{
  "test_id": "two_way_anova",
  "test_label": "Two-way ANOVA (factorial)",
  "n": 60,
  "statistic": 4.1069910940225203,
  "parameter": "2,54",
  "p_value": 0.021860268964790996,
  "estimate": "NA",
  "conf_int": null,
  "effect_size": {
    "name": "partial_eta_sq",
    "value": 0.13202791236249509,
    "ci": [0.0014655692196828708, 0.29497203400256838],
    "ci_level": 0.94999999999999996,
    "note": "two-sided CI at the run's confidence level"
  },
  "seed_used": 20261101,
  "assumptions": [
    {
      "id": "normality",
      "check": "normality (Shapiro-Wilk)",
      "statistic": 0.98498843040640327,
      "p_value": 0.66942419831272115,
      "passed": true,
      "note": "no evidence against normality"
    },
    {
      "id": "variance_homogeneity",
      "check": "variance homogeneity (Levene)",
      "statistic": 1.7085782331448909,
      "p_value": 0.1483605859287056,
      "passed": true,
      "note": "no evidence of unequal variances"
    },
    {
      "id": "sample_size",
      "check": "sample size",
      "statistic": 60,
      "p_value": "NA",
      "passed": true,
      "note": "adequate n"
    }
  ],
  "warnings": [],
  "flags": [],
  "test_label_i18n": {
    "key": "test.two_way_anova.label"
  },
  "coefficients": [
    {
      "estimate": 13.229999999999993,
      "std.error": 1.1483530880416595,
      "df": 54,
      "conf.low": 10.927690678258474,
      "conf.high": 15.532309321741513,
      "statistic": 11.520846800317953,
      "p.value": 3.6025476090880816e-16,
      "term": "OJ x 0.5"
    },
    {
      "estimate": 7.9799999999999853,
      "std.error": 1.1483530880416599,
      "df": 54,
      "conf.low": 5.6776906782584646,
      "conf.high": 10.282309321741506,
      "statistic": 6.9490821970171659,
      "p.value": 4.9841993916337506e-09,
      "term": "VC x 0.5"
    },
    {
      "estimate": 22.699999999999996,
      "std.error": 1.148353088041659,
      "df": 54,
      "conf.low": 20.397690678258478,
      "conf.high": 25.002309321741514,
      "statistic": 19.767439332367175,
      "p.value": 2.168865154112023e-26,
      "term": "OJ x 1"
    },
    {
      "estimate": 16.769999999999996,
      "std.error": 1.1483530880416595,
      "df": 54,
      "conf.low": 14.467690678258476,
      "conf.high": 19.072309321741514,
      "statistic": 14.603522361400765,
      "p.value": 2.1285815144858466e-20,
      "term": "VC x 1"
    },
    {
      "estimate": 26.059999999999995,
      "std.error": 1.1483530880416595,
      "df": 54,
      "conf.low": 23.757690678258477,
      "conf.high": 28.362309321741513,
      "statistic": 22.693368678479665,
      "p.value": 2.7631435361832791e-29,
      "term": "OJ x 2"
    },
    {
      "estimate": 26.139999999999993,
      "std.error": 1.1483530880416595,
      "df": 54,
      "conf.low": 23.837690678258475,
      "conf.high": 28.442309321741511,
      "statistic": 22.763033662910914,
      "p.value": 2.3779477414436957e-29,
      "term": "VC x 2"
    }
  ],
  "alpha": 0.050000000000000003,
  "sidedness": "non-directional",
  "imputation": {
    "strategy": "complete_case",
    "n_rows": 60,
    "n_dropped": 0,
    "n_cells_imputed": 0,
    "imputed_cols": []
  },
  "conf_level": 0.94999999999999996,
  "term_tests": [
    {
      "term": "supp",
      "test_method": "F",
      "statistic": 15.571979452497253,
      "df": 1,
      "df_resid": 54,
      "p_value": 0.00023118280977342423,
      "effect_size": 0.22382544775989269,
      "effect_size_low": 0.058648646607849769,
      "effect_size_high": 0.40207631334500726
    },
    {
      "term": "dose",
      "test_method": "F",
      "statistic": 91.999964892867141,
      "df": 2,
      "df_resid": 54,
      "p_value": 4.0462911959921633e-18,
      "effect_size": 0.77310917676061952,
      "effect_size_low": 0.66166185142056533,
      "effect_size_high": 0.83821101365786987
    },
    {
      "term": "supp:dose",
      "test_method": "F",
      "statistic": 4.1069910940225203,
      "df": 2,
      "df_resid": 54,
      "p_value": 0.021860268964790996,
      "effect_size": 0.13202791236249509,
      "effect_size_low": 0.0014655692196828708,
      "effect_size_high": 0.29497203400256838
    }
  ],
  "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": ["This tests whether supp's effect on len depends on dose (the interaction) - this dataset shows evidence that it does.", "The interaction accounts for ~13.2% of the variation in len that remains once the other effects in the model are set aside (partial eta-squared 0.132; 95% CI 0.001466 to 0.295) - a medium effect by Cohen's conventional benchmarks, which are rough guides, not thresholds of importance.", "Tested on its own (Type II), the main effect of supp on len gives F = 15.57 on 1 and 54 degrees of freedom (p < 0.001; partial eta-squared 0.2238; 95% CI 0.05865 to 0.4021).", "Tested on its own (Type II), the main effect of dose on len gives F = 92 on 2 and 54 degrees of freedom (p < 0.001; partial eta-squared 0.7731; 95% CI 0.6617 to 0.8382).", "Estimated cell means: OJ x 0.5 13.23; VC x 0.5 7.98; OJ x 1 22.7; VC x 1 16.77; OJ x 2 26.06; VC x 2 26.14.", "This result is statistically significant at the 0.05 level (p = 0.0219, n = 60)."],
  "explanations_i18n": [
    {
      "key": "exp.two_way.interaction_evidence",
      "args": {
        "factor1": "supp",
        "outcome": "len",
        "factor2": "dose"
      }
    },
    {
      "key": "exp.two_way.variance_explained_ci",
      "args": {
        "percent": "13.2",
        "outcome": "len",
        "magnitude": {
          "key": "exp.magnitude_effect.medium"
        },
        "eta_squared": "0.132",
        "ci": {
          "key": "exp.ci_semicolon",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "0.001466",
                "upper": "0.295"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.two_way.main_effect",
      "args": {
        "term": "supp",
        "outcome": "len",
        "statistic": "15.57",
        "df": "1",
        "df_resid": "54",
        "p": "p < 0.001",
        "eta_squared": "0.2238",
        "ci": {
          "key": "exp.ci_semicolon",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "0.05865",
                "upper": "0.4021"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.two_way.main_effect",
      "args": {
        "term": "dose",
        "outcome": "len",
        "statistic": "92",
        "df": "2",
        "df_resid": "54",
        "p": "p < 0.001",
        "eta_squared": "0.7731",
        "ci": {
          "key": "exp.ci_semicolon",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "0.6617",
                "upper": "0.8382"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.two_way.cell_means",
      "args": {
        "means": "OJ x 0.5 13.23; VC x 0.5 7.98; OJ x 1 22.7; VC x 1 16.77; OJ x 2 26.06; VC x 2 26.14"
      }
    },
    {
      "key": "exp.closer.significant",
      "args": {
        "alpha": "0.05",
        "p": "p = 0.0219",
        "n": "60"
      }
    }
  ]
}