Part V. Chance Variability
Chapter 16: The Law of Averages
A foreshadowing example
• A good example of where we will be going with
statistical analysis and chance variation is embodied
in Review Exercise 15.11 [p. 262]: Is the observation
of a smoker dying first among 17 out of 22 sets of
smoking discordant twins due to something real, or
could it be down to chance?
– If each twin in a pair were equally likely to die
first, what is the probability of having 17 or more
pairs where the smoking twin dies first?
Answer: 0.008 [< 1%]
Chance processes
• A chance process is any situation involving a
fixed number of repeated independent trials
that gives rise to a chance observation.
Further, the probability of any particular
outcome must be fixed across all the trials.
The Law of Averages
• The Law of Averages says that in any chance
process the chance variability in the process
will increase in absolute terms as the number
of trials increases. But the chance variability
gets smaller when expressed as a percentage
of the total number of trials.
[See Figures 1 & 2, FP&P, pp. 275 - 276].