{
  "test_id": "mann_whitney",
  "test_label": "Mann-Whitney U test",
  "n": 24,
  "statistic": 38.5,
  "parameter": "NA",
  "p_value": 0.049139176881807113,
  "estimate": -2,
  "conf_int": [-3, 0],
  "effect_size": {
    "name": "rank_biserial",
    "value": -0.46527777777777773,
    "ci": [-0.75112017732086678, -0.032520827943585927],
    "ci_level": 0.94999999999999996
  },
  "seed_used": 20261111,
  "assumptions": [
    {
      "id": "normality_by_group",
      "check": "normality by group (Shapiro-Wilk)",
      "per_group": [
        {
          "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": 0.92127733196616357,
          "p_value": 0.2966693051027024,
          "passed": true,
          "note": "no evidence against normality",
          "group": "E"
        }
      ],
      "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": 24,
      "p_value": "NA",
      "passed": true,
      "note": "adequate n"
    }
  ],
  "warnings": [],
  "flags": [
    {
      "severity": "note",
      "message": "Analysis restricted to a subpopulation (spray in C, E): 24 of 72 rows used. Report this restriction in the manuscript, and treat a post-hoc subgroup as exploratory.",
      "message_i18n": {
        "key": "flag.subpopulation",
        "args": {
          "filter": {
            "key": "prep.filter.in_levels",
            "args": {
              "column": "spray",
              "levels": "C, E"
            }
          },
          "rows_used": "24",
          "rows_total": "72"
        }
      }
    },
    {
      "severity": "note",
      "message": "p = 0.049 is borderline (near 0.05); treat the significance decision cautiously.",
      "message_i18n": {
        "key": "flag.borderline_p",
        "args": {
          "p": "0.049"
        }
      }
    }
  ],
  "test_label_i18n": {
    "key": "test.mann_whitney.label"
  },
  "alpha": 0.050000000000000003,
  "sidedness": "two-sided",
  "alternative": "two.sided",
  "alternative_sides": ["C", "E"],
  "alternative_statement": "group C minus group E differs from zero",
  "alternative_statement_i18n": {
    "key": "analysis.alternative.group_two_sided",
    "args": {
      "first": "C",
      "second": "E"
    }
  },
  "estimate_label": "Hodges-Lehmann difference in location",
  "exact": true,
  "conf_level_achieved": 0.96881355957274651,
  "imputation": {
    "strategy": "complete_case",
    "n_rows": 24,
    "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
  },
  "filter": [
    {
      "column": "spray",
      "op": "levels",
      "levels": ["C", "E"]
    }
  ],
  "rows_filtered_out": 48,
  "explanations": ["This is a rank-based comparison of count: it compares whole distributions rather than means, so it does not assume normality.", "The Hodges-Lehmann estimate of the difference in location is -2 (96.88% CI -3 to 0).", "The rank-biserial correlation is r = -0.4653 (95% CI -0.7511 to -0.03252) - a moderate effect.", "This result is statistically significant at the 0.05 level (p = 0.0491, n = 24)."],
  "explanations_i18n": [
    {
      "key": "exp.rank_based.intro",
      "args": {
        "outcome": "count"
      }
    },
    {
      "key": "exp.hodges_lehmann.location",
      "args": {
        "estimate": "-2",
        "ci": {
          "key": "exp.ci_paren",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "96.88",
                "lower": "-3",
                "upper": "0"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.rank_biserial",
      "args": {
        "r": "-0.4653",
        "ci": {
          "key": "exp.ci_paren",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "-0.7511",
                "upper": "-0.03252"
              }
            }
          }
        },
        "strength": {
          "key": "exp.strength_effect.moderate"
        }
      }
    },
    {
      "key": "exp.closer.significant",
      "args": {
        "alpha": "0.05",
        "p": "p = 0.0491",
        "n": "24"
      }
    }
  ]
}