{
  "test_id": "one_way_anova",
  "test_label": "One-way ANOVA",
  "n": 30,
  "statistic": 4.8460878623801369,
  "parameter": "2,27",
  "p_value": 0.015909958325622912,
  "estimate": "NA",
  "conf_int": null,
  "effect_size": {
    "name": "Eta2",
    "value": 0.26414829683211971,
    "ci": [0.010992313635243381, 0.49017491101772159],
    "ci_level": 0.94999999999999996,
    "note": "two-sided 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": 0.95668149041173489,
          "p_value": 0.74747344382962133,
          "passed": true,
          "note": "no evidence against normality",
          "group": "ctrl"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.93041069351503658,
          "p_value": 0.45194396031826045,
          "passed": true,
          "note": "no evidence against normality",
          "group": "trt1"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.94100519724201981,
          "p_value": 0.56425189477199533,
          "passed": true,
          "note": "no evidence against normality",
          "group": "trt2"
        }
      ],
      "passed": true
    },
    {
      "id": "variance_homogeneity",
      "check": "variance homogeneity (Levene)",
      "statistic": 1.1191856948703909,
      "p_value": 0.34122662412547378,
      "passed": true,
      "note": "no evidence of unequal variances"
    }
  ],
  "warnings": [],
  "flags": [
    {
      "severity": "warning",
      "message": "Small study (n=30): at the standard 80% power, only a very large effect (Cohen's f of 0.60 or more) could be detected reliably - the study is underpowered for anything smaller. A significant result can still be real, but treat a non-significant one as inconclusive, not as proof of no effect. Detecting a medium effect would need about 53 per group to detect f=0.25.",
      "message_i18n": {
        "key": "flag.severely_underpowered",
        "args": {
          "n": "30",
          "power_percent": "80",
          "metric": {
            "key": "power.metric.cohens_f"
          },
          "mdes": "0.60",
          "required_n": {
            "key": "power.required_n.anova",
            "args": {
              "n": "53",
              "effect": "0.25"
            }
          }
        }
      }
    }
  ],
  "test_label_i18n": {
    "key": "test.one_way_anova.label"
  },
  "alpha": 0.050000000000000003,
  "sidedness": "non-directional",
  "imputation": {
    "strategy": "complete_case",
    "n_rows": 30,
    "n_dropped": 0,
    "n_cells_imputed": 0,
    "imputed_cols": []
  },
  "conf_level": 0.94999999999999996,
  "posthoc": {
    "method_id": "tukey_hsd",
    "method": "Tukey HSD",
    "p_adjust": "single-step (Tukey)",
    "comparisons": [
      {
        "group1": "trt1",
        "group2": "ctrl",
        "estimate": -0.37099999999999955,
        "conf_low": -1.0622160514104584,
        "conf_high": 0.32021605141045939,
        "p_adjusted": 0.39087114420212687,
        "effect": -0.51018406408551631,
        "effect_low": -1.3589603745516636,
        "effect_high": 0.3521429931483242
      },
      {
        "group1": "trt2",
        "group2": "ctrl",
        "estimate": 0.49400000000000066,
        "conf_low": -0.19721605141045828,
        "conf_high": 1.1852160514104595,
        "p_adjusted": 0.19799599129970757,
        "effect": 0.91394227845203757,
        "effect_low": 0.012518029470950293,
        "effect_high": 1.7929084905533554
      },
      {
        "group1": "trt2",
        "group2": "trt1",
        "estimate": 0.86500000000000021,
        "conf_low": 0.17378394858954127,
        "conf_high": 1.556216051410459,
        "p_adjusted": 0.012006423979452951,
        "effect": 1.2891424334415049,
        "effect_low": 0.3370902911152861,
        "effect_high": 2.2125870092714361
      }
    ],
    "effect_name": "Hedges_g",
    "group_letters": {
      "ctrl": "ab",
      "trt1": "a",
      "trt2": "b"
    }
  },
  "power": {
    "method": "one-way ANOVA (pwr)",
    "n": 30,
    "alpha": 0.050000000000000003,
    "target_power": 0.80000000000000004,
    "mdes": 0.59969411928905347,
    "mdes_metric": "Cohen's f",
    "mdes_metric_i18n": {
      "key": "power.metric.cohens_f"
    },
    "required_n": 53,
    "required_n_label": "53 per group to detect f=0.25",
    "required_n_label_i18n": {
      "key": "power.required_n.anova",
      "args": {
        "n": "53",
        "effect": "0.25"
      }
    },
    "severely_underpowered": true,
    "note": null,
    "call_code": "pwr::pwr.anova.test(k = 3, n = 10, sig.level = 0.05, power = 0.8)"
  },
  "explanations": ["At least one group's mean weight differs from the others.", "The grouping explains ~26.41% of the variation in weight - a large effect (95% CI 1.099 to 49.02).", "Pairwise: trt2 differed from trt1 by 0.865 (adjusted p = 0.012).", "Compact-letter groups: ctrl=ab, trt1=a, trt2=b (groups sharing a letter are not significantly different at the adjusted threshold).", "This result is statistically significant at the 0.05 level (p = 0.0159, n = 30)."],
  "explanations_i18n": [
    {
      "key": "exp.anova.omnibus",
      "args": {
        "outcome": "weight"
      }
    },
    {
      "key": "exp.anova.variance_explained",
      "args": {
        "percent": "26.41",
        "outcome": "weight",
        "magnitude": {
          "key": "exp.magnitude_effect.large"
        },
        "ci": {
          "key": "exp.ci_paren",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "1.099",
                "upper": "49.02"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.posthoc.pair_estimate",
      "args": {
        "group1": "trt2",
        "group2": "trt1",
        "difference": "0.865",
        "p": "p = 0.012"
      }
    },
    {
      "key": "exp.posthoc.letters",
      "args": {
        "groups": "ctrl=ab, trt1=a, trt2=b"
      }
    },
    {
      "key": "exp.closer.significant",
      "args": {
        "alpha": "0.05",
        "p": "p = 0.0159",
        "n": "30"
      }
    }
  ]
}