{
  "test_id": "paired_t",
  "test_label": "Paired t-test",
  "n": 24,
  "statistic": 3.7530383765601814,
  "parameter": 23,
  "p_value": 0.0010366326745569645,
  "estimate": 2.5458333333333329,
  "conf_int": [1.1425816285944583, 3.9490850380722069],
  "effect_size": {
    "name": "Cohens_d",
    "value": 0.76608575063798301,
    "ci": [0.30304166004692951, 1.2163212534283689],
    "ci_level": 0.94999999999999996
  },
  "seed_used": 20261111,
  "assumptions": [
    {
      "id": "normality",
      "check": "normality (Shapiro-Wilk)",
      "statistic": 0.98746655604241518,
      "p_value": 0.98648938769391159,
      "passed": true,
      "note": "no evidence against normality"
    },
    {
      "id": "sample_size",
      "check": "sample size",
      "statistic": 24,
      "p_value": "NA",
      "passed": true,
      "note": "adequate n"
    }
  ],
  "warnings": [],
  "flags": [
    {
      "severity": "note",
      "message": "Values beyond Tukey's 1.5xIQR fence in: 'after' (1), 'before' (1). 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": "'after' (1), 'before' (1)"
        }
      },
      "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.paired_t.label"
  },
  "alpha": 0.050000000000000003,
  "sidedness": "two-sided",
  "alternative": "two.sided",
  "alternative_sides": ["after", "before"],
  "alternative_statement": "after minus before differs from zero",
  "alternative_statement_i18n": {
    "key": "analysis.alternative.two_sided",
    "args": {
      "first": "after",
      "second": "before"
    }
  },
  "imputation": {
    "strategy": "complete_case",
    "n_rows": 24,
    "n_dropped": 0,
    "n_cells_imputed": 0,
    "imputed_cols": []
  },
  "conf_level": 0.94999999999999996,
  "power": {
    "method": "paired t (pwr)",
    "n": 24,
    "alpha": 0.050000000000000003,
    "target_power": 0.80000000000000004,
    "mdes": 0.59718493846134701,
    "mdes_metric": "Cohen's d",
    "mdes_metric_i18n": {
      "key": "power.metric.cohens_d"
    },
    "required_n": 34,
    "required_n_label": "34 pairs to detect d=0.50",
    "required_n_label_i18n": {
      "key": "power.required_n.paired_t",
      "args": {
        "n": "34",
        "effect": "0.50"
      }
    },
    "severely_underpowered": false,
    "note": null,
    "call_code": "pwr::pwr.t.test(n = 24, sig.level = 0.05, power = 0.8, type = \"paired\")"
  },
  "explanations": ["The mean within-pair difference (after minus before) was 2.546 (95% CI 1.143 to 3.949).", "That difference is a medium effect (Cohen's d 0.7661).", "This result is statistically significant at the 0.05 level (p = 0.00104, n = 24)."],
  "explanations_i18n": [
    {
      "key": "exp.within_pair_difference",
      "args": {
        "first": "after",
        "second": "before",
        "estimate": "2.546",
        "ci": {
          "key": "exp.ci_paren",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "1.143",
                "upper": "3.949"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.cohens_d",
      "args": {
        "magnitude": {
          "key": "exp.magnitude_effect.medium"
        },
        "d": "0.7661"
      }
    },
    {
      "key": "exp.closer.significant",
      "args": {
        "alpha": "0.05",
        "p": "p = 0.00104",
        "n": "24"
      }
    }
  ]
}