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": "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_019601",
"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. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_019602",
"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 Randomized controlled trial concisely and include one example application."
}
]
} | Experiment with randomized assignment to support causal inference. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_019603",
"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 Homoskedasticity in 1–2 sentences for an advanced academic audience."
}
]
} | Assumption of constant error variance across predictor values in regression. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_019604",
"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": "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_019605",
"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 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_019606",
"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 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_019607",
"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 Multiple comparisons problem concisely and include one example application."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_019608",
"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 Type I error? Provide a precise definition and one implication."
}
]
} | Rejecting a true null; probability controlled by α. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_019609",
"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 Multiple comparisons problem concisely and include one example application."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_019610",
"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 constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_019611",
"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 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_019612",
"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 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_019613",
"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 I error? Provide a precise definition and one implication."
}
]
} | Rejecting a true null; probability controlled by α. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_019614",
"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 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_019615",
"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 Type I error in 1–2 sentences for an advanced academic audience."
}
]
} | Rejecting a true null; probability controlled by α. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_019616",
"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_019617",
"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": "What is Posterior? Provide a precise definition and one implication."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_019618",
"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 Type I error concisely and include one example application."
}
]
} | Rejecting a true null; probability controlled by α. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_019619",
"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). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_019620",
"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 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 supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_019621",
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{
"role": "user",
"content": "What is Type II error? Provide a precise definition and one implication."
}
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} | Failing to reject a false null; related to power (1-β). Implication: it constrains correct interpretation under assumptions. | {
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},
{
"role": "user",
"content": "What is Type I error? Provide a precise definition and one implication."
}
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{
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}
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{
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}
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"license": "cc-by-4.0",
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},
{
"role": "user",
"content": "Explain Randomized controlled trial concisely and include one example application."
}
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"license": "cc-by-4.0",
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{
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}
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"license": "cc-by-4.0",
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{
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}
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} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Implication: it constrains correct interpretation under assumptions. | {
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"subdomain": "stats::robustness",
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"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
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{
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{
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}
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"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
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},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
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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."
}
]
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"task": "definition",
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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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"content": "Explain Type II error concisely and include one example application."
}
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"subdomain": "stats::inference",
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"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",
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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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} | 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",
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"license": "cc-by-4.0",
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{
"role": "user",
"content": "What is Randomized controlled trial? Provide a precise definition and one implication."
}
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"license": "cc-by-4.0",
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{
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}
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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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"content": "Explain Homoskedasticity concisely and include one example application."
}
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} | Assumption of constant error variance across predictor values in regression. Example: used in applied analysis and research reporting. | {
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"task": "definition",
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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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},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"sou... | {
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{
"messages": [
{
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"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."
}
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} | Experiment with randomized assignment to support causal inference. Example: used in applied analysis and research reporting. | {
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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": [
"statistics",... | [
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{
"role": "user",
"content": "What is Homoskedasticity? Provide a precise definition and one implication."
}
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"subdomain": "stats::regression",
"task": "definition",
"difficulty": "seed",
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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."
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{
"role": "user",
"content": "Define Posterior in 1–2 sentences for an advanced academic audience."
}
]
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"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": [
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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": "Explain Randomized controlled trial concisely and include one example application."
}
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} | Experiment with randomized assignment to support causal inference. Implication: it constrains correct interpretation under assumptions. | {
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"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... | [
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{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
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{
"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. | {
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"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... | [
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{
"role": "user",
"content": "What is Type I error? Provide a precise definition and one implication."
}
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} | Rejecting a true null; probability controlled by α. Example: used in applied analysis and research reporting. | {
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"task": "definition",
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"truth_mode": "textbook_definition",
"wrapper": "micro_refresher",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
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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). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_019662",
"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... | [
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"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 constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_019663",
"domain": "master_scholars_academics",
"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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},
{
"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": "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. | {
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"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... | [
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"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). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_019665",
"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... | [
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"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
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"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 supports unit-aware quantitative modeling. | {
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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": [
"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_019667",
"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",... | [
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"source_url": "https://openstax.org/details/books/introductory-statistics",
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"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 constrains correct interpretation under assumptions. | {
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"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... | [
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"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. | {
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"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 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_019670",
"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 constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_019671",
"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": "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_019672",
"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 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_019673",
"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": "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_019674",
"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 Homoskedasticity? Provide a precise definition and one implication."
}
]
} | Assumption of constant error variance across predictor values in regression. Implication: it supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_019675",
"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 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_019676",
"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 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_019677",
"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 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_019678",
"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 Multiple comparisons problem in 1–2 sentences for an advanced academic audience."
}
]
} | Testing many hypotheses inflates false positives unless controlled (e.g., FDR). Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_019679",
"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 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_019680",
"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 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. | {
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"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 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_019682",
"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 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. | {
"id": "WUA_STAT_25K_019683",
"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 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_019684",
"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": "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_019685",
"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 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_019686",
"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 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_019687",
"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 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_019688",
"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 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_019689",
"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 Posterior in 1–2 sentences for an advanced academic audience."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_019690",
"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_019691",
"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. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_019692",
"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 Posterior? Provide a precise definition and one implication."
}
]
} | Updated distribution after observing data; proportional to prior × likelihood. Implication: it constrains correct interpretation under assumptions. | {
"id": "WUA_STAT_25K_019693",
"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 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_019694",
"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 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_019695",
"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 supports unit-aware quantitative modeling. | {
"id": "WUA_STAT_25K_019696",
"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": "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_019697",
"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 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. | {
"id": "WUA_STAT_25K_019698",
"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 Homoskedasticity in 1–2 sentences for an advanced academic audience."
}
]
} | Assumption of constant error variance across predictor values in regression. Example: used in applied analysis and research reporting. | {
"id": "WUA_STAT_25K_019699",
"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": "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_019700",
"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"
} |
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