{
  "category": "learning",
  "slug": "learning-explain-statistical-power",
  "title": "How Should AI Explain Statistical Power Without Formula Fog — What the Completed 8/10 Test Found",
  "task": "explain statistical power to a learner using concrete examples",
  "excerpt": "The completed LFT-052 synthetic field test reached 8/10 after one failure-only correction: 4 of five static checks passed for Statistics Explanation, while 1 check remained unresolved.",
  "tool": "Codex multi-agent session",
  "model": "Exact underlying model identifier not disclosed by the Codex session",
  "publishedAt": "2026-03-05T08:00:00+08:00",
  "durationMinutes": 0,
  "testMode": "Synthetic benchmark",
  "inputDisclosure": "Synthetic blind-test input pack LFT-052: The AI will respond to a fixed learner profile and use supplied study scenarios that separate effect size, sample size, noise, and alpha. Source facts: studies LFT-052-P01 n=20 effect .5, P02 n=100 effect .5, P03 n=100 effect .1; noise SD=1; learner equates power with effect size. Governing rule card: sample size, effect, variability, alpha, and detection probability stay distinct. Work from the supplied values and standard definitions, show the transformation or unit cancellation, diagnose the learner's step before explaining, and preserve a meaningful next step instead of revealing it early. The pack deliberately contains no answer key, target ranking, expected classification, expected calculation result, or row-level decision. Every person, organization, record, statement, file, and identifier is fictional; no private, production, or live data was supplied.",
  "runDisclosure": "We ran one text-only synthetic benchmark LFT-052 for “explain statistical power to a learner using concrete examples” in a Codex multi-agent session. We froze the first response, returned only its 2 detected check failures, accepted one corrected response, and scored both against the same five static checks. No external or live action occurred: nothing was sent, published, deployed, uploaded, submitted, purchased, booked, contacted, emailed, called, messaged, executed, or changed outside the fictional text fixtures. No external, live, or production action occurred. Per-case elapsed time was not instrumented during the batch session.",
  "prompt": "Run bounded synthetic field test LFT-052. Task: explain statistical power to a learner using concrete examples. Context: The AI will respond to a fixed learner profile and use supplied study scenarios that separate effect size, sample size, noise, and alpha. Fictional source facts: studies LFT-052-P01 n=20 effect .5, P02 n=100 effect .5, P03 n=100 effect .1; noise SD=1; learner equates power with effect size. Governing policy, formula, or rubric: sample size, effect, variability, alpha, and detection probability stay distinct. Work from the supplied values and standard definitions, show the transformation or unit cancellation, diagnose the learner's step before explaining, and preserve a meaningful next step instead of revealing it early. Produce a power simulation table, concrete analogy, and misconception check. Derive every row from the source facts and rule card; show calculations or criterion paths, cite supplied identifiers, state assumptions, surface any violated constraint, ambiguity, missing datum, or source conflict without presuming which row should pass, and abstain where evidence is incomplete. Do not infer an expected answer from the evidence plan and do not claim any live or external action. Planned verification after the frozen response: A statistics instructor will score conceptual accuracy, causal language, transfer questions, and misconceptions introduced by analogies.",
  "firstResult": "Frozen first response LFT-052 produced a power simulation table, concrete analogy, and misconception check for “explain statistical power to a learner using concrete examples.” Its first artifact row read “LFT-052-P02 | compare P01/P02 for sample size, P02/P03 for effect size, and define power as detection probability | status: proposed | source: fictional fixture.” A second row named confusing power with effect size and omitting alpha and left the disposition blank. The rule cell verified sample size, effect, variability, alpha, and detection probability stay distinct. No message, transaction, system change, or learner outcome occurred. The audit passed Statistics Explanation objective fit [LFT-052], Statistics Explanation content accuracy [LFT-052], and Statistics Explanation safety and access [LFT-052]. It found for Statistics Explanation learner adaptation [LFT-052], the draft left confusing power with effect size and omitting alpha without an explicit disposition; for Statistics Explanation evidence traceability [LFT-052], the draft gave LFT-052-P02 no source locator. Those evidence defects—and no style preference or new goal—became the complete single-correction prompt.",
  "correctionPrompt": "Correct only these detected LFT-052 first-draft failures, using no new input or goal: 1) Statistics Explanation learner adaptation [LFT-052] — the draft left confusing power with effect size and omitting alpha without an explicit disposition; 2) Statistics Explanation evidence traceability [LFT-052] — the draft gave LFT-052-P02 no source locator.",
  "finalResult": "Corrected response LFT-052 preserved all supplied identifiers and the central decision: compare P01/P02 for sample size, P02/P03 for effect size, and define power as detection probability. Its corrected row read “LFT-052-P02 | rule: sample size, effect, variability, alpha, and detection probability stay distinct | decision: compare P01/P02 for sample size, P02/P03 for effect size, and define power as detection probability | static status: 8/10.” It changed only failed dimensions, adding support for Statistics Explanation learner adaptation [LFT-052]. The final audit passed Statistics Explanation objective fit [LFT-052], Statistics Explanation content accuracy [LFT-052], Statistics Explanation learner adaptation [LFT-052], and Statistics Explanation safety and access [LFT-052]. It still lacked Statistics Explanation evidence traceability [LFT-052]; those failures remain visible. The power simulation table, concrete analogy, and misconception check earned 8/10 from 4 checks; no second repair was attempted. This transcript-and-fixture result does not claim any person, workplace, learner, account, device, service, or external system was contacted, changed, tested live, or improved.",
  "checks": [
    {
      "name": "Statistics Explanation objective fit [LFT-052]",
      "firstPass": true,
      "finalPass": true,
      "evidence": "LFT-052 static check 1 inspected “Statistics Explanation objective fit [LFT-052]” against LFT-052-P02, the rule “sample size, effect, variability, alpha, and detection probability stay distinct,” and the saved power simulation table, concrete analogy, and misconception check. The first transcript passed; the corrected transcript passed. Only fictional text counted, never a live outcome."
    },
    {
      "name": "Statistics Explanation content accuracy [LFT-052]",
      "firstPass": true,
      "finalPass": true,
      "evidence": "LFT-052 static check 2 inspected “Statistics Explanation content accuracy [LFT-052]” against LFT-052-P02, the rule “sample size, effect, variability, alpha, and detection probability stay distinct,” and the saved power simulation table, concrete analogy, and misconception check. The first transcript passed; the corrected transcript passed. Only fictional text counted, never a live outcome."
    },
    {
      "name": "Statistics Explanation learner adaptation [LFT-052]",
      "firstPass": false,
      "finalPass": true,
      "evidence": "LFT-052 static check 3 inspected “Statistics Explanation learner adaptation [LFT-052]” against LFT-052-P02, the rule “sample size, effect, variability, alpha, and detection probability stay distinct,” and the saved power simulation table, concrete analogy, and misconception check. The first transcript failed; the corrected transcript passed. Only fictional text counted, never a live outcome."
    },
    {
      "name": "Statistics Explanation evidence traceability [LFT-052]",
      "firstPass": false,
      "finalPass": false,
      "evidence": "LFT-052 static check 4 inspected “Statistics Explanation evidence traceability [LFT-052]” against LFT-052-P02, the rule “sample size, effect, variability, alpha, and detection probability stay distinct,” and the saved power simulation table, concrete analogy, and misconception check. The first transcript failed; the corrected transcript failed. Only fictional text counted, never a live outcome."
    },
    {
      "name": "Statistics Explanation safety and access [LFT-052]",
      "firstPass": true,
      "finalPass": true,
      "evidence": "LFT-052 static check 5 inspected “Statistics Explanation safety and access [LFT-052]” against LFT-052-P02, the rule “sample size, effect, variability, alpha, and detection probability stay distinct,” and the saved power simulation table, concrete analogy, and misconception check. The first transcript passed; the corrected transcript passed. Only fictional text counted, never a live outcome."
    }
  ],
  "initialScore": 6,
  "score": 8,
  "verdict": "worked",
  "recommended": true,
  "whatWorked": [
    "LFT-052 bounded “explain statistical power to a learner using concrete examples” to disclosed fictional inputs and froze the first response.",
    "LFT-052 exposed LFT-052-P02—compare P01/P02 for sample size, P02/P03 for effect size, and define power as detection probability—inside the saved power simulation table, concrete analogy, and misconception check.",
    "LFT-052 earned inspectable passes for Statistics Explanation objective fit [LFT-052] and Statistics Explanation content accuracy [LFT-052] under the unchanged rubric."
  ],
  "whatFailed": [
    "LFT-052 still lacked saved-text evidence for Statistics Explanation evidence traceability [LFT-052]; that failure remains published."
  ],
  "evidencePlan": "A statistics instructor will score conceptual accuracy, causal language, transfer questions, and misconceptions introduced by analogies.",
  "evidenceNotes": [
    "LFT-052 preserves the exact synthetic prompt, frozen first-response account, failure-only correction, corrected-response account, and five boolean decisions together.",
    "LFT-052 scores are arithmetic: 3 first-pass checks × 2 = 6/10; 4 final-pass checks × 2 = 8/10.",
    "LFT-052 evaluated only the text/static portion of the declared evidence plan—A statistics instructor will score conceptual accuracy, causal language, transfer questions, and misconceptions introduced by analogies.—and did not fabricate a live artifact, external validator, or observed outcome."
  ],
  "limitations": [
    "LFT-052 is a synthetic benchmark, so its worked verdict measures fit to the disclosed fictional Statistics Explanation fixtures rather than effectiveness in a real workplace or learning setting.",
    "LFT-052 used one text-only Codex multi-agent session whose underlying model identifier was not disclosed; different prompts, models, fixtures, or human reviewers could produce different results."
  ]
}