Sensitivity analysis

Sensitivity analysis is a statistical method used to determine how changing the values of specific independent variables affects a dependent variable under a given set of circumstances. Also known as what-if analysis, this method helps predict the amount by which input data in a programming model can be changed for the output data to remain relatively unchanged. Sensitivity analysis is often used by scientists and engineers to check the validity of their research or calculations. In business, the method is useful in strengthening communication and developing recommendations during the decision-making process. It is most often used in risk assessment, a business strategy that gauges the potential problems in a business model.

Background

The first use of sensitivity analysis in observational research has been attributed to a 1959 study by American statistician Jerome Cornfield and a group of colleagues. By studying groups of smokers and nonsmokers, they established a link between smoking cigarettes and lung cancer. At the time, tobacco companies disputed reports that cigarettes caused lung cancer. They claimed that genetic or environmental factors may be responsible for the increase. Cornfield's study found that smokers would need to be about nine times more likely than nonsmokers to be affected by these other factors to account for the higher occurrence of lung cancer. By using sensitivity analysis, the researchers determined that a high cancer rate was statistically unlikely without smoking being a major factor.

Since that time, sensitivity analysis has been used in other scientific fields such as sociology, criminology, and psychology. In business, sensitivity analysis can be used to determine sales forecasts in the event of an upturn or downturn in the economy. A company starts out with a projection of expected sales and then plugs in figures representing what would happen if the economy grew or contracted by a particular percentage. Financial analysts often use the method to predict the effect a fluctuating stock market would have on investment performance. Engineers can use sensitivity analysis to find potential safety issues with their projects during the planning stage. Bridge designers, for example, can input data concerning the amount of traffic a bridge can hold before it becomes structurally unsound.

Overview

There are two basic forms of sensitivity analysis—local sensitivity analysis and global sensitivity analysis. These forms can be further divided into numerous individual methods. Local sensitivity analysis examines the effect a change at a single, or "local," input factor has on the output. In global sensitivity analysis, changes are made in a range of input factors simultaneously and the effect on output is observed. At the completion of an analysis, a researcher makes a list called a sensitivity ranking that sorts the input parameters by the amount of influence each had on the model's output. The type of sensitivity analysis used to obtain results can depend on many factors. These include the reliability of the input data and the amount of resources available for the study.

One of the most common types of local sensitivity analysis is a method known as one-at-a-time sensitivity. As the name suggests, this method involves adjusting one input variable at a time, keeping the others the same, and running the equation to receive an output. Then the value is returned to its original form, the next value is changed, and the process repeated with all the input factors. This helps an analyst determine potential shortfalls with the data model, as the source of any problems is easy to identify. The method is limited by the fact that changing one value at a time does not take into account changes in multiple values at once or the interactions between values.

Differential sensitivity analysis, also called the direct method, is built on the idea of a best-case scenario in which all the input parameters are adjusted to their average values. This method is heavily reliant on algebraic equations and can be more demanding to implement than other models. While it is a commonly used method, it can run into problems if the input data falls too far outside of normal parameters. Factorial design analysis involves examining a randomly chosen number of parameters and running computations on the selected values. If a model has seven total values, for example, then researchers could decide to choose three or four and observe the changes in those. The downside of this method is that it entails running the computation model several times. The sensitivity index calculates the percentage of difference in the output when the input parameters are varied from the minimum to their maximum values. This method utilizes the parameter's entire range of possibilities.

Another type of sensitivity analysis includes noting the correlation between input and output values on a mathematical graph called scatter plots. The input and output values are plotted on a graph and compared. This method is useful for uncovering value trends and relationships that may have otherwise gone unnoticed. The relative deviation method examines the effects that occur to the model's output when each input parameter is individually adjusted by its probability density function. The probability density function is a measure of the likelihood that a random value would equal the sample value at a given point. This method is similar to the one-at-a-time method except that a much larger sample is taken from the input distribution. In the case where two sets of data have identical output distributions, but have wide and narrow input distributions, the narrow model will be more sensitive to changes in input values. The reason for this effect is called the relative deviation ratio. This method allows analysts to examine the sensitivity of the data parameters and determine if the output distribution varies widely or if the input distribution is relatively narrow.

Bibliography

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