{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"cohens-d"},"result":{"entity_type":"calculator","id":"cohens-d","calculator_id":"cohens-d","canonical_url":"https://tttkmbb.com/statistics/cohens-d","name":"Cohen's d Effect Size Calculator","title":"Cohen's d Calculator – Standardised Mean Difference, Hedges' g and Glass's Δ","category":"statistics","category_name":"Statistics & Probability","tool_name":"calculate_cohens_d","featured_mcp_tool":false,"description":"Computes the standardised difference between two group means with the pooled standard deviation (Cohen's d), the small-sample corrected Hedges' g, Glass's Δ and the common-language effect size, with Cohen's small/medium/large interpretation.","use_when":"You want to express how large the difference between two groups is in standard-deviation units, e.g. for reporting alongside a t-test, power analysis or meta-analysis.","do_not_use_when":"You need to know whether the difference is statistically significant (use t-test), the outcome is binary (use odds-ratio), or the groups are paired (d for paired designs uses the SD of the differences).","inputs":[{"name":"mean_a","label":"Mean of group A","type":"number","required":true,"description":"Sample mean of the first (treatment) group.","example":105},{"name":"sd_a","label":"SD of group A","type":"number","required":true,"exclusive_min":0,"description":"Sample standard deviation (n − 1) of group A.","example":15},{"name":"n_a","label":"n of group A","type":"integer","required":true,"min":2,"description":"Sample size of group A.","example":30},{"name":"mean_b","label":"Mean of group B","type":"number","required":true,"description":"Sample mean of the second (control) group.","example":100},{"name":"sd_b","label":"SD of group B","type":"number","required":true,"exclusive_min":0,"description":"Sample standard deviation of group B (used alone for Glass's Δ).","example":15},{"name":"n_b","label":"n of group B","type":"integer","required":true,"min":2,"description":"Sample size of group B.","example":30}],"outputs":[{"name":"cohens_d","label":"Cohen's d","type":"number","decimals":4,"description":"(mean_a − mean_b) / pooled SD. Positive when A is higher."},{"name":"hedges_g","label":"Hedges' g","type":"number","decimals":4,"description":"d × (1 − 3 / (4(n_a + n_b) − 9)): bias-corrected d for small samples."},{"name":"glass_delta","label":"Glass's Δ","type":"number","decimals":4,"description":"(mean_a − mean_b) / sd_b: uses only the control group's SD."},{"name":"pooled_sd","label":"Pooled SD","type":"number","decimals":4,"description":"√(((n_a − 1) sd_a² + (n_b − 1) sd_b²) / (n_a + n_b − 2))."},{"name":"mean_difference","label":"Mean difference","type":"number","decimals":4,"description":"mean_a − mean_b in the original units."},{"name":"common_language_effect_size","label":"Common-language effect size","type":"number","decimals":4,"description":"Φ(d / √2): probability that a random member of A scores higher than a random member of B (normal, equal variances)."},{"name":"interpretation","label":"Interpretation","type":"string","decimals":4,"description":"Cohen's benchmarks on |d|: < 0.2 negligible, 0.2 small, 0.5 medium, 0.8 large."}],"input_schema":{"type":"object","properties":{"mean_a":{"description":"Sample mean of the first (treatment) group.","type":"number","examples":[105]},"sd_a":{"description":"Sample standard deviation (n − 1) of group A.","type":"number","exclusiveMinimum":0,"examples":[15]},"n_a":{"description":"Sample size of group A.","type":"integer","minimum":2,"examples":[30]},"mean_b":{"description":"Sample mean of the second (control) group.","type":"number","examples":[100]},"sd_b":{"description":"Sample standard deviation of group B (used alone for Glass's Δ).","type":"number","exclusiveMinimum":0,"examples":[15]},"n_b":{"description":"Sample size of group B.","type":"integer","minimum":2,"examples":[30]}},"additionalProperties":false,"required":["mean_a","sd_a","n_a","mean_b","sd_b","n_b"]},"output_schema":{"type":"object","properties":{"cohens_d":{"description":"(mean_a − mean_b) / pooled SD. Positive when A is higher.","type":"number"},"hedges_g":{"description":"d × (1 − 3 / (4(n_a + n_b) − 9)): bias-corrected d for small samples.","type":"number"},"glass_delta":{"description":"(mean_a − mean_b) / sd_b: uses only the control group's SD.","type":"number"},"pooled_sd":{"description":"√(((n_a − 1) sd_a² + (n_b − 1) sd_b²) / (n_a + n_b − 2)).","type":"number"},"mean_difference":{"description":"mean_a − mean_b in the original units.","type":"number"},"common_language_effect_size":{"description":"Φ(d / √2): probability that a random member of A scores higher than a random member of B (normal, equal variances).","type":"number"},"interpretation":{"description":"Cohen's benchmarks on |d|: < 0.2 negligible, 0.2 small, 0.5 medium, 0.8 large.","type":"string"}}},"formula":"pooled_sd = √(((n_a − 1)·sd_a² + (n_b − 1)·sd_b²) / (n_a + n_b − 2)); d = (mean_a − mean_b) / pooled_sd; g = d × (1 − 3 / (4(n_a + n_b) − 9)); Δ = (mean_a − mean_b) / sd_b; CLES = Φ(d / √2)","method":"Hedges' correction uses the Hedges (1981) approximation of the exact gamma-function factor (difference below 0.1 % for n_a + n_b ≥ 20). Cohen's benchmarks are conventions, not thresholds of practical importance.","sources":[{"name":"Cohen J (1988) Statistical Power Analysis for the Behavioral Sciences, 2nd ed., Lawrence Erlbaum","url":"https://doi.org/10.4324/9780203771587","type":"textbook","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Effect size","url":"https://en.wikipedia.org/wiki/Effect_size","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. 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