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Summary 205
Hull 10 ), some of them assuming that the shape of the dependent variable’s
probability distribution is the same, whatever the value of the
independent variable.
The @RISK (pronounced ‘at risk’) computer package (also see next
section) requires the user to input a correlation coefficient to show the
strength of association between the two variables. This coefficient always
has a value between −1 and+1. Positive values indicate that higher
values of one variable are associated with higher values of the other (e.g.
higher production levels are likely to be associated with higher machine
maintenance costs). Negative coefficients imply an inverse relationship
(e.g. higher advertising expenditure by competitors is associated with
lower sales for our company). The closer the coefficient is to either −1or
+1 then the stronger is the association.
In practice, it may be possible to determine the appropriate correlation
coefficient for the simulation model by analyzing past data. Where this
is not possible the correlation can be estimated judgmentally. However,
this needs to be done with care since, as we will see in Chapter 9, biases
can occur in the assessment of covariation. In particular, prior beliefs
and expectations can lead people to see associations where none exist, or
to overestimate the degree of association when it is weak. Conversely,
if the judgment is based on observations with no expectation of an
association, then moderately strong associations that do exist are likely
to be missed, while correlations for strong associations are likely to be
underestimated. 11
Summary
In this chapter we have shown that simulation can be a powerful
tool when the direct calculation of probabilities in a decision problem
would be extremely complex. Moreover, because the approach
does not involve advanced mathematics the methods involved and the
results of analyses are accessible to decision makers who are not trained
mathematicians or statisticians. Obviously, the application of simulation
requires the use of a computer and a number of specialist computer
packages are available. Perhaps the best known is @RISK (developed
by the Palisade Corporation, Newfield, New York) which runs with
Microsoft® Excel.