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**Which Sensitivity Measure to Use?**

**Applies to:** @RISK 5.x–7.x

@RISK gives me a lot of options for sensitivities in my tornado graph: correlation coefficients, regression coefficients, mapped regression coefficients, change in output mean, and so on. How do I choose an appropriate measurement in my situation?

After a simulation, the Sensitivity Analysis window is your handy overview of sensitivities for all outputs. In the *Results* section of the @RISK ribbon, click the small tornado to open the Sensitivity Analysis window. (You can also see most of this information by clicking the tornado at the bottom of a Browse Results window for an output.)

Change in output statistic:

The change in output statistic, added in @RISK 6, is an interesting, differencing approach to sensitivity. You can select mean, mode, or a particular percentile: click the % icon at the bottom of the Sensitivity Analysis window, or the tornado icon at the bottom of the Browse Results window and select *Settings*.

The Change in Output Statistic tornado displays a degree of difference for just the two extreme bins, but the spider shows more information: the direction of the relationship, and the degree of difference for every bin.

Regression or correlation coefficients:

Regression coefficients and regression mapped values are just scaled versions of each other. Correlation coefficients are rank-order correlation, which works well for linear or non-linear correlations. In the Sensitivity Analysis window, when you select *Display Significant Inputs Using: Regression (Coefficients)*, @RISK will display R² ("RSqr") in each column. You can use R² to help you decide between correlation coefficients and regression coefficients:

- A low value of R² means that a
*linear*regression model is not very good at predicting the output from the indicated inputs. In this case, you would focus more on correlation coefficients, because rank-order correlation doesn't depend on the two distributions having similar shape or being linearly related. - If R² is high, a linear regression model is a good fit mathematically. But even here, you should look at the variables to assure yourself that they are reasonable and to rule out a problem with multicollinearity. This would be signaled, for example, when @RISK reports a significant positive relationship between two variables in the regression analysis, and a significant negative correlation between those variables in the rank-order correlation analysis.

For a more detailed explanation of correlation and regression, see Correlation Tornado versus Regression Tornado and How @RISK Computes Rank-Order Correlation.

Contribution to variance:

R² is a measure of the percentage of the variance in a given output can be traced to the inputs — as opposed to measurement errors, sampling variation, and so on. @RISK adds input variables to a regression one by one, and each variable's contribution to variance is simply bow much larger R² grows as that input is added. In other words, a regression equation should predict output values from a set of input values. A variable's contribution to variance measures how much better the equation becomes as a predictor when that input is added to the regression. Unlike a regression coefficient, this measurement is unaffected by the magnitude of the input. For more about this, see Calculating Contribution to Variance.

**See also:** All Articles about Tornado Charts

Last edited: 2018-08-15

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