Saturday, May 31, 2014

10 - Part 2: Heuristics and Biases - Chapter 10: The Law of Small Numbers

Part 2: Heuristics and Biases


Chapter 10: The Law of Small Numbers


  • S1 cannot handle statistics — e.g. lowest kidney cancer rates in U.S. counties are in mostly rural, sparsely pop’d, & located in tradit’ly Republican states in Midwest, S., W.; to explain S2 begins work, uses causal facts & suggest’ns fr. S1, (clean air? rural lifestyle?) — but highest kidney cancer rates are in same counties — correct explan’n is: sample is small, i.e. statistical, not causal
  • even sophisticated researchers have poor intuitions, poor underst. of sampling effects

The Law of Small Numbers

  • in practice psychologists do not use calcul’ns to decide on a sample size, use their judg’t, which is often flawed —often chose samples too small, 50% risk of failing to confirm true hypotheses
  • we all hv bias to believe that small samples rep. the whole pop’n

A Bias of Confidence Over Doubt

  • S1 cannnot disting. betw. degrees of belief — e.g. “In a telephone poll of 300 seniors, 60% support the president,” info abt survey ignored — people not adeq’ly sensitive to sample size
  • S1 does not doubt, suppresses ambiguity, creates coherent stories — unless the message is immed’ly negated, its assoc’ns spread as if the message were true
  • law of small numbers (small samples) is example of bias that favours certainty over doubt
  • we are prone to exagg. consistency & coherence of what we see — believe in small samples — (cf. halo effect, think we know more than we do) — S1 creates a rep’n of reality based on little data, makes too much sense

Cause and Chance

  • S1’s assoc. method looks for causes of an event — but statistics simply relates the event to other possible events, not intst’ed in causes
  • looking for causes à errors in underst. random events — e.g. sequence of births of m/f babies, BBBGGG, GGGGGG, BGBBGB, last seems more likely but all are equally likely, random — we expect the regular seq’s to result fr. cause, not random — widespread misunderst. of randomness — e.g. bombing of London, pattern w. large gaps, spies? no, randomness can look like clusters or regularity — basketball, 3-4 baskets in a row à belief in “hot hand,” but just random, cogn. illusion — investor’s seq. of good years, CEO’s acquisitions, probably all luck, random
  • best schools are small, but so are worst
  • focus on content of messages, little attention to info abt reliability —  —result in view of world simpler & more coherent than data justify  — e.g. exagg. faith in small samples
  • statistics often produce observ’ns seemingly calling for causal explan’n — but search for causes inappropr. — many facts ß chance, incl. accidents of sampling
  • causal explan’ns of chance events = wrong.

Speaking of the Law of Small Numbers


  • “Yes, the studio has had three successful films since the new CEO took over. But it is too early to declare he has a hot hand.”
  • “I won’t believe that the new trader is a genius before consulting a statistician who could estimate the likelihood of his streak being a chance event.”
  • “The sample of observations is too small to make any inferences. Let’s not follow the law of small numbers.”
  • “I plan to keep the results of the experiment secret until we have a sufficiently large sample. Otherwise we will face pressure to reach a conclusion prematurely.”

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