Tool/Probability and Statistics/No. 0914

Sensitivity Analysis

Sensitivity analysis is a way to test how changes in a model’s inputs or assumptions affect its results. Used in statistics and decision analysis, it shows which uncertain inputs have the most influence and where a change would lead to a different decision.

a tool: pick it up

Evidence: Well established
Read: 6 min
Links: 18 connections
Useful when: Deciding under uncertainty · Estimating time and cost · Forecasting · Money and investing · Reading data and statistics

01You've seen this when…

in life
A solar installer estimates that panels will pay for themselves in eight years. You lower the assumed electricity price growth, and the payback stretches beyond the time you expect to stay.
at work
The hiring plan balances if 85% of customers renew. You replace that figure with 70%, and the same spreadsheet shows three salaries the business cannot cover.
out in the world
A city forecasts enough toll revenue to fund a new bridge. At a public meeting, a resident asks the finance team to rerun the forecast with traffic 20% below its estimate.

02The idea

A spreadsheet can turn uncertain guesses into a precise-looking answer. Sales grow by 12%, construction takes nine months, maintenance costs $4,000 a year. Put them together and a cell announces that the project pays off.

Sensitivity analysis asks how that answer moves when its ingredients move. Change sales growth, construction time or maintenance costs, then calculate again. Some changes barely touch the result. Others erase the projected gain.

Two questions matter. Which inputs drive the result? And how far can those inputs move before the preferred decision changes? An uncertain input deserves more attention when plausible changes in it can reverse the choice.

A local analysis examines changes near a starting estimate. A global analysis explores a broader range, including combinations of inputs. This distinction matters when a model has thresholds, curves or interactions, where one input changes the effect of another.

Related tools emphasize different things. Scenario planning builds coherent possible futures. Stress testing examines adverse conditions. Sensitivity analysis tracks how a result responds to specified changes in its assumptions.

03How to use it

State the decision and the result that matters. Write down the choice: buy or rent, launch or wait, approve or reject. Choose an output tied to that choice, such as total cost, expected profit or completion date. This keeps the exercise focused on a decision someone can make.
Save a baseline. Record the starting inputs and calculated result. Keep them visible so each new run has a clear comparison. Label estimates as estimates, especially when a precise number rests on a rough guess.
Give uncertain inputs defensible ranges. Use supplier quotes, past projects, observed variation or expert judgments. Document why each range is plausible. A uniform change of 10% is convenient, but different inputs often have very different uncertainties.
Change one input at a time for an initial screen. Hold the others fixed and recalculate. Rank inputs by how much their plausible changes move the output. This can quickly reveal where better information would help. For complex simulations, global screening methods offer a more efficient starting point.
Test combinations and decision thresholds. Try joint changes that could occur together. Preserve relationships: higher sales may also require more staffing. Find the break-even value or boundary where the preferred option switches. Check both sides of it; a few small changes near the baseline can miss a threshold farther away.
Turn the findings into an action. Gather better evidence about the influential inputs, negotiate protection against them, reduce the commitment or choose an option that performs acceptably across the range. The value of information depends partly on whether resolving an uncertainty could change the choice.

For a large model, software can automate these runs. The judgment still lies in choosing the inputs, their ranges and the combinations to examine.

04A worked example

Consider an illustrative café deciding whether to run a weekend stall at a festival. Stall rental, transport and staffing cost $2,400. Each order contributes $8 after ingredients and payment fees. The team expects 400 orders, producing a projected profit of $800: 400 × $8 − $2,400.

What it looks like A profitable weekend with a manageable upfront commitment. The forecast presents one demand estimate and one contribution per order.

What’s actually going on Both inputs are uncertain. The team tests 250–500 orders and contributions of $6–$9 per order. At 250 orders and the baseline $8 contribution, the stall loses $400. At 400 orders and a $6 contribution, it breaks even. Combining 250 orders with a $6 contribution produces a $900 loss.

The decision boundary becomes useful. With an $8 contribution, the café needs 300 orders to cover its fixed costs. With a $6 contribution, it needs 400. The practical question is whether comparable festivals and the planned menu support demand comfortably above those thresholds.

What made it work The team connected uncertainty to a purchase decision. It identified demand and contribution per order as consequential inputs, calculated the break-even boundaries, and could now seek attendance evidence or negotiate a lower stall fee. These calculations describe what follows from the tested assumptions. Estimating the chance of a loss would also require evidence about how likely those assumptions are.

05When to reach for it

A recommendation rests on a few estimates. Growth rates, staffing needs, interest rates or completion dates dominate the business case.
Reasonable people disagree about an input. Run both estimates through the same model to see whether the disagreement changes the choice.
Better information costs money or time. Sensitivity analysis helps identify which uncertainty deserves research first.
The decision is expensive to reverse. Examine its dependence on assumptions before signing a contract or committing the budget.

It also helps when a forecast has several decimal places but its inputs came from a brief conversation. That is a useful warning sign for the appeal of precision.

06When it misleads

The model leaves out a major cause. Varying fuel prices cannot reveal an omitted permit requirement that blocks the entire project. Sensitivity analysis inherits model risk, including missing variables and mistaken relationships. Examine alternative model structures as well as different numbers.
The ranges quietly decide the answer. An input can appear unimportant because it was given a narrow range. Rankings depend on the uncertainty assigned to each input. Record the basis for those ranges and revisit them when evidence changes.
Single-input tests miss joint effects. Two individually tolerable changes can combine to produce a large loss. Curved relationships and thresholds make this especially hazardous. Broader sampling helps, though it can require many model runs.
The combinations break the underlying relationships. Testing high production with low material use may create an impossible case. Equally, combining every worst value can produce an extreme situation with little practical relevance. Explain why the combinations belong together.
A range gets treated as a probability forecast. Finding losses in several tested cases does not establish the chance of losing money. That requires justified probability distributions and dependencies.

Use the exercise to calibrate confidence. A decision that survives plausible variations has stronger support. Claiming that it will survive every surprise would restore the overconfidence the exercise was meant to reduce.

07Roots

George Dantzig’s 1963 book on linear programming included a problem as concrete as assembling a low-cost diet that met nutritional requirements. Food prices and nutrient limits determine which menu is cheapest. Change them, and a different menu can become preferable. Questions about how solutions respond to changing costs and constraints became part of optimization’s practical toolkit.

Computer simulation widened the problem. At Oak Ridge National Laboratory, statistician Max D. Morris developed a screening method published in 1991 for models with many inputs. His method took short walks through a grid of possible input values, changing one input at each step. Repeating those walks in different regions helped identify strong or uneven effects while limiting the number of model runs.

Mathematician Ilya Sobol developed methods that divide a model’s output variation into contributions from inputs and their combinations. These became central to global sensitivity analysis. Andrea Saltelli and colleagues later brought a range of methods together in their 2008 textbook for researchers using mathematical models. The technique has several roots in optimization, mathematical modeling and decision analysis; its development reflects a shared problem: deciding how much confidence to place in a result built from uncertain ingredients.

08How solid is this?

Sensitivity analysis has well-developed mathematical methods used across optimization, statistics and scientific modeling. Its conclusions depend on the model, input ranges and dependencies; performing it alone does not establish probabilities or guarantee a sound decision.

10Origin and sources

Developed across mathematical modeling, optimization and decision analysis, with no single inventor. Max D. Morris’s screening method (1991) and Ilya Sobol’s variance-based methods were major developments in global sensitivity analysis.

[1]Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press.
[2]Morris, M. D. (1991). Factorial Sampling Plans for Preliminary Computational Experiments. Technometrics, 33(2), 161–174.
[3]Sobol, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55(1–3), 271–280.
[4]Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., & Tarantola, S. (2008). Global Sensitivity Analysis: The Primer. John Wiley & Sons.

Suggest an edit· Updated 2026-10-02