Sensitivity Analysis Explained: Understanding What Drives Your Results

Sensitivity analysis is an analytical technique that examines how variations in input variables affect a model's output, revealing which factors most influence results and where uncertainty matters most. By systematically changing inputs and observing how outputs respond, organizations can focus attention on high-impact variables, assess model robustness, and make more informed decisions.

In any model or projection, some inputs drive results far more than others. Sensitivity analysis identifies these critical factors - the levers that matter - so decision-makers know where to concentrate effort and attention.

Why Sensitivity Analysis Matters

Focus on What Matters

Organizations have limited resources for analysis and action:

• Not every input deserves equal attention
• Some variables drive results; others barely register
• Effort should concentrate on high-impact factors
• Sensitivity analysis reveals where to focus

Understanding sensitivity guides resource allocation.

Assess Model Reliability

Models are only as good as their inputs:

• How much do uncertain inputs affect conclusions?
• Which assumptions most influence the output?
• Where would being wrong have the biggest impact?
• How confident should we be in the results?

Sensitivity analysis reveals model reliability.

Communicate Uncertainty

Stakeholders need to understand projection uncertainty:

• Which factors create the most variability?
• What would change the conclusion?
• Where are the key uncertainties?
• What risks should we monitor?

Sensitivity analysis enables honest communication about uncertainty.

Prioritize Data Quality Efforts

Data quality work should focus on high-impact data:

• Improving accuracy of sensitive inputs yields big returns
• Low-sensitivity inputs can tolerate more uncertainty
• Investment in data quality should be proportional to impact
• Sensitivity analysis guides data quality priorities

This understanding optimizes data quality investments.

Types of Sensitivity Analysis

One-at-a-Time (OAT) Analysis

The simplest approach - vary one input while holding others constant:

Process:

1. Establish baseline values for all inputs
2. Change one input by a fixed amount or percentage
3. Observe the change in output
4. Repeat for each input
5. Compare output changes to identify most sensitive inputs

Advantages:

• Simple to implement and understand
• Clear isolation of individual effects
• Easy to communicate results

Limitations:

• Ignores interactions between inputs
• May miss non-linear effects
• Can be misleading when inputs correlate

OAT provides a starting point but not the complete picture.

Tornado Analysis

A visual approach that ranks inputs by influence:

Process:

1. Define reasonable ranges for each input
2. Calculate output at low and high values for each input
3. Plot results as horizontal bars ordered by impact
4. The resulting diagram resembles a tornado

Interpretation:

• Longest bars represent most influential inputs
• Short bars represent factors with minimal impact
• The shape immediately communicates relative importance

Tornado diagrams are highly effective for communication.

Spider Diagrams

Visualize how output changes across input ranges:

Process:

1. Establish baseline output
2. Vary each input through its range
3. Plot output change on Y-axis against input change on X-axis
4. Each input becomes a line on the diagram

Interpretation:

• Steeper lines indicate higher sensitivity
• Curved lines reveal non-linear relationships
• Crossing lines show where one factor becomes more important than another

Spider diagrams reveal relationship shapes, not just magnitudes.

Global Sensitivity Analysis

Examine sensitivity across the entire input space:

Techniques:

• Monte Carlo simulation with correlation analysis
• Variance decomposition methods
• Morris screening
• Sobol indices

Advantages:

• Captures interactions between inputs
• Accounts for non-linearities
• Examines full range of possibilities

Complexity:

• Requires more sophisticated methods
• Computationally intensive
• Results harder to communicate

Global methods provide comprehensive understanding but require more effort.

Conducting Sensitivity Analysis

Define the Model

Start with a clear model specification:

• What are the inputs?
• What is the output of interest?
• What relationships connect inputs to outputs?
• What is the model's purpose?

Without a clear model, sensitivity analysis is impossible.

Identify Input Ranges

Establish reasonable ranges for each input:

Historical ranges: What values have we observed? Expert judgment: What do experts consider plausible? Uncertainty estimates: What is the probability distribution? Operational constraints: What values are actually possible?

Ranges should be realistic, not arbitrary.

Execute the Analysis

Run the sensitivity calculations:

Manual methods: Spreadsheet-based for simple models Simulation software: For complex or non-linear models AI-powered platforms: Tools like Codd AI Analytics can automatically identify sensitive variables and explain their impact through natural language

Ensure calculations are accurate and documented.

Interpret Results

Draw meaningful conclusions:

• Which inputs drive the most variation in output?
• Are there threshold effects or non-linearities?
• Do inputs interact significantly?
• How reliable is the baseline projection?

Interpretation connects analysis to action.

Communicate Findings

Share results appropriately:

Executive summary: Key drivers and implications Visual displays: Tornado diagrams, spider charts Detailed documentation: Full methodology and results Action recommendations: What to do based on findings

Tailor communication to the audience.

Practical Applications

Financial Modeling

Sensitivity analysis is standard in finance:

Investment decisions: Which assumptions most affect NPV or IRR? Valuation: What drives company value most? Budgeting: Where does forecast uncertainty concentrate? Risk assessment: Which factors create downside risk?

Financial models without sensitivity analysis provide false precision.

Pricing Decisions

Price optimization depends on sensitivity:

Demand sensitivity: How do volume and revenue respond to price changes? Competitive dynamics: How sensitive are results to competitor pricing? Cost structure: How do margins respond to input cost changes? Elasticity estimation: What is price elasticity of demand?

Sensitivity analysis informs pricing strategy.

Operational Planning

Operations benefit from understanding sensitivities:

Capacity planning: How sensitive is utilization to demand assumptions? Inventory management: Which forecasts most affect optimal inventory? Resource allocation: Where do small changes in assumptions most affect resource needs? Process improvement: Which factors most influence process outcomes?

Sensitivity focuses operational improvement efforts.

Project Management

Projects involve numerous uncertain estimates:

Schedule risk: Which activities most affect completion date? Budget risk: Which cost estimates most affect total budget? Resource risk: Where do staffing assumptions most affect outcomes? Scope risk: Which requirements most affect delivery?

Sensitivity analysis guides project risk management.

Strategic Planning

Strategy depends on uncertain assumptions:

Market growth: How sensitive is strategy success to growth rates? Competitive response: How much do competitor actions affect outcomes? Technology evolution: How sensitive are plans to technology assumptions? Regulatory changes: How would different regulatory scenarios affect strategy?

Sensitivity analysis stress-tests strategic plans.

Best Practices

Start with Key Uncertainties

Focus initial analysis on inputs that are:

• Highly uncertain
• Potentially high-impact
• Subject to management influence
• Important to stakeholders

Not every input needs detailed sensitivity analysis.

Use Realistic Ranges

Sensitivity analysis quality depends on range quality:

• Too narrow: Understates true uncertainty
• Too wide: Produces meaningless results
• Unrealistic: Analyzes impossible scenarios

Invest effort in establishing credible ranges.

Look for Interactions

One-at-a-time analysis may miss important dynamics:

• Do inputs move together in reality?
• Are there multiplicative effects?
• Do threshold interactions exist?
• Does the importance of one input depend on another's value?

At minimum, test key suspected interactions.

Consider Non-Linearities

Linear sensitivity may not hold across full range:

• Does sensitivity change at different input levels?
• Are there threshold effects?
• Do diminishing returns apply?
• Is there a point of inflection?

Test sensitivity at multiple points, not just around baseline.

Connect to Action

Sensitivity analysis should drive decisions:

• Focus improvement efforts on sensitive factors
• Monitor high-sensitivity inputs more closely
• Hedge against negative outcomes from sensitive inputs
• Invest in reducing uncertainty where it matters most

Analysis without action is wasted.

Document Thoroughly

Record the analysis completely:

• Model specification
• Input ranges and their justification
• Methodology used
• Results obtained
• Conclusions drawn
• Actions recommended

Documentation enables review and replication.

Common Pitfalls

Ignoring Correlations

Real inputs often correlate:

• Economic factors tend to move together
• Costs and revenues may be linked
• Customer behaviors cluster

Treating inputs as independent can produce misleading results.

Over-Interpreting Precision

Sensitivity analysis provides relative insight:

• "Input A is twice as sensitive as Input B" is more reliable than
• "A 1% change in A produces exactly 2.3% change in output"

Communicate appropriate precision.

Analyzing the Wrong Model

Sensitivity of a flawed model is not useful:

• Validate the model before analyzing sensitivity
• Check that relationships are correctly specified
• Verify that important factors are included
• Ensure the model reflects reality

Sensitivity analysis cannot fix a bad model.

Single-Method Reliance

Different methods reveal different insights:

• OAT may miss interactions
• Global methods may obscure individual effects
• Tornado diagrams hide non-linearities
• Spider diagrams complicate with many inputs

Use multiple methods for comprehensive understanding.

Failure to Update

Sensitivity changes as conditions change:

• Input ranges shift over time
• Relationships evolve
• New factors become relevant
• Old sensitivities may no longer apply

Update sensitivity analysis regularly.

Advanced Techniques

Probabilistic Sensitivity Analysis

Combine sensitivity with probability:

• Assign probability distributions to inputs
• Run Monte Carlo simulation
• Identify which inputs contribute most to output variance
• Calculate probability of specific outcomes

Probabilistic methods link sensitivity to risk quantification.

Design of Experiments

Structured approaches to multi-factor sensitivity:

• Factorial designs
• Latin hypercube sampling
• Orthogonal arrays

These methods efficiently explore multi-dimensional input spaces.

Machine Learning for Sensitivity

Use ML to identify sensitivities:

• Train models on simulation results
• Use feature importance measures
• Apply SHAP values for individual predictions
• Leverage interpretable ML for global understanding

ML methods can handle complex, high-dimensional problems.

Sensitivity analysis transforms models from black boxes into transparent tools for decision-making. By revealing what matters most, sensitivity analysis focuses attention, communicates uncertainty, and enables confident action even when inputs remain uncertain.