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May 2012 1 MILO SCHIELD, Augsburg College Director, W. M. Keck Statistical Literacy Project US Rep, International Statistical Literacy Project Member,

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Presentation on theme: "May 2012 1 MILO SCHIELD, Augsburg College Director, W. M. Keck Statistical Literacy Project US Rep, International Statistical Literacy Project Member,"— Presentation transcript:

1 May 2012 1 MILO SCHIELD, Augsburg College Director, W. M. Keck Statistical Literacy Project US Rep, International Statistical Literacy Project Member, International Statistical Institute May, 2012 Schield@Augsburg.edu Related paper at www.StatLit.org/pdf/2012Schield-MAA.pdf Big Data Creates Beguiling Coincidences

2 May 2012 2 Coincidence?.

3 May 2012 Run of Heads (Red Cells): Chance of 5 Touching: 1 in 32 (2^5) www.StatLit.org/Excel/2012Schield-Runs.xls

4 May 2012 Run of 10 heads (Ones): Chance = 1 in 1,024 (2^10) www.StatLit.org/Excel/2012Schield-Runs.xls

5 May 2012 Clusters: Grains of Rice Chance of Red: One in 10 www.StatLit.org/Excel/2012Schield-Rice.xls

6 May 2012 Clusters: Grains of Rice Five cells touch: 1 chance in 100,000

7 May 2012 7 Runs and clusters are much more likely than expected! When students press F9, they often get: RUNSCLUSTERS a run of 10 heads:a cluster of six squares: one chance in 2^10one chance in 10^6 a “thousand-year flood” every year a “million-year flood” every year They get unlikely results every time!

8 May 2012 WHY? HOW? 8 Coincidence is much more likely than expected!!!

9 May 2012 9 Explanation #1 The question is ambiguous What is the chance of “that”? At a specific place or anywhere? Paint the target before or after the shooting? Before or after the fact (ex post vs. ex ante)? Consider a run of 8 heads: One chance in 256 at a pre-designated spot Close to 50% somewhere in the next 256 flips

10 May 2012. 10 #2 Law of Very Large Numbers with Compression/Overlap

11 May 2012 11 Students must see that “coincidence”: is much more common than expected 1. may involve an ambiguity (ex-ante/ex-post) 3. may still be a sign of causation. 1854 cholera outbreak in London at a pump. 2. may involve Law of Very-Large Numbers. Unlikely is almost certain given enough tries

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