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Finding the right balance in management
decisions, February 23, 2007, 2D.

Most
people understand that if you toss a coin many times, you
should see about the same numbers of heads and tails. The
reason for that has to do with odds and probability. When
flipping a coin, the only two likely outcomes are “heads”
and “tails.” The odds of getting a head on a particular
toss are one out of two. Likewise, the odds of getting a
tail on any particular toss are also one out of two. The
expression “one out of two” means that the outcome of
interest occurs once in two potential outcomes and each of
the potential outcomes is equally likely to occur.

Statisticians use the notions of probability to help
forecast and predict the likelihood of certain events
occurring or not occurring. They also use those concepts to
refute or not refute certain claims or statements. For
example, if you believed that a certain coin was unbalanced,
meaning that it yielded either more heads than tails or vice
versa, you could run an experiment to test your hypothesis.
You could toss the coin in a similar manner 1,000 times and
record the numbers of heads and tails that you observed
across the trials in the experiment. If you believed that
the coin yielded more heads than tails, you would want to
observe the number of heads that appeared over the trials in
your experiment.

In 1,000
tosses of a balanced coin, you should expect to see 500
heads and 500 tails. What if, after tossing your coin 1,000
times, you observed 501 heads and 499 tails? You would
probably not conclude that the coin is unbalanced. On the
other hand, if you observed 999 heads and one tail you
probably would conclude that the coin is unbalanced in favor
of heads.

At what
point do you move from concluding that the coin is not
unbalanced to concluding that it is unbalanced? If 501
heads are not enough evidence to conclude that the coin is
unbalanced, but 999 heads are, where is the point where the
conclusion changes? Are 600 heads enough proof? 700
heads? 800 heads? 900 heads? Before beginning the
experiment, you must decide upon the number of heads that
will be the dividing point between concluding that the coin
is unbalanced and balanced. How is that point selected?
The field of statistics gives us answers to that question.

Statisticians use the notions of probability, error,
hypothesis testing, and sampling theory to help determine
the points where conclusions switch from one alternative to
another. Techniques that use these concepts can be of
tremendous value to managers and organizational leaders. Is
there more demand for the new product than for the old one?
Does one machine produce fewer defects than another? Do men
and women receive equal compensation in this company? Does
the new advertising campaign create more awareness among
consumers? With proper instruction, managers and decision
makers can learn to apply statistical thinking and
problem-solving techniques to a wide range of organizational
issues.

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