Tornado plot

 

Tornado plots provide a simple summary of the degree of influence each input variable has on the amount of uncertainty of an output. In a Tornado plot, input variables are ordered from top down according to the degree of influence they have.

A Tornado plot can be created from the Results Viewer Insert ribbon by clicking this icon:

 

The following is an example of the default Tornado plot:

  • The Output variable is the NPV
  • The type of Tornado shown evaluates the Conditional Mean (see below))
  • Market growth is the most influential input variable (hence the longest bar)

 

The horizontal axis shows the possible value of the output variable (NPV). The Number of Bars option controls the number of input variables that are plotted. ‘Auto’ will include all variables that have a statistically significant relationship to the output. Replacing this with, for example, a value of 5 will show only the 5 most significant input variables, or fewer if there are less than five that are significant. Additional variables can be added to the chart, or removed, by manually checking the boxes in the Inputs list.

There are several different type of Tornado plots available, which measure influence by different statistical methods. The Conditional Mean approach is the default. They are, starting with the most generally useful:

  • Conditional mean– determines the mean of the output for the lowest and highest tranches of the input variable, and uses these to define the ends of the tornado bar. This is one of the most useful plots to produce because it allows the user to see how the output mean is sensitive to each input variable, and it uses values that are meaningful to the decision-maker.
  • Conditional cumulative percentile– determines the specified percentile of the output for the lowest and highest tranches of the input variable, and uses these to define the ends of the tornado bar. This is also one of the most useful plots to produce because it allows the user to see how the output tails are sensitive to each input variable, and it uses values that are meaningful to the decision-maker.
  • Rank correlation – is the most common option. It calculates the rank correlation between the set of values generated for the output and each input in turn. It is a crude form of sensitivity analysis, popular because of its simplicity, but mostly useful for identifying key variables that should be analyzed in more detail. The scale runs from -1 (completely negatively linearly correlated) through 0 (no linear correlation), to 1 (completely positively linearly correlated). This means that it is difficult to evaluate the effect of correlation on the output in terms that are most familiar to the decision maker (e.g. dollars).
  • Proportional contribution to spread – is another common option. It is derived from the rank order correlation and attempts to assess what fraction of the total uncertainty is due to each input variable. It works well when the input variables are uncorrelated and reasonably linearly related to the output (e.g. costs, sales volumes and prices for a financial analysis, or task durations for a project schedule analysis) but can break down when these assumptions are strongly violated.
  • Contribution to variance– is similar to the Proportional contribution to spread option, except that it rescales the analysis to give an approximation of the amount of the output’s spread that is contributed by each input. The analysis is therefore subject to the same assumptions as the first two options. It is commonly termed ‘Contribution to variance’ because it is based on the fact that the variance of the sum of variables can be determined from variance of each independent variable and their correlation structure. However, once each variance contribution has been estimated it is converted to standard deviation (i.e. one takes the square root) to provide values that are meaningful to the decision maker.
  • Conditional standard deviation– determines the standard deviation of the output for the lowest and highest tranches of the input variable, and uses these to define the ends of the tornado bar. This plot is only useful in special circumstances where one is studying an output variable’s spread only.
  • Conditional coefficient of variation– determines the coefficient of variation of the output for the lowest and highest tranches of the input variable. This plot is only useful in special circumstances where one is studying an output variable’s coefficient of variation (standard deviation divided by mean) only.

 

The format of the plot can be comprehensively adjusted by clicking on the various control buttons in the Tornado Options tab:

The following editing tabs are available:

 

 

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