{
  "test_id": "paired_t",
  "test_label": "Paired t-test",
  "n": 10,
  "statistic": 4.0621276833820366,
  "parameter": 9,
  "p_value": 0.0028328901973842702,
  "estimate": 1.5800000000000001,
  "conf_int": [0.70011423672301754, 2.4598857632769824],
  "effect_size": {
    "name": "Cohens_d",
    "value": 1.2845575625910546,
    "ci": [0.41462776455165207, 2.1180165154689807],
    "ci_level": 0.94999999999999996
  },
  "seed_used": 20261101,
  "assumptions": [
    {
      "id": "normality",
      "check": "normality (Shapiro-Wilk)",
      "statistic": 0.82987133192879448,
      "p_value": 0.033341608630307849,
      "passed": false,
      "note": "evidence of non-normality"
    },
    {
      "id": "sample_size",
      "check": "sample size",
      "statistic": 10,
      "p_value": "NA",
      "passed": true,
      "note": "adequate n"
    }
  ],
  "warnings": [],
  "flags": [
    {
      "severity": "warning",
      "message": "The paired differences appear non-normal; consider the non-parametric alternative (Wilcoxon signed-rank test).",
      "message_i18n": {
        "key": "flag.non_normal_differences",
        "args": {
          "test_id": {
            "key": "test.wilcoxon_signed_rank.label"
          }
        }
      },
      "trigger": "normality (Shapiro-Wilk)",
      "suggested_tests": ["wilcoxon_signed_rank"]
    },
    {
      "severity": "warning",
      "message": "Small study (n=10): at the standard 80% power, only a very large effect (Cohen's d of 1.00 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 34 pairs to detect d=0.50.",
      "message_i18n": {
        "key": "flag.severely_underpowered",
        "args": {
          "n": "10",
          "power_percent": "80",
          "metric": {
            "key": "power.metric.cohens_d"
          },
          "mdes": "1.00",
          "required_n": {
            "key": "power.required_n.paired_t",
            "args": {
              "n": "34",
              "effect": "0.50"
            }
          }
        }
      }
    }
  ],
  "test_label_i18n": {
    "key": "test.paired_t.label"
  },
  "alpha": 0.050000000000000003,
  "sidedness": "two-sided",
  "alternative": "two.sided",
  "alternative_sides": ["extra_2", "extra_1"],
  "alternative_statement": "extra_2 minus extra_1 differs from zero",
  "alternative_statement_i18n": {
    "key": "analysis.alternative.two_sided",
    "args": {
      "first": "extra_2",
      "second": "extra_1"
    }
  },
  "imputation": {
    "strategy": "complete_case",
    "n_rows": 10,
    "n_dropped": 0,
    "n_cells_imputed": 0,
    "imputed_cols": []
  },
  "conf_level": 0.94999999999999996,
  "power": {
    "method": "paired t (pwr)",
    "n": 10,
    "alpha": 0.050000000000000003,
    "target_power": 0.80000000000000004,
    "mdes": 0.99600434927142312,
    "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": true,
    "note": null,
    "call_code": "pwr::pwr.t.test(n = 10, sig.level = 0.05, power = 0.8, type = \"paired\")"
  },
  "explanations": ["The mean within-pair difference (extra_2 minus extra_1) was 1.58 (95% CI 0.7001 to 2.46).", "That difference is a large effect (Cohen's d 1.285).", "This result is statistically significant at the 0.05 level (p = 0.00283, n = 10)."],
  "explanations_i18n": [
    {
      "key": "exp.within_pair_difference",
      "args": {
        "first": "extra_2",
        "second": "extra_1",
        "estimate": "1.58",
        "ci": {
          "key": "exp.ci_paren",
          "args": {
            "ci": {
              "key": "exp.ci",
              "args": {
                "level": "95",
                "lower": "0.7001",
                "upper": "2.46"
              }
            }
          }
        }
      }
    },
    {
      "key": "exp.cohens_d",
      "args": {
        "magnitude": {
          "key": "exp.magnitude_effect.large"
        },
        "d": "1.285"
      }
    },
    {
      "key": "exp.closer.significant",
      "args": {
        "alpha": "0.05",
        "p": "p = 0.00283",
        "n": "10"
      }
    }
  ]
}