{
  "id": "effect-size",
  "version": "754ff8fbeb7d",
  "status": "published",
  "name": "Effect Size Calculator",
  "question": "What is the effect size (Cohen’s d)?",
  "summary": "Computes the effect size between two independent groups as Cohen’s d and Hedges’ g, from the two means, standard deviations and sample sizes, or from a t statistic.",
  "category": "statistics",
  "subcategory": "tests",
  "url": "https://www.acalculator.org/statistics/effect-size-calculator",
  "markdown": "https://www.acalculator.org/statistics/effect-size-calculator.md",
  "kind": "function",
  "method": "Cohen’s d = (M₁ − M₂) ÷ √[((n₁ − 1)SD₁² + (n₂ − 1)SD₂²) ÷ (n₁ + n₂ − 2)], or d = t × √(1 ÷ n₁ + 1 ÷ n₂); Hedges’ g = d × (1 − 3 ÷ (4(n₁ + n₂) − 9)).",
  "assumptions": [
    "The two groups are independent (between-subjects), and the standard deviations are sample standard deviations.",
    "The pooled SD weights each group’s variance by its degrees of freedom, n − 1.",
    "The size labels are Cohen’s benchmarks for |d| (0.2 small, 0.5 medium, 0.8 large); they are rough guides, not rules."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "From",
        "description": "Work from the means and standard deviations of the two groups, or from a t statistic.",
        "type": "string",
        "enum": [
          "means",
          "t"
        ]
      },
      "m1": {
        "title": "Mean of group 1",
        "description": "The mean of group 1.",
        "type": "number",
        "minimum": -1000000000000000,
        "maximum": 1000000000000000
      },
      "s1": {
        "title": "Standard deviation of group 1",
        "description": "The standard deviation of group 1, 0 or more.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      },
      "n1": {
        "title": "Size of group 1",
        "description": "The number of people or observations in group 1, at least 2.",
        "type": "integer",
        "minimum": 2,
        "maximum": 1000000000
      },
      "m2": {
        "title": "Mean of group 2",
        "description": "The mean of group 2.",
        "type": "number",
        "minimum": -1000000000000000,
        "maximum": 1000000000000000
      },
      "s2": {
        "title": "Standard deviation of group 2",
        "description": "The standard deviation of group 2, 0 or more.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      },
      "n2": {
        "title": "Size of group 2",
        "description": "The number of people or observations in group 2, at least 2.",
        "type": "integer",
        "minimum": 2,
        "maximum": 1000000000
      },
      "t": {
        "title": "t statistic",
        "description": "The t value of an independent-samples (Student’s) t-test of the two groups.",
        "type": "number",
        "minimum": -1000000,
        "maximum": 1000000
      }
    }
  },
  "outputs": {
    "d": {
      "label": "Cohen’s d",
      "description": "The difference in means divided by the pooled standard deviation.",
      "format": "number"
    },
    "g": {
      "label": "Hedges’ g",
      "description": "Cohen’s d × J: corrected for the bias of small samples.",
      "format": "number"
    },
    "size": {
      "label": "Size of the effect",
      "description": "Cohen’s label for |d|: small from 0.2, medium from 0.5, large from 0.8.",
      "format": "text"
    },
    "j": {
      "label": "Correction factor J",
      "description": "1 − 3 ÷ (4(n₁ + n₂) − 9).",
      "format": "number"
    },
    "diff": {
      "label": "Difference in means",
      "description": "Mean of group 1 − mean of group 2.",
      "format": "number"
    },
    "pooled": {
      "label": "Pooled standard deviation",
      "description": "√[((n₁ − 1)SD₁² + (n₂ − 1)SD₂²) ÷ (n₁ + n₂ − 2)].",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": "means",
      "m1": 8.7,
      "s1": 0.82,
      "n1": 10,
      "m2": 7.7,
      "s2": 0.95,
      "n2": 10,
      "t": 2.52
    },
    "outputs": {
      "d": 1.1269081150666909,
      "g": 1.0792922792188024,
      "size": "large",
      "j": 0.9577464788732394,
      "diff": 1,
      "pooled": 0.8873837952092657
    },
    "text": "Cohen’s d is 1.1269 (large effect) and Hedges’ g is 1.0793."
  },
  "examples": [
    {
      "given": {
        "from": "means",
        "m1": 8.7,
        "s1": 0.82,
        "n1": 10,
        "m2": 7.7,
        "s2": 0.95,
        "n2": 10
      },
      "expect": {
        "d": 1.1269081150666909,
        "g": 1.0792922792188024,
        "j": 0.9577464788732394,
        "pooled": 0.8873837952092657,
        "diff": 1,
        "size": "large"
      },
      "source": "Lakens, D. (2013), Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs, Frontiers in Psychology 4, 863, formulas 1, 2 and 4 (movie ratings: M = 8.7, SD = 0.82 and M = 7.7, SD = 0.95, n = 10 each; t(18) = 2.52; Cohen’s d_s = 1.13, Hedges’s g_s = 1.08; small 0.2, medium 0.5, large 0.8), https://pmc.ncbi.nlm.nih.gov/articles/PMC3840331 (retrieved 2026-10-18); hand calculation in content.mdx"
    },
    {
      "given": {
        "from": "t",
        "t": 2.52,
        "n1": 10,
        "n2": 10
      },
      "expect": {
        "d": 1.1269782606598941,
        "g": 1.0793594609137014,
        "size": "large"
      },
      "source": "Lakens, D. (2013), Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs, Frontiers in Psychology 4, 863, formulas 1, 2 and 4 (movie ratings: M = 8.7, SD = 0.82 and M = 7.7, SD = 0.95, n = 10 each; t(18) = 2.52; Cohen’s d_s = 1.13, Hedges’s g_s = 1.08; small 0.2, medium 0.5, large 0.8), https://pmc.ncbi.nlm.nih.gov/articles/PMC3840331 (retrieved 2026-10-18); hand calculation in content.mdx: 2.52 × √(1/10 + 1/10) = 1.127"
    },
    {
      "given": {
        "from": "means",
        "m1": 100,
        "s1": 15,
        "n1": 30,
        "m2": 105,
        "s2": 15,
        "n2": 40
      },
      "expect": {
        "d": -0.3333333333333333,
        "g": -0.3296432964329643,
        "j": 0.988929889298893,
        "pooled": 15,
        "size": "small"
      },
      "source": "Lakens, D. (2013), Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs, Frontiers in Psychology 4, 863, formulas 1, 2 and 4 (movie ratings: M = 8.7, SD = 0.82 and M = 7.7, SD = 0.95, n = 10 each; t(18) = 2.52; Cohen’s d_s = 1.13, Hedges’s g_s = 1.08; small 0.2, medium 0.5, large 0.8), https://pmc.ncbi.nlm.nih.gov/articles/PMC3840331 (retrieved 2026-10-18); hand calculation in content.mdx: −5 ÷ 15 = −0.3333; J = 1 − 3 ÷ 271"
    }
  ],
  "sources": [
    "Lakens, D. (2013), Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs, Frontiers in Psychology 4, 863. Formula 1 (Cohen’s d_s from means and the pooled SD), formula 2 (d_s = t × √(1 ÷ n₁ + 1 ÷ n₂)), formula 4 (Hedges’s g_s = d_s × (1 − 3 ÷ (4(n₁ + n₂) − 9))); movie ratings example, d_s = 1.13 and g_s = 1.08; Cohen’s benchmarks 0.2, 0.5 and 0.8. https://pmc.ncbi.nlm.nih.gov/articles/PMC3840331 (retrieved 2026-10-18)"
  ],
  "related": [
    "t-test",
    "standard-deviation",
    "sample-size",
    "statistical-significance",
    "z-score"
  ],
  "changelog": []
}