prompt dict | response string | meta dict | fact_sources list | artifacts dict |
|---|---|---|---|---|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Multiple comparisons problem in 1–2 sentences for an advanced academic audience."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022201",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Type I error concisely and include one example application."
}
]
} | Rejecting a true null; probability controlled by α. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022202",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stati... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Randomized controlled trial in 1–2 sentences for an advanced academic audience."
}
]
} | Experiment with randomized assignment to support causal inference. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022203",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Multiple comparisons problem concisely and include one example application."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022204",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Type II error in 1–2 sentences for an advanced academic audience."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022205",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stati... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Randomized controlled trial concisely and include one example application."
}
]
} | Experiment with randomized assignment to support causal inference. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022206",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Type II error concisely and include one example application."
}
]
} | Failing to reject a false null; related to power (1-β). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022207",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stati... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Posterior concisely and include one example application."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022208",
"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Type I error? Provide a precise definition and one implication."
}
]
} | Rejecting a true null; probability controlled by α. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022209",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Randomized controlled trial? Provide a precise definition and one implication."
}
]
} | Experiment with randomized assignment to support causal inference. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022210",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Multiple comparisons problem? Provide a precise definition and one implication."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022211",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stat... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Randomized controlled trial? Provide a precise definition and one implication."
}
]
} | Experiment with randomized assignment to support causal inference. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022212",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Type I error in 1–2 sentences for an advanced academic audience."
}
]
} | Rejecting a true null; probability controlled by α. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022213",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Multiple comparisons problem? Provide a precise definition and one implication."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022214",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Multiple comparisons problem concisely and include one example application."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022215",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Randomized controlled trial concisely and include one example application."
}
]
} | Experiment with randomized assignment to support causal inference. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022216",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Posterior in 1–2 sentences for an advanced academic audience."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022217",
"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Type I error concisely and include one example application."
}
]
} | Rejecting a true null; probability controlled by α. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022218",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Randomized controlled trial concisely and include one example application."
}
]
} | Experiment with randomized assignment to support causal inference. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022219",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Type II error concisely and include one example application."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022220",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stati... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Randomized controlled trial concisely and include one example application."
}
]
} | Experiment with randomized assignment to support causal inference. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022221",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
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{
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{
"role": "user",
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}
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},
{
"role": "user",
"content": "Explain Randomized controlled trial concisely and include one example application."
}
]
} | Experiment with randomized assignment to support causal inference. Example: used in applied analysis and research reporting. | {
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{
"role": "user",
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
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{
"role": "user",
"content": "What is Homoskedasticity? Provide a precise definition and one implication."
}
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{
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}
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"license": "cc-by-4.0",
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"content": "Define Homoskedasticity in 1–2 sentences for an advanced academic audience."
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"license": "cc-by-4.0",
"tags": [
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{
"role": "user",
"content": "Explain Homoskedasticity concisely and include one example application."
}
]
} | Assumption of constant error variance across predictor values in regression. Example: used in applied analysis and research reporting. | {
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"domain": "master_scholars_academics",
"subdomain": "stats::regression",
"task": "definition",
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"truth_mode": "textbook_definition",
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{
"role": "user",
"content": "What is Posterior? Provide a precise definition and one implication."
}
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{
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"content": "Explain Homoskedasticity concisely and include one example application."
}
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"license": "cc-by-4.0",
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{
"role": "user",
"content": "Explain Posterior concisely and include one example application."
}
]
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"license": "cc-by-4.0",
"tags": [
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{
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},
{
"role": "user",
"content": "What is Type II error? Provide a precise definition and one implication."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it supports unit-aware quantitative modeling. | {
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"subdomain": "stats::inference",
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{
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"content": "What is Type II error? Provide a precise definition and one implication."
}
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"subdomain": "stats::inference",
"task": "definition",
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"truth_mode": "textbook_definition",
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"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stati... | [
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{
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{
"role": "user",
"content": "Explain Homoskedasticity concisely and include one example application."
}
]
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"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
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{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
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{
"messages": [
{
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},
{
"role": "user",
"content": "What is Multiple comparisons problem? Provide a precise definition and one implication."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it constrains correct interpretation under assumptions. | {
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"task": "definition",
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"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
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"messages": [
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Posterior in 1–2 sentences for an advanced academic audience."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Example: used in applied analysis and research reporting. | {
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"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
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"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
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{
"role": "user",
"content": "Explain Type II error concisely and include one example application."
}
]
} | Failing to reject a false null; related to power (1-β). Example: used in applied analysis and research reporting. | {
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"subdomain": "stats::inference",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
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{
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Type I error? Provide a precise definition and one implication."
}
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"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
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{
"role": "user",
"content": "Define Type I error in 1–2 sentences for an advanced academic audience."
}
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"subdomain": "stats::inference",
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"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
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"messages": [
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
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{
"role": "user",
"content": "Define Homoskedasticity in 1–2 sentences for an advanced academic audience."
}
]
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"messages": [
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"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Type II error concisely and include one example application."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it supports unit-aware quantitative modeling. | {
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{
"role": "user",
"content": "Explain Homoskedasticity concisely and include one example application."
}
]
} | Assumption of constant error variance across predictor values in regression. Example: used in applied analysis and research reporting. | {
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{
"role": "user",
"content": "What is Posterior? Provide a precise definition and one implication."
}
]
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Type II error concisely and include one example application."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it constrains correct interpretation under assumptions. | {
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"subdomain": "stats::inference",
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"license": "cc-by-4.0",
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"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
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{
"role": "user",
"content": "Define Homoskedasticity in 1–2 sentences for an advanced academic audience."
}
]
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"subdomain": "stats::regression",
"task": "definition",
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"license": "cc-by-4.0",
"tags": [
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"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
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"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Multiple comparisons problem concisely and include one example application."
}
]
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"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
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{
"role": "user",
"content": "What is Multiple comparisons problem? Provide a precise definition and one implication."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it supports unit-aware quantitative modeling. | {
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"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
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"license": "cc-by-4.0",
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"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
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{
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Randomized controlled trial in 1–2 sentences for an advanced academic audience."
}
]
} | Experiment with randomized assignment to support causal inference. Implication: it supports unit-aware quantitative modeling. | {
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{
"role": "user",
"content": "Define Type I error in 1–2 sentences for an advanced academic audience."
}
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"subdomain": "stats::inference",
"task": "definition",
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"license": "cc-by-4.0",
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"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
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{
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
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{
"role": "user",
"content": "Explain Type II error concisely and include one example application."
}
]
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"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
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"messages": [
{
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Posterior in 1–2 sentences for an advanced academic audience."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Example: used in applied analysis and research reporting. | {
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"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
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{
"role": "user",
"content": "Explain Homoskedasticity concisely and include one example application."
}
]
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{
"role": "user",
"content": "Define Homoskedasticity in 1–2 sentences for an advanced academic audience."
}
]
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"license": "cc-by-4.0",
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{
"role": "user",
"content": "Define Homoskedasticity in 1–2 sentences for an advanced academic audience."
}
]
} | Assumption of constant error variance across predictor values in regression. Implication: it supports unit-aware quantitative modeling. | {
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"subdomain": "stats::regression",
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"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Posterior concisely and include one example application."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Example: used in applied analysis and research reporting. | {
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"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
... | [
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{
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"sou... | {
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{
"messages": [
{
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
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{
"role": "user",
"content": "Define Posterior in 1–2 sentences for an advanced academic audience."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Implication: it supports unit-aware quantitative modeling. | {
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"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
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{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
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{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Posterior? Provide a precise definition and one implication."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Example: used in applied analysis and research reporting. | {
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"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
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"messages": [
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{
"role": "user",
"content": "What is Homoskedasticity? Provide a precise definition and one implication."
}
]
} | Assumption of constant error variance across predictor values in regression. Implication: it constrains correct interpretation under assumptions. | {
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"subdomain": "stats::regression",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stat... | [
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"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
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{
"role": "user",
"content": "Define Posterior in 1–2 sentences for an advanced academic audience."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Implication: it supports unit-aware quantitative modeling. | {
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"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
... | [
{
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{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
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{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Posterior concisely and include one example application."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022262",
"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Posterior in 1–2 sentences for an advanced academic audience."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022263",
"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Posterior in 1–2 sentences for an advanced academic audience."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022264",
"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Multiple comparisons problem? Provide a precise definition and one implication."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022265",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Type I error concisely and include one example application."
}
]
} | Rejecting a true null; probability controlled by α. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022266",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stati... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Type II error? Provide a precise definition and one implication."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022267",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Type II error in 1–2 sentences for an advanced academic audience."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022268",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Multiple comparisons problem? Provide a precise definition and one implication."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022269",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Randomized controlled trial in 1–2 sentences for an advanced academic audience."
}
]
} | Experiment with randomized assignment to support causal inference. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022270",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Homoskedasticity concisely and include one example application."
}
]
} | Assumption of constant error variance across predictor values in regression. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022271",
"domain": "master_scholars_academics",
"subdomain": "stats::regression",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Type II error concisely and include one example application."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022272",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Type I error concisely and include one example application."
}
]
} | Rejecting a true null; probability controlled by α. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022273",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stati... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Type II error in 1–2 sentences for an advanced academic audience."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022274",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stati... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Type II error? Provide a precise definition and one implication."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022275",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stati... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Posterior? Provide a precise definition and one implication."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022276",
"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Homoskedasticity concisely and include one example application."
}
]
} | Assumption of constant error variance across predictor values in regression. Implication: it constrains correct interpretation under assumptions. | {
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"domain": "master_scholars_academics",
"subdomain": "stats::regression",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
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},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Type II error concisely and include one example application."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022278",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Posterior? Provide a precise definition and one implication."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022279",
"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Homoskedasticity concisely and include one example application."
}
]
} | Assumption of constant error variance across predictor values in regression. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022280",
"domain": "master_scholars_academics",
"subdomain": "stats::regression",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Homoskedasticity? Provide a precise definition and one implication."
}
]
} | Assumption of constant error variance across predictor values in regression. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022281",
"domain": "master_scholars_academics",
"subdomain": "stats::regression",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stat... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Type II error? Provide a precise definition and one implication."
}
]
} | Failing to reject a false null; related to power (1-β). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022282",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
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"license": "cc-by-4.0",
"tags": [
"statistic... | [
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"evidence_type": "standard",
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Homoskedasticity concisely and include one example application."
}
]
} | Assumption of constant error variance across predictor values in regression. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022283",
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"task": "definition",
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"license": "cc-by-4.0",
"tags": [
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"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
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} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Multiple comparisons problem concisely and include one example application."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022284",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Multiple comparisons problem concisely and include one example application."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022285",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Multiple comparisons problem? Provide a precise definition and one implication."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022286",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Homoskedasticity concisely and include one example application."
}
]
} | Assumption of constant error variance across predictor values in regression. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022287",
"domain": "master_scholars_academics",
"subdomain": "stats::regression",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Homoskedasticity in 1–2 sentences for an advanced academic audience."
}
]
} | Assumption of constant error variance across predictor values in regression. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022288",
"domain": "master_scholars_academics",
"subdomain": "stats::regression",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stat... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Posterior concisely and include one example application."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022289",
"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Homoskedasticity in 1–2 sentences for an advanced academic audience."
}
]
} | Assumption of constant error variance across predictor values in regression. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022290",
"domain": "master_scholars_academics",
"subdomain": "stats::regression",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Posterior concisely and include one example application."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022291",
"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Randomized controlled trial? Provide a precise definition and one implication."
}
]
} | Experiment with randomized assignment to support causal inference. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022292",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Multiple comparisons problem? Provide a precise definition and one implication."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022293",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Posterior in 1–2 sentences for an advanced academic audience."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022294",
"domain": "master_scholars_academics",
"subdomain": "stats::bayes",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Multiple comparisons problem? Provide a precise definition and one implication."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022295",
"domain": "master_scholars_academics",
"subdomain": "stats::robustness",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Randomized controlled trial in 1–2 sentences for an advanced academic audience."
}
]
} | Experiment with randomized assignment to support causal inference. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022296",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Explain Randomized controlled trial concisely and include one example application."
}
]
} | Experiment with randomized assignment to support causal inference. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022297",
"domain": "master_scholars_academics",
"subdomain": "stats::design",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Type I error in 1–2 sentences for an advanced academic audience."
}
]
} | Rejecting a true null; probability controlled by α. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_022298",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "advanced",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"stati... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "Define Type II error in 1–2 sentences for an advanced academic audience."
}
]
} | Failing to reject a false null; related to power (1-β). Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_022299",
"domain": "master_scholars_academics",
"subdomain": "stats::inference",
"task": "definition",
"difficulty": "seed",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistic... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide precise definitions; avoid fluff."
},
{
"role": "user",
"content": "What is Homoskedasticity? Provide a precise definition and one implication."
}
]
} | Assumption of constant error variance across predictor values in regression. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_022300",
"domain": "master_scholars_academics",
"subdomain": "stats::regression",
"task": "definition",
"difficulty": "core",
"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statisti... | [
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
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