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 a number of different disciplines, including business analysis, investing, environmental studies, engineering, physics and chemistry.

### 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 models composed or studies done 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, in relation to 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 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.

### 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 best data to be collected for future analyses to evaluate basic assumptions regarding investment and return on investment (ROI), or to optimize the allocation of 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.

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.

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 a number of differential equations. The importance of various inputs and the effects of variance in the inputs on model outcomes can be analyzed.

### Refining Computer Models

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.