# How Is Sensitivity Analysis Used?

Sensitivity analysis is an analysis method that is used to identify how much variations in the input values for a given variable will impact the results for a mathematical model. Sensitivity analysis can be applied in several different disciplines, including business analysis, investing, environmental studies, engineering, physics, and chemistry.

### Key Takeaways

• Sensitivity analysis is used to identify how much variations in the input values for a given variable impact the results for a mathematical model.
• Sensitivity analysis can identify the best data to be collected for analyses to evaluate a project's return on investment (ROI).
• Sensitivity analysis helps engineers create more reliable, robust designs by assessing points of uncertainty in the design's structure.

## Understanding Sensitivity Analysis

Sensitivity analysis is concerned with the uncertainty inherent in mathematical models where the values for the inputs used in the model can vary. It is the companion analytical tool to uncertainty analysis, and the two are often used together. All of the models composed and studies executed, to draw conclusions or inferences for policy decisions, are based on assumptions regarding the validity of the inputs used in calculations.

For example, in equity valuation, the return on assets (ROA) ratio assumes that a valid, accurate calculation of a company's assets can be figured out and that it is reasonable to analyze profits, or returns, concerning assets as a means of evaluating a company for investment purposes.

The conclusions drawn from studies or mathematical calculations can be significantly altered, depending on such things as how a certain variable is defined or the parameters chosen for a study. When the results of a study or computation do not significantly change due to variations in underlying assumptions, they are considered to be robust. If variations in foundational inputs or assumptions significantly change outcomes, sensitivity analysis can be employed to determine how changes in inputs, definitions, or modeling can improve the accuracy or robustness of any results.

## How Sensitivity Analysis Is Used

Sensitivity analysis can be helpful in various situations, including forecasting or predicting as well as identifying where improvements or adjustments need to be made in a process. However, the use of historical data can sometimes lead to inaccurate results when forecasting since past results don't necessarily lead to future outcomes. Below are a few common applications of sensitivity analysis.

### Return on Investment

In a business context, sensitivity analysis can be used to improve decisions based on certain calculations or modeling. A company can use sensitivity analysis to identify the inputs which have the biggest impact on the return on a company's investment (ROI). The inputs that have the greatest affect returns should then be considered more carefully. Sensitivity analysis can also be used to allocate assets and resources.

One simple example of sensitivity analysis used in business is an analysis of the effect of including a certain piece of information in a company's advertising, comparing sales results from ads that differ only in whether or not they include the specific piece of information.

### Climate Models

Computer models are commonly used in weather, environmental, and climate change forecasting. Sensitivity analysis can be used to improve such models by analyzing how various systematic sampling methods, inputs, and model parameters affect the accuracy of results or conclusions obtained from the computer models.

### Scientific Research

The disciplines of physics and chemistry often employ sensitivity analysis to evaluate results and conclusions. Sensitivity analysis has proven particularly useful in the evaluation and adjustment of kinetic models that involve using several differential equations. The importance of various inputs and the effects of variance in the inputs on model outcomes can be analyzed.

### Engineering

It is standard practice in engineering to use computer models to test the design of structures before they are built. Sensitivity analysis helps engineers create more reliable, robust designs by assessing points of uncertainty or wide variations in possible inputs and their corresponding effects on the viability of the model. Refinement of computer models can significantly impact the accuracy of evaluations of such things as bridge stress ability or tunneling risks.