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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