{
  "test_id": "kruskal_wallis",
  "test_label": "Kruskal-Wallis test",
  "n": 72,
  "statistic": 54.691344622371446,
  "parameter": 5,
  "p_value": 1.5108444394185103e-10,
  "estimate": "NA",
  "conf_int": null,
  "effect_size": {
    "name": "epsilon_squared",
    "value": 0.77030062848410485,
    "ci": [0.73024445725537557, 0.83356451399964004],
    "ci_level": 0.94999999999999996,
    "note": "two-sided percentile-bootstrap CI at the run's confidence level"
  },
  "seed_used": 20261101,
  "assumptions": [
    {
      "id": "normality_by_group",
      "check": "normality by group (Shapiro-Wilk)",
      "per_group": [
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.95757467665337959,
          "p_value": 0.74872928313885267,
          "passed": true,
          "note": "no evidence against normality",
          "group": "A"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.95030650949219897,
          "p_value": 0.64147033116692287,
          "passed": true,
          "note": "no evidence against normality",
          "group": "B"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.85906682835297732,
          "p_value": 0.047589415197298569,
          "passed": false,
          "note": "evidence of non-normality",
          "group": "C"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.75063134382034025,
          "p_value": 0.0027132354459518922,
          "passed": false,
          "note": "evidence of non-normality",
          "group": "D"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.92127733196616357,
          "p_value": 0.2966693051027024,
          "passed": true,
          "note": "no evidence against normality",
          "group": "E"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.88475312240287929,
          "p_value": 0.10086380624210638,
          "passed": true,
          "note": "no evidence against normality",
          "group": "F"
        }
      ],
      "passed": false,
      "informational": true,
      "note": "evidence of non-normality - normality is not assumed by this rank-based test"
    },
    {
      "id": "sample_size",
      "check": "sample size",
      "statistic": 72,
      "p_value": "NA",
      "passed": true,
      "note": "adequate n"
    }
  ],
  "warnings": [
    "Ties are present. z-quantiles were corrected for ties."
  ],
  "flags": [],
  "test_label_i18n": {
    "key": "test.kruskal_wallis.label"
  },
  "alpha": 0.050000000000000003,
  "sidedness": "non-directional",
  "imputation": {
    "strategy": "complete_case",
    "n_rows": 72,
    "n_dropped": 0,
    "n_cells_imputed": 0,
    "imputed_cols": []
  },
  "conf_level": 0.94999999999999996,
  "posthoc": {
    "method_id": "dunn",
    "method": "Dunn's test",
    "p_adjust": "holm",
    "comparisons": [
      {
        "group1": "A",
        "group2": "B",
        "p_adjusted": 1,
        "effect": -0.13888888888888884,
        "effect_low": -0.54503205611753902,
        "effect_high": 0.32004893275311486
      },
      {
        "group1": "A",
        "group2": "C",
        "p_adjusted": 2.3469258807161552e-05,
        "effect": 0.99305555555555558,
        "effect_low": 0.98226568170382667,
        "effect_high": 0.99728965470926634
      },
      {
        "group1": "B",
        "group2": "C",
        "p_adjusted": 5.0978692364958697e-06,
        "effect": 0.99305555555555558,
        "effect_low": 0.98226568170382667,
        "effect_high": 0.99728965470926634
      },
      {
        "group1": "A",
        "group2": "D",
        "p_adjusted": 0.012764598641952429,
        "effect": 0.95138888888888884,
        "effect_low": 0.87976528495958162,
        "effect_high": 0.98078262764549229
      },
      {
        "group1": "B",
        "group2": "D",
        "p_adjusted": 0.0048233253208378804,
        "effect": 0.95833333333333326,
        "effect_low": 0.89639844679693503,
        "effect_high": 0.98356333586779898
      },
      {
        "group1": "C",
        "group2": "D",
        "p_adjusted": 0.58570895655937694,
        "effect": -0.72222222222222232,
        "effect_low": -0.88179237760100249,
        "effect_high": -0.41429126304368658
      },
      {
        "group1": "A",
        "group2": "E",
        "p_adjusted": 0.0011785985881994378,
        "effect": 1,
        "effect_low": 1,
        "effect_high": 1
      },
      {
        "group1": "B",
        "group2": "E",
        "p_adjusted": 0.00034509526336561096,
        "effect": 1,
        "effect_low": 1,
        "effect_high": 1
      },
      {
        "group1": "C",
        "group2": "E",
        "p_adjusted": 1,
        "effect": -0.46527777777777773,
        "effect_low": -0.75112017732086678,
        "effect_high": -0.032520827943585927
      },
      {
        "group1": "D",
        "group2": "E",
        "p_adjusted": 1,
        "effect": 0.32638888888888884,
        "effect_low": -0.13193913780376604,
        "effect_high": 0.66974208988486761
      },
      {
        "group1": "A",
        "group2": "F",
        "p_adjusted": 1,
        "effect": -0.19444444444444442,
        "effect_low": -0.58395686563106997,
        "effect_high": 0.2678460110710803
      },
      {
        "group1": "B",
        "group2": "F",
        "p_adjusted": 1,
        "effect": -0.034722222222222265,
        "effect_low": -0.4670027877300475,
        "effect_high": 0.41095344633486114
      },
      {
        "group1": "C",
        "group2": "F",
        "p_adjusted": 3.3344618777777657e-06,
        "effect": -1,
        "effect_low": -1,
        "effect_high": -1
      },
      {
        "group1": "D",
        "group2": "F",
        "p_adjusted": 0.0038381619821371772,
        "effect": -0.95833333333333326,
        "effect_low": -0.98356333586779898,
        "effect_high": -0.89639844679693503
      },
      {
        "group1": "E",
        "group2": "F",
        "p_adjusted": 0.0002496148448982694,
        "effect": -1,
        "effect_low": -1,
        "effect_high": -1
      }
    ],
    "effect_name": "rank_biserial",
    "group_letters": {
      "A": "a",
      "B": "a",
      "C": "b",
      "D": "b",
      "E": "b",
      "F": "a"
    }
  },
  "power": {
    "method": null,
    "n": "NA",
    "mdes": "NA",
    "mdes_metric": null,
    "mdes_metric_i18n": null,
    "required_n": "NA",
    "required_n_label": null,
    "required_n_label_i18n": null,
    "severely_underpowered": null,
    "note": "Power is not calculated for this test. The matching parametric test gives a rough guide.",
    "call_code": null
  },
  "explanations": ["At least one group's distribution of count differs from the others (ranks, not means, are compared).", "The grouping accounts for ~77.03% of the variation in the ranks of count (epsilon-squared) - a large effect (95% CI 73.02 to 83.36).", "Pairwise: A differed from C (adjusted p < 0.001).", "Pairwise: B differed from C (adjusted p < 0.001).", "Pairwise: A differed from D (adjusted p = 0.0128).", "Pairwise: B differed from D (adjusted p = 0.00482).", "Pairwise: A differed from E (adjusted p = 0.00118).", "Pairwise: B differed from E (adjusted p < 0.001).", "Pairwise: C differed from F (adjusted p < 0.001).", "Pairwise: D differed from F (adjusted p = 0.00384).", "Pairwise: E differed from F (adjusted p < 0.001).", "Compact-letter groups: A=a, B=a, C=b, D=b, E=b, F=a (groups sharing a letter are not significantly different at the adjusted threshold).", "This result is statistically significant at the 0.05 level (p < 0.001, n = 72)."],
  "explanations_i18n": [
    {
      "key": "exp.kruskal.omnibus",
      "args": {
        "outcome": "count"
      }
    },
    {
      "key": "exp.kruskal.effect_size",
      "args": {
        "percent": "77.03",
        "outcome": "count",
        "magnitude": {
          "key": "exp.magnitude_effect.large"
        },
        "ci": {
          "key": "exp.ci_paren",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "73.02",
                "upper": "83.36"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "A",
        "group2": "C",
        "p": "p < 0.001"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "B",
        "group2": "C",
        "p": "p < 0.001"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "A",
        "group2": "D",
        "p": "p = 0.0128"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "B",
        "group2": "D",
        "p": "p = 0.00482"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "A",
        "group2": "E",
        "p": "p = 0.00118"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "B",
        "group2": "E",
        "p": "p < 0.001"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "C",
        "group2": "F",
        "p": "p < 0.001"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "D",
        "group2": "F",
        "p": "p = 0.00384"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "E",
        "group2": "F",
        "p": "p < 0.001"
      }
    },
    {
      "key": "exp.posthoc.letters",
      "args": {
        "groups": "A=a, B=a, C=b, D=b, E=b, F=a"
      }
    },
    {
      "key": "exp.closer.significant",
      "args": {
        "alpha": "0.05",
        "p": "p < 0.001",
        "n": "72"
      }
    }
  ]
}