# Understanding Sensitivity Analysis - A Guide for Decision Makers

## Introduction

Sensitivity analysis is a method used to evaluate how different values of an independent variable impact a particular dependent variable. Its purpose is to determine how sensitive a system is to changes in the parameters of the model or the values of external variables. By observing the range of outcomes and the degree of change, it is possible to identify which independent variables have the most influence on the behavior of a given system.

### Overview of the Different Types of Sensitivity Analysis

- Univariate Sensitivity Analysis
- Multivariate Sensitivity Analysis
- Global Sensitivity Analysis
- Local Sensitivity Analysis
- Tornado Analysis

## Univariate Sensitivity Analysis

Univariate Sensitivity Analysis (USA) is a type of sensitivity analysis that examines the influence of one variable at a time on a model or simulation results. It is a structured approach to understanding the behavior of complex systems or models by looking at how various changes to the inputs of the system affect the output of the system.

### Definition and Purpose

Univariate Sensitivity Analysis is used to determine the most important factors in a model or simulation. It helps identify those factors that could have the greatest impact on the outcome of the model or simulation. By isolating each factor, USA can assess the interaction between different factors and their respective effect on the model or simulation. This helps to identify the optimum values for each of the model parameters.

### Examples

There are a variety of applications for Univariate Sensitivity Analysis. One example is in engineering design where USA can be used to optimize the design of a product. USA can be used to identify the most influential parameters in a system and to determine the best values for these parameters. It can also be used to identify which factors are most sensitive to changes in the model. USA can be used to analyze economic models to help identify and quantify the risk associated with a particular investment decision.

USA can also be used for medical research. It can be used to study the effect of changes to different treatments, such as drug dosages, on the health outcomes of patients. This type of analysis helps to inform clinical decisions and can be used to identify optimal treatment plans.

## Partial Derivative Sensitivity Analysis

Partial derivative sensitivity analysis (PDSA) is a technique used to identify the impact of changes in input variables on the output of a system or model. By taking partial derivatives of the function with respect to the various input variables, PDSA can determine the sensitivity of the model to changes in input variables. It provides insight into which variables have the most influence on the output of the system, and which variables can be adjusted to maximize desired outcomes.

### Definition and Purpose

The purpose of partial derivative sensitivity analysis is to determine the impact of certain variables on the output of the system. By considering a particular variable and taking a partial derivative of the model’s function with respect to that variable, the rate of change in the output in relation to a change in that variable is determined.

### Examples

One example of partial derivative sensitivity analysis is in the field of economics, where this method can be used to estimate the effect of changes in the price of a good or service on the equilibrium quantity of the good or service. By taking the partial derivative of the demand function with respect to the price variable, the sensitivity of demand to changes in price can be determined.

Another example is in the field of finance, where PDSA can be used to identify the sensitivity of investment returns to changes in the underlying variables, such as the interest rate, the duration of the investment, the volatility of the returns, or the liquidity of the investment. By taking a partial derivative of the return on the investment with respect to each of these variables, the sensitivity of the returns to the underlying variables can be identified.

## Probabilistic Sensitivity Analysis

Probabilistic sensitivity analysis is a method of analyzing the future performance of projects and investments. By simulating different scenarios within a stochastic system, this type of sensitivity analysis is able to identify the range of possible outcomes associated with uncertainty in variables, such as input costs, demand, interest rates, or production levels. The goal is to provide insight into how these variables will affect the results of an enterprise in the future.

### Definition and Purpose

Probabilistic sensitivity analysis is used in advanced Monte Carlo analysis to identify the areas of uncertainty that have the greatest impact on a given project. This type of analysis also provides insight into the risk associated with various decision choices and enables decision-makers to make well informed decisions. The results of this type of sensitivity analysis are usually represented as an uncertainty distribution or risk profile. This makes it easy to compare different scenarios and make decisions based on the uncertainty levels.

### Examples

One of the most common uses of probabilistic sensitivity analysis is in financial and investment decision-making. For example, a financial decision-maker may use this type of analysis to simulate different scenarios of future stock prices and identify the most favorable investment opportunities. The same approach can be used in other industries, such as energy and production, to identify the most profitable production strategies or the most cost efficient energy sources.

Another example of the use of probabilistic sensitivity analysis is for modeling portfolio losses. In this case, the analysis can be used to identify the investment strategies that have the lowest amount of risk associated with them. This type of analysis can also be used in research and development to identify the most promising areas for innovation and the most cost effective processes for product development.

## Trend Analysis

Trend analysis is a type of sensitivity analysis that identifies the overall direction of an investment or the forces impacting it. It will typically involve tracking an asset’s price, production rate, costs, or profit over time. This type of analysis is usually done over an extended period of time in order to identify patterns and trends that may not be perceptible in shorter time frames.

### Definition and Purpose

Trend analysis is employed to identify and measure longterm direction, magnitude, and rate of change of price or performance for an asset or investment. It helps investors, or project managers, understand how to best utilize those trends in order to maximize returns or curtail losses.

### Examples

An example of trend analysis would be an investor analyzing the price of a stock for a particular company over the past five years in order to gain an understanding of the long-term price movements. Another example could be an engineering firm analyzing the production rate of a project over the past five years in order to try and predict the likely rate of production at future points in time.

- Stock prices
- Production rates
- Costs of manufactured products
- Gross profit margin
- Net profits

## Regression Analysis

Regression analysis is a statistical tool used to predict values by analyzing a relationship between variables. It is used to determine the impact of a change in one or more independent variables– such as prices, wages, or resource utilization–on a dependent variable, such as sales or profits. In sensitivity analysis, regression analysis is used to identify how changes in relevant inputs (independent variables) will affect the output (dependent variable).

### Definition and Purpose

Regression analysis is used in sensitivity analysis to identify how changes in relevant inputs will affect the output. The purpose of conducting this type of analysis is to gauge the level of risk associated with the project being assessed. By calculating the level of sensitivity of certain parameters, management can evaluate the confidence level of the project in its current form as well as make decisions as to whether certain assumptions should be adjusted or certain design choices should be modified.

### Examples

One real-world example of regression analysis being used in sensitivity analysis can be found in the business of creating computer software. A development team might use regression analysis to determine the sensitivity of their program's performance to the various hardware options chosen for the deployment environment. In this case, the hardware components of the target system could be seen as inputs for the regression analysis and the performance of the program as the output. By running the analysis, the team can determine the most efficient combination of hardware components to maximize their program's performance.

Another example involves cost analysis. In this case, the cost analysis would involve using regression analysis to examine certain cost parameters, such as labor costs and material costs. The output of this analysis would be a measure of how sensitive the overall cost of a project is to changes in the individual parameter values. This type of analysis can be extremely useful in understanding the potential savings or losses associated with particular alterations in the project's cost structure.

## Conclusion

Sensitivity analysis is a great tool for undertaking financial decisions. It allows decision makers to evaluate the risks being taken and to plan for any possible changes in the future. This type of analysis allows for the calculation of the maximum amounts of return that can be expected in specific directions. Overall, the primary benefit of using sensitivity analysis for decision making is its ability to minimize risk and make decisions with confidence.

In summary, there are four types of sensitivity analysis that can be used in decision-making. These include: One-way Sensitivity analysis, Two-way Sensitivity analysis, Scenario analysis, and Tornado analysis. Each one has its own advantages and disadvantages that must be considered before being used. It is important to understand the different types of analysis and their advantages and disadvantages in order to choose the most suitable one for your particular situation.