Chapter 17 STATS.docx

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30 Mar 2012
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Chapter 17
Thinking about Chances
The idea of probability
Favouritism in choosing subjects for a sample survey or allotting patients to treatment and
placebo groups in a medical experiment is as undesirable as it is in awarding first possession of
the ball in football
Chance behaviour is unpredictable in the short run but has a regular and predictable pattern in the
long run
Probability describes what happens in very many trails, and we must actually observe many coin
tosses or many babies to pin down a probability
We call a phenomenon random if individual outcomes are uncertain but there is nonetheless a
regular distribution of outcomes in a large number of repetitions
The probability of any outcome of a random phenomenon is a number between 0 and 1 that
describes the proportion of times the outcome would occur in a very long series of repetitions
An out come with probability 0 never occurs
An outcome with probability 1 happens one very repetition
An outcome with probability ½ happens half the time
Probability just gives us a language to describe the long-term regularity of random behavior
Law of averages
Law of averages states that in a large number of independent repetitions of a random
phenomenon averages or proportions are likely to become more stable as the number of trials
increases, whereas sums or counts are likely to become more variable
A personal probability of an outcome is a number between 0 and 1 that expresses an indvidiuals’
judgement of how likely the outcome is
Because they express indvidiaul opinion, they can’t be said to be right or wrong
There is no reason why a person’s degree of confidence in the outcome of one try must agree with
the results of many tries
Once we understand that “personal judgment of how likely” and “what happens in many
repetitions” are different ideas, we have a good start toward understanding why the public and the
experts disagree so strongly about what is risky and what isn’t
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