columna API reference - v0.3.0
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    Benchmarks: columna/advanced vs pandas / polars / scipy / numpy

    Generated 2026-09-15 · Node v24.19.0 · scale 1 · median of 5 runs after a warm-up (heavy cases fewer). Python: numpy 1.26.4, scipy 1.14.0, pandas 2.2.2, polars 1.44.1.

    How to read: every row is one columna/advanced function on synthetic data of the stated size. The Python column times the closest equivalent on data of the same size and distribution — not the same numbers (numerical agreement: advanced-convergence.md). Where Python has no equivalent (statsmodels / sklearn / lifelines are not installed, or the tool is Minitab-only) the cell is "—". Comparisons are throughput only: columna often computes more per call (full Minitab table: SE, CI, diagnostics, unusual observations), and the scipy.optimize rows use a generic BFGS on the same likelihood rather than a purpose-built estimator.

    Regenerate: pnpm run bench:advanced (TS → Python → this file). Quick pass: BENCH_SCALE=0.1 pnpm run bench:advanced.

    Function (size) columna Python equivalent Python columna vs Python
    normal.cdf × 1000000 108.9 ms scipy 42.5 ms 2.6× slower
    normal.ppf × 1000000 288.2 ms scipy 50.2 ms 5.7× slower
    t(10).cdf × 100000 23.0 ms scipy 20.7 ms 1.1× slower
    t(10).ppf × 100000 653.9 ms scipy 186.9 ms 3.5× slower
    chi2(5).sf × 100000 12.4 ms scipy 15.9 ms 1.3× faster
    f(3,20).ppf × 100000 770.6 ms scipy 133.0 ms 5.8× slower
    gamma(2.5,3).cdf × 100000 15.1 ms scipy 15.1 ms 1.0× faster
    beta(2,5).ppf × 10000 106.6 ms scipy 20.8 ms 5.1× slower
    weibull(1.8,50).ppf × 1000000 39.4 ms scipy 67.2 ms 1.7× faster
    binomial(50,0.3).cdf × 100000 46.4 ms scipy 8.90 ms 5.2× slower
    poisson(4).pmf × 100000 2.91 ms scipy 7.68 ms 2.6× faster
    nctCdf × 10000 6.76 ms scipy 9.63 ms 1.4× faster
    ptukey × 1000 1.07 s scipy 7.77 s 7.2× faster
    qtukey × 200 1.86 s scipy 22.17 s 12× faster
    Function (size) columna Python equivalent Python columna vs Python
    ttest1 n=100000 0.52 ms scipy 1.01 ms 1.9× faster
    ttest2 (Welch) n=100000+100000 1.47 ms scipy 0.96 ms 1.5× slower
    ttestPaired n=100000 1.31 ms scipy 1.32 ms 1.0× faster
    ztest1 n=100000 0.41 ms numpy 0.049 ms 8.5× slower
    propTest1 (exact) 350/1000 0.19 ms scipy 0.38 ms 2.0× faster
    propTest2 Fisher 120/400 vs 90/380 0.085 ms scipy 0.56 ms 6.6× faster
    poissonRateTest1 (exact) 120 events 0.072 ms scipy 0.11 ms 1.5× faster
    varTest1 (χ²) n=100000 0.39 ms scipy 0.20 ms 2.0× slower
    varTest1 (Bonett) n=100000 9.29 ms — — —
    corrTest Pearson n=100000 2.90 ms scipy 2.13 ms 1.4× slower
    corrTest Spearman n=100000 61.8 ms scipy 20.4 ms 3.0× slower
    grubbs n=100000 0.83 ms numpy 0.32 ms 2.6× slower
    dixon n=25 (cached null distribution) 0.050 ms — — —
    Function (size) columna Python equivalent Python columna vs Python
    anova 5 × 20000 0.50 ms scipy 0.59 ms 1.2× faster
    levene 5 × 20000 15.2 ms scipy 1.49 ms 10× slower
    bartlett 5 × 20000 0.65 ms scipy 0.43 ms 1.5× slower
    bonett 5 × 20000 8.12 ms — — —
    tukeyHSD 6 × 5000 0.34 ms scipy 333.6 ms 987× faster
    fisherLSD 6 × 5000 0.21 ms — — —
    dunnett 6 × 5000 6.86 ms scipy 22.7 ms 3.3× faster
    hsuMCB 6 × 5000 3.63 ms — — —
    gamesHowell 6 × 5000 48.7 ms — — —
    equalVariances (Levene) 6 × 5000 3.48 ms scipy 0.60 ms 5.8× slower
    Function (size) columna Python equivalent Python columna vs Python
    chi2test 20×20 table 0.039 ms scipy 0.088 ms 2.3× faster
    chi2gof 50 categories 0.004 ms scipy 0.025 ms 5.7× faster
    crosstab n=1000000 60.4 ms pandas 291.9 ms 4.8× faster
    polars 8.60 ms 7.0× slower
    Function (size) columna Python equivalent Python columna vs Python
    andersonDarling n=100000 32.9 ms scipy 20.3 ms 1.6× slower
    shapiroWilk n=5000 1.90 ms scipy 0.22 ms 8.5× slower
    ryanJoiner n=100000 34.0 ms — — —
    kolmogorovSmirnov (Lilliefors) n=100000 18.5 ms scipy 8.72 ms 2.1× slower
    individualDistributionID n=10000 104.2 ms scipy 107.2 ms 1.0× faster
    Function (size) columna Python equivalent Python columna vs Python
    mannWhitney (asymptotic) 20000+20000 42.5 ms scipy 2.58 ms 16× slower
    mannWhitney (exact) 40+40 3.17 ms scipy 0.24 ms 13× slower
    kruskal 5 × 20000 36.6 ms scipy 14.2 ms 2.6× slower
    signTest n=100000 18.7 ms scipy 0.68 ms 28× slower
    wilcoxonSigned (asymptotic) n=20000 18.4 ms scipy 1.41 ms 13× slower
    wilcoxonSigned (exact) n=50 0.43 ms scipy 0.43 ms 1.0× faster
    moodMedian 5 × 20000 18.1 ms scipy 1.25 ms 15× slower
    friedman 5000 blocks × 5 6.91 ms scipy 152.2 ms 22× faster
    runsTest n=1000000 9.76 ms numpy 1.21 ms 8.1× slower
    Function (size) columna Python equivalent Python columna vs Python
    tost1 n=100000 0.40 ms numpy 0.16 ms 2.5× slower
    tost2 n=100000+100000 1.41 ms numpy 0.34 ms 4.1× slower
    power 2-sample t (solve n) × 50 18.3 ms — — —
    power one-way ANOVA (solve effect) × 20 16.8 ms — — —
    Function (size) columna Python equivalent Python columna vs Python
    descriptiveStats n=1000000 108.8 ms pandas 415.2 ms 3.8× faster
    polars 12.8 ms 8.5× slower
    descriptiveStats by 10 groups n=1000000 139.3 ms pandas 97.9 ms 1.4× slower
    polars 20.2 ms 6.9× slower
    graphicalSummary n=100000 73.2 ms — — —
    poissonGof n=1000000 24.9 ms numpy 21.8 ms 1.1× slower
    boxplotStats n=1000000 115.6 ms numpy 18.4 ms 6.3× slower
    mainEffectsPlot 3 factors n=1000000 156.2 ms pandas 160.6 ms 1.0× faster
    polars 49.7 ms 3.1× slower
    interactionPlot 4×5 n=1000000 186.8 ms pandas 356.8 ms 1.9× faster
    polars 19.6 ms 9.5× slower
    intervalPlot 10 groups n=1000000 45.3 ms pandas 65.9 ms 1.5× faster
    polars 24.6 ms 1.8× slower
    ecdf n=1000000 171.6 ms numpy 59.6 ms 2.9× slower
    dotplot n=1000000 69.9 ms numpy 42.3 ms 1.7× slower
    causeAndEffect 6 categories × 5 causes 0.041 ms — — —
    Function (size) columna Python equivalent Python columna vs Python
    ols n=100000, p=10 (full diagnostics) 136.1 ms numpy 43.9 ms 3.1× slower
    fittedLine (quadratic) n=100000 40.3 ms numpy 8.94 ms 4.5× slower
    stepwise n=10000, p=8 61.3 ms — — —
    bestSubsets n=10000, p=8 (255 fits) 455.2 ms — — —
    logit n=100000, p=5 393.4 ms scipy.optimize 119.3 ms 3.3× slower
    poissonRegression n=100000, p=5 439.2 ms scipy.optimize 117.7 ms 3.7× slower
    ologit n=10000, p=3, 4 levels 80.1 ms — — —
    mlogit n=10000, p=3, 3 classes 57.6 ms — — —
    linearModel 'y ~ a*b + x' n=100000 242.8 ms numpy 131.8 ms 1.8× slower
    nls (2 params, LM) n=10000 86.5 ms scipy 5.14 ms 17× slower
    orthogonalRegression (jackknife SE) n=5000 1.35 ms scipy 5.50 ms 4.1× faster
    pls n=2000, p=10, 3 comp (LOO CV) 936.3 ms — — —
    stabilityStudy 5 batches × 8 times 13.6 ms — — —
    Function (size) columna Python equivalent Python columna vs Python
    controlChart I-MR (Nelson 1–8) n=1000000 623.7 ms numpy 17.9 ms 35× slower
    controlChart X̄-R subgroups of 5 n=1000000 168.6 ms numpy 12.2 ms 14× slower
    controlChart P n=100000 32.6 ms numpy 0.13 ms 252× slower
    ewma n=1000000 116.5 ms pandas 15.3 ms 7.6× slower
    polars 8.25 ms 14× slower
    cusum n=1000000 106.8 ms numpy 19.6 ms 5.4× slower
    movingAverage span 5 n=1000000 103.9 ms pandas 33.0 ms 3.1× slower
    polars 5.52 ms 19× slower
    gChart n=100000 10.2 ms scipy 0.11 ms 95× slower
    tChart (Weibull) n=100000 32.5 ms scipy 253.9 ms 7.8× faster
    t2Chart p=5 n=100000 74.1 ms numpy 14.4 ms 5.1× slower
    mewma p=3 n=100000 (h given) 16.3 ms numpy 319.2 ms 20× faster
    mewma h calibration (ARL₀ 200, p=3) 441.3 ms — — —
    generalizedVarianceChart p=3, 10000 subgroups × 5 20.1 ms numpy 153.9 ms 7.7× faster
    Function (size) columna Python equivalent Python columna vs Python
    capability n=1000000 126.7 ms numpy 14.6 ms 8.7× slower
    capabilitySixpack n=100000 87.6 ms — — —
    boxCoxLambda n=100000 551.5 ms scipy 497.0 ms 1.1× slower
    johnsonFit n=100000 42.2 ms — — —
    weibullFit n=100000 15.0 ms scipy 290.1 ms 19× faster
    toleranceInterval n=100000 33.5 ms — — —
    Function (size) columna Python equivalent Python columna vs Python
    gageRR crossed 10 parts × 3 operators × 3 0.11 ms — — —
    gageLinearity 5 refs × 12 0.010 ms — — —
    gageType1 n=50 0.009 ms — — —
    attributeAgreement Fleiss κ 3 raters × 500 0.15 ms — — —
    acceptanceSampling n=125,c=3 OC curve 0.011 ms scipy 0.054 ms 4.9× faster
    Function (size) columna Python equivalent Python columna vs Python
    pareto n=1000000, 30 categories 17.1 ms pandas 100.2 ms 5.8× faster
    polars 14.4 ms 1.2× slower
    runChart n=100000 49.3 ms — — —
    multiVari 3 factors n=100000 40.4 ms pandas 30.1 ms 1.3× slower
    symmetryTest n=100000 5.61 ms — — —
    Function (size) columna Python equivalent Python columna vs Python
    trendAnalysis quadratic n=100000 22.7 ms numpy 7.60 ms 3.0× slower
    decompose (12) n=100000 13.1 ms — — —
    stl (12) n=10000 3.73 s — — —
    ets winters-add n=10000 48.8 ms — — —
    acf 40 lags n=100000 13.3 ms numpy 0.48 ms 27× slower
    pacf 40 lags n=100000 7.86 ms — — —
    ccf ±20 lags n=100000 17.4 ms numpy 18.5 ms 1.1× faster
    ljungBox 20 lags n=100000 8.88 ms — — —
    arima (1,1,1) CSS-ML n=2000 5.38 ms — — —
    arima (1,1,1)(1,1,1)₁₂ n=600 5.64 ms — — —
    autoArima n=500 82.2 ms — — —
    periodogram n=20000 12.8 ms scipy 0.44 ms 29× slower
    cumulativePeriodogram n=20000 15.8 ms — — —
    Function (size) columna Python equivalent Python columna vs Python
    fullFactorial 12 factors (4096 runs) 0.39 ms — — —
    fractionalFactorial 2^(8-3) 0.050 ms — — —
    aliasStructure 2^(10-4), order ≤ 3 0.80 ms — — —
    plackettBurman 23 factors 0.11 ms — — —
    ccd 6 factors 0.072 ms — — —
    boxBehnken 7 factors 0.036 ms — — —
    taguchi L243 0.37 ms — — —
    definitiveScreening 10 factors 0.013 ms — — —
    mixtureDesign 4 components lattice degree 3 0.18 ms — — —
    analyzeEffects 2^7 with interactions 0.087 ms — — —
    analyzeDoe 2^6 × 2 replicates (linearModel) 5.09 ms — — —
    analyzeTaguchi L27 × 3 replicates 0.042 ms — — —
    analyzeMixture 3 components quadratic 0.020 ms — — —
    responseOptimizer 2 responses, 3 factors 0.29 ms — — —
    nestedAnova 3 levels n=10000 3.27 ms — — —
    Function (size) columna Python equivalent Python columna vs Python
    reliabilityFit Weibull censored n=10000 58.6 ms scipy 6.55 ms 9.0× slower
    kaplanMeier n=100000 89.6 ms numpy 9.35 ms 9.6× slower
    logRank 3 groups n=100000 76.0 ms — — —
    coxPH n=10000, p=3 38.7 ms — — —
    fineGray n=3000, p=2 881.4 ms — — —
    lifeRegression Weibull n=10000, p=2 49.4 ms scipy.optimize 47.8 ms 1.0× slower
    altRegression Arrhenius n=10000 30.6 ms — — —
    powerLawNHPP n=10000 failures 1.33 ms numpy 0.040 ms 34× slower
    probitAnalysis 8 doses × 100 0.15 ms scipy.optimize 2.52 ms 16× faster
    demonstrationTestPlan × 100 0.068 ms — — —
    estimationTestPlan × 20 2.30 ms — — —
    probabilityPlot n=10000 3.66 ms — — —
    Function (size) columna Python equivalent Python columna vs Python
    pca n=100000, p=10 44.5 ms numpy 9.17 ms 4.9× slower
    factorAnalysis ML + varimax n=10000, p=8, 2 factors 12.9 ms — — —
    promax 20 × 3 loadings 0.024 ms — — —
    kmeans k=4 n=100000, p=5 494.2 ms — — —
    hclust average n=1500, p=5 37.3 ms scipy 35.1 ms 1.1× slower
    clusterVariables 30 variables n=10000 14.7 ms scipy 3.00 ms 4.9× slower
    discriminant LDA 3 classes n=10000, p=5 7.25 ms — — —
    correspondence 30×30 table 0.98 ms numpy 0.089 ms 11× slower
    multipleCorrespondence 4 variables n=5000 26.8 ms numpy 2.01 ms 13× slower
    itemAnalysis 20 items n=10000 40.1 ms numpy 6.05 ms 6.6× slower
    manova one-way 5 groups n=10000, p=4 3.63 ms — — —
    manovaModel 'a*b' n=10000, p=3 80.9 ms numpy 4.98 ms 16× slower
    mixedModel RI 100 groups n=10000 56.3 ms — — —
    glmm binomial PQL 50 groups n=5000 37.6 ms — — —
    Function (size) columna Python equivalent Python columna vs Python
    cart regression n=10000, p=5 293.2 ms — — —
    randomForest 30 trees n=3000, p=5 1.00 s — — —
    treeNet 50 trees n=3000, p=5 2.24 s — — —
    mars n=3000, p=5 1.21 s — — —
    crossValidate ols 5-fold n=10000 324.2 ms — — —
    autoModel (ols, cart, rf 20) 3-fold n=2000 2.45 s — — —
    Function (size) columna Python equivalent Python columna vs Python
    random.normal × 1000000 39.5 ms numpy 9.00 ms 4.4× slower
    random.gamma × 1000000 68.6 ms numpy 13.6 ms 5.1× slower
    random.poisson × 1000000 51.3 ms numpy 23.3 ms 2.2× slower
    • 172 functions timed; 110 comparisons against Python libraries: columna faster or equal in 34, slower in 76.
    • Largest gaps vs the fastest Python library: controlChart.p (251.9× slower), gChart (94.5× slower), controlChart.imr (34.8× slower), powerLawNHPP (33.7× slower), periodogram (29.3× slower), signTest (27.5× slower), acf (27.5× slower), movingAverage (18.8× slower).
    • Largest wins: tukeyHSD (986.5× faster), friedman (22.0× faster), mewma (19.6× faster), weibullFit (19.3× faster), probitAnalysis (16.3× faster), dist.qtukey (11.9× faster), tChart (7.8× faster), generalizedVarianceChart (7.7× faster).

    Notes: all timings are single-threaded JavaScript (V8 JIT, no WebAssembly / GPU) versus compiled C / Fortran / Rust kernels on the Python side.

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    Benchmarks: vs pandas / polars / scipy / numpy