Enter both measurement SDs for d_av, or leave both blank to skip it.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"paired-means\"\n          ]\n        }\n      },\n      {\n        \"key\": \"sdSecond\",\n        \"label\": \"SD of the second measurement (optional)\",\n        \"value\": \"\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Enter both measurement SDs for d_av, or leave both blank to skip it.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"paired-means\"\n          ]\n        }\n      },\n      {\n        \"key\": \"correlation\",\n        \"label\": \"Correlation between measurements (optional)\",\n        \"value\": \"\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Between -1 and 1; leave blank to skip d_rm.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"paired-means\"\n          ]\n        }\n      },\n      {\n        \"key\": \"a\",\n        \"label\": \"Group 1 events\",\n        \"value\": \"15\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Whole number of zero or more.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"two-by-two\"\n          ]\n        }\n      },\n      {\n        \"key\": \"b\",\n        \"label\": \"Group 1 non-events\",\n        \"value\": \"85\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Whole number of zero or more.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"two-by-two\"\n          ]\n        }\n      },\n      {\n        \"key\": \"c\",\n        \"label\": \"Group 2 events\",\n        \"value\": \"30\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Whole number of zero or more.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"two-by-two\"\n          ]\n        }\n      },\n      {\n        \"key\": \"d\",\n        \"label\": \"Group 2 non-events\",\n        \"value\": \"70\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Whole number of zero or more.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"two-by-two\"\n          ]\n        }\n      },\n      {\n        \"key\": \"t\",\n        \"label\": \"t statistic\",\n        \"value\": \"2.5\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"From a pooled-variance two-sample t test.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"t-statistic\"\n          ]\n        }\n      },\n      {\n        \"key\": \"f\",\n        \"label\": \"F statistic\",\n        \"value\": \"5.2\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Zero or more.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"f-statistic\"\n          ]\n        }\n      },\n      {\n        \"key\": \"df1\",\n        \"label\": \"Effect degrees of freedom\",\n        \"value\": \"2\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Whole number of at least 1.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"f-statistic\"\n          ]\n        }\n      },\n      {\n        \"key\": \"df2\",\n        \"label\": \"Error degrees of freedom\",\n        \"value\": \"45\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Whole number of at least 1.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"f-statistic\"\n          ]\n        }\n      },\n      {\n        \"key\": \"r\",\n        \"label\": \"Correlation r\",\n        \"value\": \"0.42\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Strictly between -1 and 1.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"correlation\"\n          ]\n        }\n      },\n      {\n        \"key\": \"sampleSize\",\n        \"label\": \"Sample size\",\n        \"value\": \"50\",\n        \"type\": \"text\",\n        \"maxLength\": 40,\n        \"help\": \"Whole number of at least 4.\",\n        \"showWhen\": {\n          \"mode\": [\n            \"correlation\"\n          ]\n        }\n      }\n    ],\n    \"registrationFamily\": \"statistical-analysis-reference\",\n    \"input\": false,\n    \"note\": \"Runs on your device. Enter summaries for one input type; intervals use the noncentral t or F distribution where noted, and the JSON report and CSV hold every measure.\",\n    \"experience\": {\n      \"automatic\": false,\n      \"single\": false,\n      \"inputMaxLength\": 1000000,\n      \"inputMode\": \"text\",\n      \"label\": \"Summary values\",\n      \"placeholder\": \"Enter values in the form fields\",\n      \"help\": \"This calculator reads the form fields below; there is no text box. 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\nTurn group summaries, paired differences, 2 x 2 counts or a published t, F or r into standardized effect sizes with confidence intervals. Every measure is labelled with the groups and standard deviation it uses.\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 Effect size calculator\n\n1. Choose the input type that matches what you have: two groups, paired differences, event counts or a test statistic.\n2. Enter the summary values and the confidence level.\n3. Calculate, then read each measure with its interval and the standard deviation it divides by.\n4. Download the JSON report or the CSV table of every measure.\n\n## Useful next steps\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- [Pooled summary statistics](https://happytails.ai/en/calculators/pooled-summary-statistics/) ([Markdown](https://happytails.ai/en/calculators/pooled-summary-statistics.md))\n\n- [Box plot comparison](https://happytails.ai/en/calculators/box-plot-comparison/) ([Markdown](https://happytails.ai/en/calculators/box-plot-comparison.md))\n\n## Which d is which\n\nd\\_s divides the mean difference by the pooled SD of two independent groups (Cohen 1988). Hedges g multiplies it by the exact small-sample correction J. Glass delta uses the SD of group 2 only. For paired data, d\\_z divides the mean difference by the SD of the differences, d\\_av by the average of the two SDs (enter both, or leave both blank to skip it) and d\\_rm adjusts d\\_z for the correlation (Lakens 2013, Frontiers in Psychology 4:863). These measures are not interchangeable, so report which one you used.\n\n### How the intervals are found\n\nIntervals for d\\_s, d\\_z and d from a t statistic invert the noncentral t distribution (Steiger and Fouladi 1997), computed accurately even for very large effects; the g interval multiplies those limits by J. A normal-approximation interval from the Hedges and Olkin (1985) variance is also listed. The partial eta squared interval inverts the noncentral F distribution with N = df1 + df2 + 1. Odds and risk ratios use log intervals (Woolf 1955; Katz et al. 1978), the risk difference a Wald interval, and r a Fisher z interval.\n\n### Assumptions and limits\n\nGroup SDs are sample SDs with n - 1. If any 2 x 2 cell is zero, 0.5 is added to every cell before ratios are computed, and the report says so. Conversions such as d to r or d to a log odds ratio (Chinn 2000, Statistics in Medicine 19:3127) assume roughly normal data. The d to r conversion allows unequal group sizes: r = d / sqrt(d^2 + a) with a = (n1 + n2)^2 / (n1 n2) (Borenstein et al. 2009, Introduction to Meta-Analysis, chapter 7). An effect size describes these data; it does not show importance or cause.\n"
}