{
  "test_id": "mixed_model",
  "test_label": "Linear mixed-effects model (random intercept and slope)",
  "n": 578,
  "statistic": 244.20974183932759,
  "parameter": "1,48.7",
  "p_value": 1.295140609985065e-20,
  "estimate": 8.4530515096816892,
  "conf_int": [7.3658860448869268, 9.5402169744764524],
  "effect_size": null,
  "seed_used": 20261110,
  "assumptions": [
    {
      "id": "normality",
      "check": "normality (Shapiro-Wilk)",
      "statistic": 0.9891373863507863,
      "p_value": 0.00027850824823834764,
      "passed": false,
      "note": "evidence of non-normality"
    },
    {
      "id": "normality_blups",
      "check": "random-intercept normality (Shapiro-Wilk on BLUPs)",
      "statistic": 0.98747370444106841,
      "p_value": 0.87044293454709887,
      "passed": true,
      "note": "no evidence against normality"
    },
    {
      "id": "normality_blups",
      "check": "random-slope normality (Shapiro-Wilk on BLUPs)",
      "statistic": 0.990637800904553,
      "p_value": 0.95988928026088782,
      "passed": true,
      "note": "no evidence against normality"
    }
  ],
  "warnings": [],
  "flags": [
    {
      "severity": "warning",
      "message": "The model's residuals appear non-normal. There is no drop-in non-parametric alternative for this model - interpret p-values cautiously (with n = 578 the central limit theorem softens this concern) and consider transforming the outcome if the skew is strong.",
      "message_i18n": {
        "key": "flag.non_normal_residuals_no_alternative",
        "args": {
          "n": "578"
        }
      },
      "trigger": "normality (Shapiro-Wilk)"
    },
    {
      "severity": "warning",
      "message": "p-value from the Kenward-Roger F-test for 'Time'; random intercept + slope on 'Time' per Chick.",
      "message_i18n": {
        "key": "analysis.effect_note.mixed_lmer",
        "args": {
          "term": "Time",
          "slope": {
            "key": "analysis.effect_note.random_slope",
            "args": {
              "column": "Time"
            }
          },
          "cluster": "Chick",
          "method": {
            "key": "analysis.effect_note.method_kenward_roger"
          }
        }
      }
    },
    {
      "severity": "note",
      "message": "Values beyond Tukey's 1.5xIQR fence in: 'weight' (9). 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": "'weight' (9)"
        }
      },
      "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.mixed_model.label_random_slope"
  },
  "coefficients": [
    {
      "term": "(Intercept)",
      "estimate": 29.178000559442363,
      "std.error": 1.9574324983714237,
      "df": 48.908585168829688,
      "statistic": 14.90626143364757,
      "p.value": 8.0988112760738447e-20,
      "conf.low": 25.244206701772399,
      "conf.high": 33.111794417112328
    },
    {
      "term": "Time",
      "estimate": 8.4530515096816892,
      "std.error": 0.54091873429502157,
      "df": 48.736687535409537,
      "statistic": 15.627211582343392,
      "p.value": 1.295140609985065e-20,
      "conf.low": 7.3658860448869268,
      "conf.high": 9.5402169744764524
    }
  ],
  "alpha": 0.050000000000000003,
  "sidedness": "two-sided",
  "estimate_label": "Time",
  "imputation": {
    "strategy": "complete_case",
    "n_rows": 578,
    "n_dropped": 0,
    "n_cells_imputed": 0,
    "imputed_cols": []
  },
  "conf_level": 0.94999999999999996,
  "term_tests": [
    {
      "term": "Time",
      "test_method": "F",
      "statistic": 244.20974183932759,
      "df": 1,
      "df_resid": 48.736687535409537,
      "p_value": 1.295140609985065e-20
    }
  ],
  "df_method": "kenward_roger",
  "primary_multilevel": false,
  "variance_components": [
    {
      "group": "Chick",
      "term": "(Intercept)",
      "variance": 140.53768534828194,
      "sd": 11.854859145020743
    },
    {
      "group": "Chick",
      "term": "Time",
      "variance": 14.143737884765519,
      "sd": 3.7608161195099021
    },
    {
      "group": "Chick",
      "term": "(Intercept)",
      "var2": "Time",
      "sd": -0.95080345057824822
    },
    {
      "group": "Residual",
      "variance": 163.50536833419358,
      "sd": 12.786921769299818
    }
  ],
  "variance_components_ci": "not_computed_random_slope",
  "random_slope": "Time",
  "cluster_sizes": {
    "min": 2,
    "median": 12,
    "max": 12,
    "singletons": 0
  },
  "predictor_levels": [
    {
      "predictor": "Time",
      "level": "within"
    }
  ],
  "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.",
    "call_code": null
  },
  "explanations": ["Each 1-unit increase in Time is associated with a 8.453-unit increase in weight (95% CI 7.366 to 9.54).", "With a random slope on Time, the share of the variation that lies between Chicks depends on the value of Time, so no single ICC is reported; the variance components give each part separately.", "This result is statistically significant at the 0.05 level (p < 0.001, n = 578)."],
  "explanations_i18n": [
    {
      "key": "exp.mixed.increase",
      "args": {
        "term": "Time",
        "difference": "8.453",
        "outcome": "weight",
        "ci": {
          "key": "exp.ci_paren",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "7.366",
                "upper": "9.54"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.mixed.icc_slope",
      "args": {
        "slope": "Time",
        "cluster": "Chick"
      }
    },
    {
      "key": "exp.closer.significant",
      "args": {
        "alpha": "0.05",
        "p": "p < 0.001",
        "n": "578"
      }
    }
  ]
}