{
  "test_id": "kruskal_wallis",
  "test_label": "Kruskal-Wallis test",
  "n": 71,
  "statistic": 37.342717694256208,
  "parameter": 5,
  "p_value": 5.1128295119371503e-07,
  "estimate": "NA",
  "conf_int": null,
  "effect_size": {
    "name": "epsilon_squared",
    "value": 0.53346739563223156,
    "ci": [0.42559294139717213, 0.69728493677124082],
    "ci_level": 0.94999999999999996,
    "note": "two-sided percentile-bootstrap CI at the run's confidence level"
  },
  "seed_used": 20261111,
  "assumptions": [
    {
      "id": "normality_by_group",
      "check": "normality by group (Shapiro-Wilk)",
      "per_group": [
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.91662568818427614,
          "p_value": 0.259184144181969,
          "passed": true,
          "note": "no evidence against normality",
          "group": "casein"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.93758339227754028,
          "p_value": 0.52644988544924698,
          "passed": true,
          "note": "no evidence against normality",
          "group": "horsebean"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.96931284120061467,
          "p_value": 0.90347338009699862,
          "passed": true,
          "note": "no evidence against normality",
          "group": "linseed"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.97913808080876996,
          "p_value": 0.96117950886243597,
          "passed": true,
          "note": "no evidence against normality",
          "group": "meatmeal"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.94640285529556489,
          "p_value": 0.50637676192137626,
          "passed": true,
          "note": "no evidence against normality",
          "group": "soybean"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.92808839227006124,
          "p_value": 0.36029036930694958,
          "passed": true,
          "note": "no evidence against normality",
          "group": "sunflower"
        }
      ],
      "passed": true,
      "informational": true,
      "note": "no evidence against normality - normality is not assumed by this rank-based test"
    },
    {
      "id": "sample_size",
      "check": "sample size",
      "statistic": 71,
      "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": 71,
    "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": "casein",
        "group2": "horsebean",
        "p_adjusted": 2.0808168293690061e-05,
        "effect": 0.94999999999999996,
        "effect_low": 0.87079890751712252,
        "effect_high": 0.98113977691629028
      },
      {
        "group1": "casein",
        "group2": "linseed",
        "p_adjusted": 0.010325336756470205,
        "effect": 0.78472222222222232,
        "effect_low": 0.527049059206809,
        "effect_high": 0.91025991045153387
      },
      {
        "group1": "horsebean",
        "group2": "linseed",
        "p_adjusted": 0.58301395656025834,
        "effect": -0.66666666666666674,
        "effect_low": -0.86175517590397044,
        "effect_high": -0.29981246139695256
      },
      {
        "group1": "casein",
        "group2": "meatmeal",
        "p_adjusted": 0.6273878719314282,
        "effect": 0.42424242424242425,
        "effect_low": -0.029646776563203203,
        "effect_high": 0.73308502273238707
      },
      {
        "group1": "horsebean",
        "group2": "meatmeal",
        "p_adjusted": 0.0092166097993047844,
        "effect": -0.8727272727272728,
        "effect_low": -0.95179019656002051,
        "effect_high": -0.68493353747718899
      },
      {
        "group1": "linseed",
        "group2": "meatmeal",
        "p_adjusted": 0.48150709371962963,
        "effect": -0.52272727272727271,
        "effect_low": -0.78665497642905957,
        "effect_high": -0.097266817780839218
      },
      {
        "group1": "casein",
        "group2": "soybean",
        "p_adjusted": 0.099376503747535636,
        "effect": 0.64285714285714279,
        "effect_low": 0.29987717652735968,
        "effect_high": 0.83866963260238059
      },
      {
        "group1": "horsebean",
        "group2": "soybean",
        "p_adjusted": 0.083390942550497602,
        "effect": -0.82857142857142851,
        "effect_low": -0.93045171954375283,
        "effect_high": -0.60777129721486278
      },
      {
        "group1": "linseed",
        "group2": "soybean",
        "p_adjusted": 0.98995368025577801,
        "effect": -0.27976190476190471,
        "effect_low": -0.62978953825840545,
        "effect_high": 0.16470567329955027
      },
      {
        "group1": "meatmeal",
        "group2": "soybean",
        "p_adjusted": 0.98995368025577801,
        "effect": 0.27272727272727271,
        "effect_low": -0.18306309105663002,
        "effect_high": 0.6320160061132486
      },
      {
        "group1": "casein",
        "group2": "sunflower",
        "p_adjusted": 0.98995368025577801,
        "effect": 0.0069444444444444198,
        "effect_low": -0.43378491258531127,
        "effect_high": 0.44499227578105605
      },
      {
        "group1": "horsebean",
        "group2": "sunflower",
        "p_adjusted": 9.1736975946665754e-06,
        "effect": -0.98333333333333339,
        "effect_low": -0.99377948307782693,
        "effect_high": -0.95573437573608777
      },
      {
        "group1": "linseed",
        "group2": "sunflower",
        "p_adjusted": 0.0062496701540595634,
        "effect": -0.88888888888888884,
        "effect_low": -0.95520708687149958,
        "effect_high": -0.7375624185479569
      },
      {
        "group1": "meatmeal",
        "group2": "sunflower",
        "p_adjusted": 0.58301395656025834,
        "effect": -0.45454545454545459,
        "effect_low": -0.74998658166429188,
        "effect_high": -0.0079046836152213019
      },
      {
        "group1": "soybean",
        "group2": "sunflower",
        "p_adjusted": 0.071495100142169712,
        "effect": -0.73809523809523814,
        "effect_low": -0.88533556477398612,
        "effect_high": -0.45630812181230396
      }
    ],
    "effect_name": "rank_biserial",
    "group_letters": {
      "casein": "a",
      "horsebean": "b",
      "linseed": "bc",
      "meatmeal": "ac",
      "soybean": "abc",
      "sunflower": "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 weight differs from the others (ranks, not means, are compared).", "The grouping accounts for ~53.35% of the variation in the ranks of weight (epsilon-squared) - a large effect (95% CI 42.56 to 69.73).", "Pairwise: casein differed from horsebean (adjusted p < 0.001).", "Pairwise: casein differed from linseed (adjusted p = 0.0103).", "Pairwise: horsebean differed from meatmeal (adjusted p = 0.00922).", "Pairwise: horsebean differed from sunflower (adjusted p < 0.001).", "Pairwise: linseed differed from sunflower (adjusted p = 0.00625).", "Compact-letter groups: casein=a, horsebean=b, linseed=bc, meatmeal=ac, soybean=abc, sunflower=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 = 71)."],
  "explanations_i18n": [
    {
      "key": "exp.kruskal.omnibus",
      "args": {
        "outcome": "weight"
      }
    },
    {
      "key": "exp.kruskal.effect_size",
      "args": {
        "percent": "53.35",
        "outcome": "weight",
        "magnitude": {
          "key": "exp.magnitude_effect.large"
        },
        "ci": {
          "key": "exp.ci_paren",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "42.56",
                "upper": "69.73"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "casein",
        "group2": "horsebean",
        "p": "p < 0.001"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "casein",
        "group2": "linseed",
        "p": "p = 0.0103"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "horsebean",
        "group2": "meatmeal",
        "p": "p = 0.00922"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "horsebean",
        "group2": "sunflower",
        "p": "p < 0.001"
      }
    },
    {
      "key": "exp.posthoc.pair",
      "args": {
        "group1": "linseed",
        "group2": "sunflower",
        "p": "p = 0.00625"
      }
    },
    {
      "key": "exp.posthoc.letters",
      "args": {
        "groups": "casein=a, horsebean=b, linseed=bc, meatmeal=ac, soybean=abc, sunflower=a"
      }
    },
    {
      "key": "exp.closer.significant",
      "args": {
        "alpha": "0.05",
        "p": "p < 0.001",
        "n": "71"
      }
    }
  ]
}