Static Decision Tree

A single-page, colour-coded flowchart covering every supported statistical test

The flowchart below covers every test in this section. Click a test node to open its method page. Colours encode the scale level of the outcome; a dashed border indicates a non-parametric test. Use the zoom controls (or mouse-wheel + Ctrl) to enlarge the diagram, and drag to pan.

Nominal outcome
Ordinal outcome
Interval / ratio outcome
Interdependence (no outcome)
Parametric (solid border)
Non-parametric (dashed border) 

flowchart TD
    START["Research question"]:::root --> Q2{"Differences or<br/>associations?"}
    START --> Q_INT{"Exploratory<br/>structure?"}

    Q2 -->|Differences| QD1{"Kind of difference?"}
    Q2 -->|Associations| QA1{"Variable count?"}

    QD1 -->|Central tendency| QD2{"Outcome scale?"}
    QD1 -->|Variances| VAR["Variance tests<br/>(chi-sq, F, Levene)"]:::metric
    QD1 -->|Proportions| QDPROP{"Single variable vs. expected?"}

    QDPROP -->|Dichotomous| BIN["Binomial test"]:::nominal
    QDPROP -->|Categorical| CHI_GOF["Chi-sq goodness-of-fit"]:::nominal

    QD2 -->|Interval/ratio| QD3{"Number of groups?"}
    QD2 -->|Ordinal| QD6{"Groups &amp; pairing?"}
    QD2 -->|Nominal| QDPROP

    QD3 -->|2 groups| QD4{"Independent/paired?"}
    QD3 -->|3+ groups| QD5{"Factors &amp; design?"}

    QD4 -->|Indep. normal| TT["Independent t-test"]:::metric
    QD4 -->|Indep. non-normal| MWU["Mann-Whitney U"]:::metric_np
    QD4 -->|Paired normal| PT["Paired t-test"]:::metric
    QD4 -->|Paired non-normal| WSR["Wilcoxon signed-rank"]:::metric_np
    QD4 -->|Paired sign only| SGN["Sign test"]:::metric_np

    QD5 -->|1 between normal| OWA["One-way ANOVA"]:::metric
    QD5 -->|2+ between normal| FA["Factorial ANOVA"]:::metric
    QD5 -->|1 within normal| RM1["One-way rmANOVA"]:::metric
    QD5 -->|Mixed design| RMM["Factorial/mixed rmANOVA"]:::metric
    QD5 -->|Indep. non-normal| KW["Kruskal-Wallis"]:::metric_np
    QD5 -->|Paired non-normal| FR["Friedman"]:::metric_np

    QD6 -->|2 indep.| MWU
    QD6 -->|2 paired| WSR
    QD6 -->|&gt;2 indep.| KW
    QD6 -->|&gt;2 paired| FR

    QA1 -->|Two variables| QA2{"Scale levels?"}
    QA1 -->|More than two| QA5{"DV scale?"}

    QA2 -->|Both nominal| CHIC["Chi-sq contingency"]:::nominal
    QA2 -->|Both ordinal| SPE["Spearman"]:::ordinal_np
    QA2 -->|Ord + interval| SPE
    QA2 -->|Interval linear| PEA["Pearson"]:::metric
    QA2 -->|Interval directed| SLR["Simple linear regression"]:::metric
    QA2 -->|Interval non-norm| KEN["Kendall tau"]:::metric_np

    QA5 -->|Interval| MLR["Multiple linear regression"]:::metric
    QA5 -->|Dichotomous| LOG["Logistic regression"]:::nominal
    QA5 -->|Ordinal| ORL["Ordinal logistic regression"]:::ordinal
    QA5 -->|Nominal k+| MNL["Multinomial logistic regression"]:::nominal

    Q_INT -->|Reduce variables| FAC["Factor analysis"]:::interdep
    Q_INT -->|Group cases| QCL{"Scale/size?"}

    QCL -->|Mixed/small| HCL["Hierarchical clustering"]:::interdep
    QCL -->|Metric/large| KMC["K-means"]:::interdep
    QCL -->|Mixed/xlarge| TSC["Two-step clustering"]:::interdep

    click TT  "differences/central-tendency/independent-t-test.html"
    click MWU "differences/central-tendency/mann-whitney-u.html"
    click PT  "differences/central-tendency/paired-t-test.html"
    click WSR "differences/central-tendency/wilcoxon-signed-rank.html"
    click SGN "differences/central-tendency/sign-test.html"
    click OWA "differences/central-tendency/one-way-anova.html"
    click FA  "differences/central-tendency/factorial-anova.html"
    click RM1 "differences/central-tendency/rm-anova-one-way.html"
    click RMM "differences/central-tendency/rm-anova-factorial.html"
    click KW  "differences/central-tendency/kruskal-wallis.html"
    click FR  "differences/central-tendency/friedman.html"
    click VAR "differences/variances.html"
    click BIN "differences/proportions/binomial-test.html"
    click CHI_GOF "differences/proportions/chi-square-goodness-of-fit.html"
    click CHIC "associations/chi-square-contingency.html"
    click SPE "associations/spearman-correlation.html"
    click PEA "associations/pearson-correlation.html"
    click KEN "associations/kendall-tau.html"
    click SLR "associations/simple-linear-regression.html"
    click MLR "associations/multiple-regression.html"
    click LOG "associations/logistic-regression.html"
    click ORL "associations/ordinal-logistic-regression.html"
    click MNL "associations/multinomial-logistic-regression.html"
    click FAC "interdependence/factor-analysis.html"
    click HCL "interdependence/cluster-analysis.html"
    click KMC "interdependence/cluster-analysis.html"
    click TSC "interdependence/cluster-analysis.html"

    classDef metric fill:#2A9D8F,stroke:#1d6e65,color:#fff
    classDef metric_np fill:#2A9D8F,stroke:#1d6e65,color:#fff,stroke-dasharray:6 4
    classDef nominal fill:#F4A261,stroke:#b4743f,color:#000
    classDef ordinal fill:#E9C46A,stroke:#a88a42,color:#000
    classDef ordinal_np fill:#E9C46A,stroke:#a88a42,color:#000,stroke-dasharray:6 4
    classDef interdep fill:#6A4C93,stroke:#4a3468,color:#fff
    classDef root fill:#ffffff,stroke:#333,color:#000,font-weight:bold

Tabular alternative (screen-reader friendly)

Scenario Recommended test Notes
2 independent groups, metric outcome, normal, equal variances Independent t-test Welch variant is default in R
2 independent groups, metric outcome, normal, unequal variances Welch’s t-test Same page as independent t-test
2 independent groups, non-normal or ordinal Mann-Whitney U Rank-based
2 paired groups, metric outcome, normal differences Paired t-test Normality on differences
2 paired groups, non-normal or ordinal Wilcoxon signed-rank Rank-based
2 paired groups, direction only Sign test Assumption-light; lower power
3+ groups, 1 between factor, normal One-way ANOVA Welch variant if variances differ
3+ groups, 2+ between factors, normal Factorial ANOVA Type III SS recommended
3+ repeated measurements, normal One-way rmANOVA Sphericity via Mauchly; GG correction
Mixed between x within design, normal Factorial/mixed rmANOVA Interaction is often primary
3+ groups, non-normal or ordinal Kruskal-Wallis Dunn post-hoc with Bonferroni
3+ repeated measurements, non-normal or ordinal Friedman Pairwise Wilcoxon post-hoc
Single proportion vs. expected Binomial test Exact
Categorical variable vs. expected distribution Chi-squared goodness-of-fit Expected counts >= 5
Single variance vs. reference Chi-squared variance test Normality required
Two variances F-test Normality required
Three or more variances Levene’s test Median-based is robust
Two nominal variables Chi-squared contingency Fisher’s exact if sparse
Two ordinal or one ordinal plus one continuous Spearman correlation Rank-based
Two continuous, linear, bivariate normal Pearson correlation Linearity matters
Two continuous, tied or small n Kendall’s tau Use tau-b with ties
Two continuous, directed (IV -> DV) Simple linear regression OLS with diagnostics
Continuous DV, 2+ predictors Multiple linear regression VIF, residual plots
Dichotomous DV, 1+ predictors Logistic regression Odds ratios, McFadden R^2
Ordinal DV, 1+ predictors Ordinal logistic regression Proportional odds
Nominal DV (k+), 1+ predictors Multinomial logistic regression Relative-risk ratios
Reduce variables (find latent dimensions) Exploratory factor analysis Parallel analysis for k
Group cases, mixed types or small n Hierarchical cluster analysis Dendrogram, Ward linkage
Group cases, metric, large n K-means Elbow + silhouette
Group cases, mixed types, very large n Two-step cluster analysis Gower + PAM