# Tuesday week 1

### So you think you can do statistics? Lecture 1a: Human brain and small sample sizes

1) 2) 3) 4) 5) The human brain works in both a fast (System 1) and slow (System 2) mode. System 1 is quick, efficient, and prone to errors particularly with respect to probabilities. One such heuristic is called “Representative Heuristic” by Tversky and Kahneman. It explains why people systematically estimate higher probabilities for things that seem similar or that make sense (causally). When people rely on representativeness to make judgments, they are likely to judge wrongly because the fact that something is more representative does not actually make it more likely. Similarly, people often neglect base rates. Base rates describe the underlying proportions of various subgroups in the population. And information at hand is used while neglecting information that is not available (“What you see is what you get” – WYSIWYG). And people tend to create causal stories that make sense where there is any sort of pattern observed. Random chance causes pattern (we’ll keep covering this). One type of pattern that is caused just by chance is that extremes are more likely with small sample sizes. Simulation with marbles of sample size n=7 and sample size n=4. Our results: Group 1 Group 2 Group 3 Group 4 Group 5 TOTAL 7Trials 24 Successes 4Trial 0 20 25 16 18 103 1 0 0 0 1 29 20 40 26 25 140 Successes 2 0 3 5 1 11

6)

Probability of Extreme Event for A Sample of Size 7 0.009709

Probability of Extreme Event for A Sample of Size 4 0.078571

Many patterns can arise simply from this phenomena. For example, cancer rates in small populations are more likely to be extremely high or extremely low than in large populations.

Big Ideas:

Humans are not programmed to think statistically Bigger sample is better -> more precise Chance causes patterns Easy for patterns to mislead Bigger samples provide more information for differentiating chance from interesting pattern

7) General syllabus is as follows (though we will stay flexible): 8) Expectations and Grading: Read some fun readings and/or watch videos as assigned before each class; There may be some fairly small written homework assignments; Participate in class discussion and hands-on activities (marbles -> coding); Think! 40% Class discussion participation (grade assigned each week) 20% In-class projects and small homework assignments (grades assigned as needed) 40% Final student presentation / report (presentation required, report optional)