{
  "test_id": "welch_t",
  "test_label": "Welch's t-test",
  "n": 60,
  "statistic": 1.915268268695268,
  "parameter": 55.30943268264059,
  "p_value": 0.060634507880934066,
  "estimate": 3.6999999999999993,
  "conf_int": [-0.17101561836716456, 7.5710156183671629],
  "effect_size": {
    "name": "Cohens_d",
    "value": 0.49452014054508575,
    "ci": [-0.021510104383973203, 1.0064209690211456],
    "ci_level": 0.94999999999999996
  },
  "seed_used": 20261101,
  "assumptions": [
    {
      "id": "normality_by_group",
      "check": "normality by group (Shapiro-Wilk)",
      "per_group": [
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.91784337938922911,
          "p_value": 0.023587728999479349,
          "passed": false,
          "note": "evidence of non-normality",
          "group": "OJ"
        },
        {
          "id": "normality",
          "check": "normality (Shapiro-Wilk)",
          "statistic": 0.96567145254977405,
          "p_value": 0.42844646300978823,
          "passed": true,
          "note": "no evidence against normality",
          "group": "VC"
        }
      ],
      "passed": false
    },
    {
      "id": "variance_homogeneity",
      "check": "variance homogeneity (Levene)",
      "statistic": 1.2135720656945042,
      "p_value": 0.27517646161440734,
      "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": [
    {
      "severity": "warning",
      "message": "Outcome appears non-normal; consider the non-parametric alternative (Mann-Whitney U test).",
      "message_i18n": {
        "key": "flag.non_normal_with_alternative",
        "args": {
          "test_id": {
            "key": "test.mann_whitney.label"
          }
        }
      },
      "trigger": "normality by group (Shapiro-Wilk)",
      "suggested_tests": ["mann_whitney"]
    },
    {
      "severity": "note",
      "message": "The result was not significant; at n=60 this study could detect Cohen's d >= 0.74 (80% power), so treat a null result as inconclusive, not as evidence of no effect.",
      "message_i18n": {
        "key": "flag.nonsignificant_power",
        "args": {
          "n": "60",
          "metric": {
            "key": "power.metric.cohens_d"
          },
          "mdes": "0.74",
          "power_percent": "80"
        }
      }
    }
  ],
  "test_label_i18n": {
    "key": "test.welch_t.label"
  },
  "alpha": 0.050000000000000003,
  "sidedness": "two-sided",
  "alternative": "two.sided",
  "alternative_sides": ["OJ", "VC"],
  "alternative_statement": "group OJ minus group VC differs from zero",
  "alternative_statement_i18n": {
    "key": "analysis.alternative.group_two_sided",
    "args": {
      "first": "OJ",
      "second": "VC"
    }
  },
  "estimate_label": "mean in group OJ minus mean in group VC",
  "imputation": {
    "strategy": "complete_case",
    "n_rows": 60,
    "n_dropped": 0,
    "n_cells_imputed": 0,
    "imputed_cols": []
  },
  "group_means": {
    "mean in group OJ": 20.663333000000002,
    "mean in group VC": 16.963332999999999
  },
  "conf_level": 0.94999999999999996,
  "power": {
    "method": "two-sample t (pwr)",
    "n": 60,
    "alpha": 0.050000000000000003,
    "target_power": 0.80000000000000004,
    "mdes": 0.73562923671845126,
    "mdes_metric": "Cohen's d",
    "mdes_metric_i18n": {
      "key": "power.metric.cohens_d"
    },
    "required_n": 64,
    "required_n_label": "64 per group to detect d=0.50",
    "required_n_label_i18n": {
      "key": "power.required_n.two_sample_t",
      "args": {
        "n": "64",
        "effect": "0.50"
      }
    },
    "severely_underpowered": false,
    "note": null,
    "call_code": "pwr::pwr.t2n.test(n1 = 30, n2 = 30, sig.level = 0.05, power = 0.8)"
  },
  "explanations": ["The mean len in OJ was 3.7 higher than in VC (OJ 20.66 vs VC 16.96; 95% CI -0.171 to 7.571).", "That difference is a small effect (Cohen's d 0.4945).", "This result is not statistically significant at the 0.05 level (p = 0.0606, n = 60)."],
  "explanations_i18n": [
    {
      "key": "exp.mean_difference.higher",
      "args": {
        "outcome": "len",
        "group1": "OJ",
        "difference": "3.7",
        "group2": "VC",
        "mean1": "20.66",
        "mean2": "16.96",
        "ci": {
          "key": "exp.ci_semicolon",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "-0.171",
                "upper": "7.571"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.cohens_d",
      "args": {
        "magnitude": {
          "key": "exp.magnitude_effect.small"
        },
        "d": "0.4945"
      }
    },
    {
      "key": "exp.closer.not_significant",
      "args": {
        "alpha": "0.05",
        "p": "p = 0.0606",
        "n": "60"
      }
    }
  ]
}