10 - 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
- 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
- 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
- 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.
- “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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