{
  "test_id": "mann_whitney",
  "test_label": "Mann-Whitney U test",
  "n": 120,
  "statistic": 2177.5,
  "parameter": "NA",
  "p_value": 0.047842160793405197,
  "estimate": 4.5000707071192636,
  "conf_int": [0.099945894485119008, 8.4999993860372083],
  "effect_size": {
    "name": "rank_biserial",
    "value": 0.2097222222222222,
    "ci": [0.0054233336101637527, 0.39721527196241568],
    "ci_level": 0.94999999999999996
  },
  "seed_used": 1,
  "assumptions": [
    {
      "id": "normality_by_group",
      "check": "normality by group (Shapiro-Wilk)",
      "per_group": [
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.956279577278774,
          "p_value": 0.031030730309071816,
          "passed": false,
          "note": "evidence of non-normality",
          "group": "A"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.67555915358703922,
          "p_value": 3.0849101141375795e-10,
          "passed": false,
          "note": "evidence of non-normality",
          "group": "B"
        }
      ],
      "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": 120,
      "p_value": "NA",
      "passed": true,
      "note": "adequate n"
    }
  ],
  "warnings": [],
  "flags": [
    {
      "severity": "note",
      "message": "p = 0.048 is borderline (near 0.05); treat the significance decision cautiously.",
      "message_i18n": {
        "key": "flag.borderline_p",
        "args": {
          "p": "0.048"
        }
      }
    },
    {
      "severity": "note",
      "message": "Values beyond Tukey's 1.5xIQR fence in: 'days' (8). Descriptive only - nothing has been removed or changed; check whether these reflect genuine extreme cases or data-entry errors.",
      "message_i18n": {
        "key": "sanity.outlier_values",
        "args": {
          "columns": "'days' (8)"
        }
      },
      "code": "outlier_values",
      "citations": ["Tukey's 1.5xIQR fence is a descriptive convention for flagging unusually extreme values, not a definition of error or a license to remove data - some 'outliers' are genuine biological extremes (Tukey, J.W., 1977, Exploratory Data Analysis, Addison-Wesley)."]
    }
  ],
  "test_label_i18n": {
    "key": "test.mann_whitney.label"
  },
  "alpha": 0.050000000000000003,
  "sidedness": "two-sided",
  "alternative": "two.sided",
  "alternative_sides": ["A", "B"],
  "alternative_statement": "group A minus group B differs from zero",
  "alternative_statement_i18n": {
    "key": "analysis.alternative.group_two_sided",
    "args": {
      "first": "A",
      "second": "B"
    }
  },
  "estimate_label": "Hodges-Lehmann difference in location",
  "exact": false,
  "conf_level_achieved": 0.94999999999999996,
  "imputation": {
    "strategy": "complete_case",
    "n_rows": 120,
    "n_dropped": 0,
    "n_cells_imputed": 0,
    "imputed_cols": []
  },
  "conf_level": 0.94999999999999996,
  "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": ["This is a rank-based comparison of days: it compares whole distributions rather than means, so it does not assume normality.", "The Hodges-Lehmann estimate of the difference in location is 4.5 (95% CI 0.09995 to 8.5).", "The rank-biserial correlation is r = 0.2097 (95% CI 0.005423 to 0.3972) - a weak effect.", "This result is statistically significant at the 0.05 level (p = 0.0478, n = 120)."],
  "explanations_i18n": [
    {
      "key": "exp.rank_based.intro",
      "args": {
        "outcome": "days"
      }
    },
    {
      "key": "exp.hodges_lehmann.location",
      "args": {
        "estimate": "4.5",
        "ci": {
          "key": "exp.ci_paren",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "0.09995",
                "upper": "8.5"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.rank_biserial",
      "args": {
        "r": "0.2097",
        "ci": {
          "key": "exp.ci_paren",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "0.005423",
                "upper": "0.3972"
              }
            }
          }
        },
        "strength": {
          "key": "exp.strength_effect.weak"
        }
      }
    },
    {
      "key": "exp.closer.significant",
      "args": {
        "alpha": "0.05",
        "p": "p = 0.0478",
        "n": "120"
      }
    }
  ]
}