Choosing a statistical method

Start with your question and study design. Explore suitable methods, understand their assumptions, and open a calculator when the design fits.

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Decision map

Expand a question to follow a branch. Select a method to read the recommendation. The map and guided questions use the same decision rules.

What do you want to find out?

Compare groups or a reference
What kind of outcome are you comparing?
- Numeric measurements, such as blood pressure
  How many groups or conditions?
  - One sample against a reference
    What is the quantity you want to compare?
    Mean against a reference
    Symmetric location against a reference
    Median / direction against a reference
  - Two groups or conditions
    How are the two samples related?
    Different independent subjects
    What comparison answers your question?
    Difference in means (Welch)
    Distribution / rank comparison
    Difference in means with exchangeable labels
    Matched pairs / the same subjects twice
    What feature of the paired differences matters?
    Mean change
    Symmetric location using signed ranks
    Direction only / sign test
    Additional repeated or clustered structure
    What is the repeated or clustered outcome?
    Continuous / Gaussian, random intercept adequate
    Binary, count, or other non-Gaussian outcome
    Gaussian hierarchical Bayesian analysis
    I’m unsure about the dependence structure
    I’m not sure
  - Three or more / factorial design
    Which design describes the observations?
    One factor, independent groups
    What comparison do you need across independent groups?
    Means, allowing unequal variances
    Means with a justified common variance
    Rank distributions
    Planned pairwise / control comparisons
    Which comparisons were planned?
    All pairs, common-variance means
    All pairs, unequal-variance means
    Independent-group rank comparisons (Holm)
    Several means against one control
    Same subjects in several conditions
    Which repeated-measurement question fits?
    One within-subject factor, mean comparison
    Rank comparison across conditions
    Repeated outcomes plus between-subject predictors
    Multiple factors / adjusted comparison
    What model structure do you need?
    Two between-subjects factors
    Three between-subjects factors
    One group factor plus one covariate
    Repeated outcomes plus predictors
    Other grouped continuous observations
    Several continuous outcomes jointly
    I’m not sure
- Ordered ratings, such as mild / moderate / severe
  How are the ordered outcomes grouped?
  - Two independent groups
  - Two paired conditions, meaningful symmetric differences
  - Three or more independent groups
  - Three or more repeated conditions
  - Adjust for predictors
  - Unsure about pairing or rating differences
- Two categories, such as event / no event
  How were the binary observations collected?
  - One independent sample vs expected proportion
    What expected distribution are you comparing against?
    Binary proportion, exact test
    Binary proportion, large-sample approximation
    Several category counts vs expected counts
  - Independent groups
    What form of comparison do you need?
    Contingency table with adequate expected counts
    Sparse 2×2 count table
    Sparse table larger than 2×2
    Two proportions with adequate expected counts
  - Same subjects twice / matched pairs
  - Same subjects in three or more conditions
  - Adjust for predictors
  - Clustered observations / repeated predictors
- Several unordered categories
  What categorical question are you asking?
  - One variable vs an expected distribution
    What expected distribution are you comparing against?
    Binary proportion, exact test
    Binary proportion, large-sample approximation
    Several category counts vs expected counts
  - Association in independent groups
    What form of comparison do you need?
    Contingency table with adequate expected counts
    Sparse 2×2 count table
    Sparse table larger than 2×2
    Two proportions with adequate expected counts
  - Paired categories with more than two levels
  - Adjust for predictors
- Time until an event, with possible censoring
  Which time-to-event question?
  - Estimate survival curves
  - Unadjusted comparison of survival groups
  - Cox regression with covariates
  - Parametric survival / extrapolation
  - Competing risks
- Variability rather than location
  Which variability question?
  - One normal population variance vs reference
  - Two independent normal population variances
  - Compare groups with median-centered Levene
- I’m not sure
Examine a relationship
What variables are related?
- Two numeric variables
  Which association do you want to quantify?
  - Linear association
  - Monotonic rank association
  - Rank concordance with tied ranks
  - One predictor and a numeric outcome
- Ordered variables / monotonic relationship
- Two categorical variables
  What form of comparison do you need?
  - Contingency table with adequate expected counts
  - Sparse 2×2 count table
  - Sparse table larger than 2×2
  - Two proportions with adequate expected counts
- Predict an outcome or adjust for covariates
  What outcome do you want to model?
  - Continuous numeric outcome
    How many predictors and what dependence structure?
    One predictor, independent observations
    Several predictors, independent observations
    Repeated / clustered observations
  - Binary outcome
  - Ordered categories
  - Unordered categories (3+)
  - Event count or rate
    What count model is justified?
    Poisson mean–variance relationship
    Overdispersion consistent with an NB2 model
    Repeated / clustered counts
  - Time to event with censoring
  - Repeated / clustered outcome
    What is the repeated or clustered outcome?
    Continuous / Gaussian, random intercept adequate
    Binary, count, or other non-Gaussian outcome
    Gaussian hierarchical Bayesian analysis
    I’m unsure about the dependence structure
Model or predict an outcome
What outcome do you want to model?
- Continuous numeric outcome
  How many predictors and what dependence structure?
  - One predictor, independent observations
  - Several predictors, independent observations
  - Repeated / clustered observations
- Binary outcome
- Ordered categories
- Unordered categories (3+)
- Event count or rate
  What count model is justified?
  - Poisson mean–variance relationship
  - Overdispersion consistent with an NB2 model
  - Repeated / clustered counts
- Time to event with censoring
- Repeated / clustered outcome
  What is the repeated or clustered outcome?
  - Continuous / Gaussian, random intercept adequate
  - Binary, count, or other non-Gaussian outcome
  - Gaussian hierarchical Bayesian analysis
  - I’m unsure about the dependence structure
Describe data or estimate a quantity
What do you want to describe or estimate?
- Numeric summaries
- One mean and confidence interval
- Difference between independent means
- One proportion and confidence interval
- Difference between independent proportions
- Categorical rater agreement
- Questionnaire internal consistency
Explore structure or classify observations
What structure are you exploring?
- Reduce numeric variables
  What should the reduced representation mean?
  - Components summarizing observed variation
  - Explore latent factors
  - Evaluate a prespecified factor model
- Discover groups of observations
  Which data and grouping approach?
  - Numeric data, partition into k groups
  - Numeric data, nested Ward hierarchy
  - Mixed numeric / categorical data or two-step
- Classify known group labels
- Relate two sets of numeric variables
Plan a study or use a specialist method
Which specialist task?
- Sample size and study design
  What design are you planning?
  - Common mean, proportion, ANOVA or regression design
  - Noninferiority / equivalence
  - Cluster randomized trial
  - Survival trial
  - Group sequential / futility
  - Adaptive sample-size re-estimation
  - Bayesian trial simulation
- Survival analysis
  Which time-to-event question?
  - Estimate survival curves
  - Unadjusted comparison of survival groups
  - Cox regression with covariates
  - Parametric survival / extrapolation
  - Competing risks
- Combine study evidence
  What evidence synthesis?
  - Pool study effects
  - Explore study-level moderators
- Observational causal analysis
  Which observational strategy matches your identification assumptions?
  - Propensity matching
  - Propensity weighting
  - Augmented inverse probability weighting
  - Difference-in-differences
- Health economics / patient simulation
  What decision or simulation task?
  - Decision tree rollback
  - Cohort Markov / cost effectiveness
  - Patient microsimulation
  - Probabilistic sensitivity analysis
  - One-way sensitivity analysis
  - Budget impact
  - Patient flow / resources
- Experimental design / process statistics
  Which experiment or process task?
  - Factorial experimental design
  - Response surface
  - Process capability
  - Control charts
- Pharmacology / bioequivalence
  Which pharmacology task?
  - Noncompartmental analysis
  - Compartmental PK
  - Exposure–response
  - Crossover bioequivalence
- Bayesian modeling
  Which Bayesian model?
  - Bayesian regression
  - Gaussian hierarchical model