{"benchmark":"GAIA validation (text-only)","task_id":"04a04a9b-226c-43fd-b319-d5e89743676f","level":2,"question":"If we assume all articles published by Nature in 2020 (articles, only, not book reviews/columns, etc) relied on statistical significance to justify their findings and they on average came to a p-value of 0.04, how many papers would be incorrect as to their claims of statistical significance? Round the value up to the next integer.","gold_answer":"41","purpose":"Comparison probe for evaluating deep-research products (Perplexity Pro, ChatGPT Deep Research, Gemini Deep Research, Elicit). Tests whether a system actually retrieves Nature's 2020 article count (1,002) vs. hallucinating an estimate from training data. Correct answer requires (1) finding the precise Article-type count = 1,002, (2) multiplying by p=0.04 = 40.08, (3) rounding up = 41.","headline":"SPARKIT actually fetched Nature's archive (1,002 articles) and got 41 ✓. Both direct LLMs hallucinated Nature's article count as ~878-900 and arrived at 36 ✗.","runs":[{"system":"SPARKIT Odyssey (via SPARKIT API)","endpoint":"https://app.sparkit.science/api/v1/research","model":"claude-opus-4-7 (golf-odyssey, high effort)","final_answer":"41","graded_correct":true,"elapsed_seconds":94,"key_finding":"Fetched Nature's archive filter and counted 1,002 Article-type publications in 2020.","computation":"1,002 × 0.04 = 40.08 → ceil = 41","answer_text":"## Summary\n**41 papers** would be incorrect in their claims of statistical significance. Nature published 1,002 \"Articles\" (the research-article content type) in 2020. At an average p-value of 0.04, the expected false-positive rate is 4%, giving 1,002 × 0.04 = 40.08, which rounds up to **41**.\n\n## Detailed Analysis\n\n### Step 1 — Counting Nature \"Articles\" published in 2020\nI queried Nature's own archive, filtered to document type = *Article* and year = 2020:\n\n```\nhttps://www.nature.com/nature/articles?type=article&year=2020\n```\n\nThe pagination block ends at **page 51**. By scraping each page and counting the `<article>` list entries:\n\n| Page | # of articles |\n|------|---------------|\n| 1 | 20 |\n| 25 | 20 |\n| 50 | 20 |\n| 51 | 2 |\n\nSo pages 1–50 each contain 20 articles, and page 51 contains 2:\n\n$$\nN = 50 \\times 20 + 2 = 1{,}002 \\text{ articles}\n$$\n\nThis count excludes News, News & Views, Comments, Editorials, Reviews, Perspectives, Book Reviews, Career columns, Outlooks, Correspondence, etc., because we filtered specifically by `type=article`.\n\n### Step 2 — Applying the p-value interpretation\nA p-value is the probability of observing a result at least as extreme as the one obtained, *assuming the null hypothesis is true*. Treating the stated p = 0.04 as the average Type I error rate, the expected number of papers whose statistically significant claims are actually false positives is:\n\n$$\n1002 \\times 0.04 = 40.08\n$$\n\n### Step 3 — Rounding up\n$$\n\\lceil 40.08 \\rceil = 41\n$$\n\n### Final Answer\n**41 papers** would be incorrect in their claims of statistical significance."},{"system":"Direct Claude Opus 4.7","endpoint":"anthropic.com /v1/messages (chat completion)","model":"claude-opus-4-7 (high effort)","final_answer":"36","graded_correct":false,"elapsed_seconds":8,"key_finding":"Hallucinated 'approximately 900 research articles' without lookup.","computation":"900 × 0.04 = 36 (estimated count was wrong)","answer_text":"# Solving for Incorrect Statistical Significance Claims\n\n## Step 1: Determine Nature's 2020 Article Count\n\nNature published approximately **900 research articles** in 2020 (excluding book reviews, columns, editorials, news, etc.).\n\n## Step 2: Understand What p = 0.04 Means\n\nA p-value of 0.04 means there is a 4% probability that the observed results occurred by chance, assuming the null hypothesis is true. In other words, if we assume all these papers' null hypotheses were actually true, 4% would show \"significant\" results purely by random chance (Type I error / false positive).\n\n## Step 3: Calculate Incorrect Claims\n\n$$900 \\text{ articles} \\times 0.04 = 36 \\text{ articles}$$\n\n## Answer\n\n**36 papers** would be incorrect in their claims of statistical significance.\n\n### Important Caveat\n\nThis is actually a common misinterpretation of p-values. A p-value of 0.04 does *not* mean there's a 4% chance the finding is wrong. It means: *if the null hypothesis were true*, there's a 4% chance of observing data this extreme. The actual false discovery rate depends on:\n- The prior probability that the hypotheses being tested are true\n- Statistical power of the studies\n- Publication bias\n\nUnder realistic assumptions (e.g., Ioannidis's work), the true false discovery rate at p = 0.04 could be much higher than 4% — potentially 25-30% or more — meaning the real number of \"incorrect\" findings could be substantially larger than 36."},{"system":"Direct GPT-5.5","endpoint":"openai.com /v1/chat/completions","model":"gpt-5.5 (default reasoning)","final_answer":"36","graded_correct":false,"elapsed_seconds":95,"key_finding":"Started by refusing the framing on statistical grounds, then hallucinated '878 Nature articles in 2020' to give 36 as a hypothetical.","computation":"878 × 0.04 = 35.12 → ceil = 36","answer_text":"A p-value of 0.04 **does not literally mean** there is a 4% chance the paper's claim is wrong. But if we make the simplifying assumption that \"p = 0.04\" implies a 4% error rate:\n\nUsing an article-only count of **878 Nature articles in 2020**:\n\n\\[\n878 \\times 0.04 = 35.12\n\\]\n\nRounded up:\n\n\\[\n\\lceil 35.12 \\rceil = 36\n\\]\n\n**Answer: 36 papers** under that simplifying assumption."}]}