statzel — Statistical methods

Every test in the app, with a short description. Click any entry for the detail page.

Describe

Simulation

Monte Carlo simulation propagates uncertainty through a formula by drawing each input from its own distribution thousands of times and repo…

Distribution calculators

The normal distribution calculator returns tail probabilities and critical values for a Normal(μ, σ) variable — the z-table, computed exact…
The t distribution calculator returns tail probabilities and critical values for Student's t on a given number of degrees of freedom — the …
The chi-square distribution calculator returns tail probabilities and critical values for χ² on a given number of degrees of freedom.
The F distribution calculator returns tail probabilities and critical values for F on a pair of numerator and denominator degrees of freedo…
The binomial distribution calculator returns exact probabilities and quantiles for the number of successes in n independent trials with suc…
The Poisson distribution calculator returns exact probabilities and quantiles for a count with mean λ.
The exponential distribution calculator returns tail probabilities and quantiles for a waiting time with rate λ, whose mean is 1/λ.
The uniform distribution calculator returns probabilities and quantiles for a value equally likely anywhere between a minimum and a maximum.
The log-normal distribution calculator returns probabilities and quantiles for a positive variable whose logarithm is normal.
The Weibull distribution calculator returns probabilities and quantiles for a lifetime with a given shape and scale.

Summaries

Descriptive statistics summarise every selected column at once: n, missing, mean, SD, SE, 95% CI of the mean, median, IQR, min/Q1/Q3/max, s…
Distribution fitting estimates a chosen family by maximum likelihood — normal, log-normal, gamma, Weibull, exponential or Poisson — with AI…
Circular statistics summarise directional data with the mean direction, resultant length and circular SD, plus the Rayleigh test of uniform…

Standalone plots

A histogram shows the distribution of a single numeric column, binned by the Freedman-Diaconis rule (2·IQR / n^{1/3}) unless you set the bi…
A box-and-whisker plot summarises one or many numeric columns, with whiskers reaching 1.5·IQR and anything beyond drawn as an outlier; addi…
A violin plot renders a per-group kernel density symmetrically about each category, with an optional median-IQR box overlay.
A raincloud plot combines a half-violin density, a box plot and every jittered raw observation per group, showing distribution shape, summa…
An estimation plot (Cumming / Gardner-Altman) shows jittered raw data for two groups beside the mean difference and its 95% bootstrap CI — …
An interactive dot diagram lets you drag a cutoff across the data while sensitivity, specificity, PPV, NPV, accuracy and Youden's J update …
A Q-Q plot draws empirical quantiles against standard-normal quantiles with a mean ± SD reference line, so points hugging the line indicate…
A P-P plot draws the empirical CDF against the theoretical Normal(μ̂, σ̂) CDF, so points on the y = x line indicate a normal fit.
Ordered bar chart of category counts (descending) with cumulative-percentage line on the right y-axis and an 80% reference. Standard 80/20 …
A scatter plot draws two numeric columns against each other, with optional grouping by category and an optional LOESS smoother.
A bubble plot adds a third dimension to a scatter by sizing each point from a numeric column, with bubble area rescaled linearly to a 6–32 …
A strip (jitter) plot draws one dot per observation along a single numeric axis, with slight vertical jitter so overlapping values stay vis…
A Shewhart control chart plots measurements against run order with a centre line at the mean and warning (±2σ) and action (±3σ) limits.
A Youden plot draws each subject's or lab's two paired measurements against each other with median crosshairs, so the quadrant pattern sepa…
A polar plot draws points on angle and radius axes, for circular data such as compass bearings, hour of day or season of year.
A waterfall chart starts each bar at the running total, taking the palette colour when positive and staying red when negative so changes st…
Plot y = f(x) for a user-typed mathematical expression over a range. Whitelist exposes Math.* (sin, cos, exp, log, sqrt, pow, abs, …) and c…
A contour plot interpolates scattered (X, Y, Z) points onto a regular grid by Gaussian-kernel smoothing and draws iso-value lines — the 2-D…
A radar (spider) chart turns several numeric columns into the spokes of a circle and draws each row as a polygon through its value on every…
A ternary plot normalises three numeric components to a composition summing to one and places each row inside an equilateral triangle, each…

Signal & numerical

Data smoothing overlays a de-noised curve on a raw series using Savitzky-Golay, a moving average or LOWESS, and reports the residual RMSE.
Peak detection locates local maxima and reports each peak's position, height, prominence, and approximate width.
Multi-peak deconvolution fits a sum of overlapping lineshapes — Gaussian, Lorentzian or pseudo-Voigt — plus an optional baseline, reporting…
Interpolation resamples an (X, Y) curve on a uniform grid using a natural cubic spline or linear segments.
Numerical calculus integrates and differentiates a sampled (X, Y) curve, giving the trapezoidal cumulative integral and the central-differe…

Reference intervals

A parametric reference interval covers the central fraction of a Gaussian distribution as mean ± z·SD, defaulting to 95% — the 2.5th to the…
A non-parametric reference interval takes percentiles directly from the data by the CLSI EP28-A3 method, with 90% bootstrap CIs on each lim…
Checks whether a small validation sample is consistent with a published or transferred reference interval, via an exact binomial test on th…

Normality

Shapiro–Wilk tests whether a sample comes from a normally distributed population — the default normality screen for samples up to a few tho…
The Lilliefors-corrected Kolmogorov–Smirnov test checks normality by comparing the empirical CDF against the normal CDF, with the mean and …
Anderson–Darling tests normality with more weight on the tails than Kolmogorov–Smirnov, making it better at catching heavy tails and outlie…
The Lilliefors test checks normality with the same statistic as Kolmogorov–Smirnov but the correct null distribution for when μ and σ are e…
D'Agostino–Pearson K² test combines sample skewness and kurtosis into a single omnibus normality test.
The Shapiro–Francia test checks normality from the squared correlation between the sorted data and the expected normal order statistics — a…

Outliers

Dixon's Q test flags a single extreme value in a very small sample (3 ≤ n ≤ 30) by comparing its gap from the nearest neighbour against the…
Tukey's fence rule flags observations outside Q1 − k·IQR or Q3 + k·IQR — robust, distribution-free, and the rule behind the standard box pl…
Grubbs' test tests whether the single most extreme value in a sample is a statistical outlier under a Normal model.
The ROUT method (Motulsky & Brown 2006) identifies outliers from residuals around the median with a Benjamini-Hochberg FDR step-up at a cho…

Compare

Parametric

Tests whether the mean of one sample differs from a specified null value μ₀.
The two-sample t-test asks whether two independent groups have equal means — Welch's version (unequal variances) by default, with classical…
Tests whether the mean of the within-pair differences is zero. The right test for before/after or two-methods-on-same-subjects designs.
The nested t-test compares two groups when each subject contributes sub-replicates, fitting a random-intercept model with group fixed and s…
One-way analysis of variance extends the two-sample t-test to k ≥ 2 independent groups by partitioning total variance into between-group an…
Nested ANOVA extends the nested t-test to k ≥ 2 groups, fitting the mixed model y ~ group + (1 | subject).
Two-way ANOVA tests the main effects of two factors and, optionally, the interaction between them.
Three-way ANOVA tests the main effects of three factors together with any subset of their two-way and three-way interactions.
ANCOVA tests group differences after adjusting for one or more numeric covariates. Combines ANOVA's group test with linear regression's con…
MANOVA tests whether the joint vector of group means differs across two or more numeric dependent variables at once.
Repeated-measures ANOVA compares within-subject conditions in a one-way or mixed design, where each subject contributes one observation per…

Non-parametric

The Mann-Whitney U (Wilcoxon rank-sum) test compares two independent groups using ranks rather than means — the non-parametric counterpart …
The Wilcoxon signed-rank test compares paired measurements by ranking their absolute differences — the non-parametric counterpart to the pa…
The one-sample Wilcoxon signed-rank test compares a sample against a hypothesised median — the non-parametric alternative to a one-sample t…
The Kruskal-Wallis H test compares k ≥ 2 independent groups on ranks — the non-parametric counterpart to one-way ANOVA.
The Friedman test compares k ≥ 2 within-subject conditions by ranking within each subject — the non-parametric counterpart to repeated-meas…

Robust / variance

The F-test compares two variances for equality; it is sensitive to non-normality, so prefer Levene's test when the data have heavy tails.
Yuen's t-test compares trimmed means using Winsorised variances, staying robust to outliers and skew, in both independent and paired forms.

Equivalence

Two One-Sided Tests (TOST) declare two means equivalent when their difference falls entirely within ±Δ, so a significant result means the d…
TOST for proportions declares two proportions equivalent when their difference falls within ±δ — the proportions analogue of the TOST equiv…
A non-inferiority test rejects the hypothesis that the new arm is worse than the reference by ≥ δ, concluding instead that it is no worse b…

Categorical

Contingency / proportions

Pearson's chi-square test of independence asks whether two categorical variables are related, comparing observed cell counts against the co…
Fisher's exact test checks independence in a 2 × 2 (or larger) contingency table using the exact hypergeometric p-value, so no large-sample…
The exact binomial test compares an observed proportion against a hypothesised value π₀.
McNemar's test tests symmetry in a 2 × 2 table of paired binary observations. The paired counterpart to chi-square / Fisher.
Cochran-Armitage trend test on an ordered binomial tests whether the success proportion increases (or decreases) monotonically across order…
Cochran's Q tests whether the success rate stays constant across k ≥ 3 repeated binary measurements on the same subjects — McNemar's test e…
The Cochran–Mantel–Haenszel test pools the within-stratum odds ratios of a 2 × 2 × k table into a single common OR while controlling for th…
The 2 × 2 calculator turns the four cell counts of an exposure × outcome table into every standard effect measure — RD, RR, OR and NNT with…
The multinomial (chi-square) goodness-of-fit test asks whether one categorical column's counts match expected proportions, equal by default.
Log-linear regression fits a Poisson model to the contingency table of two or three categorical variables, with likelihood-ratio tests for …
The Bayesian contingency test quantifies evidence for association between two categorical variables as a Bayes factor (BF₁₀), using an inde…

Logistic regression

Binary logistic regression models log-odds of a 0/1 outcome as a linear function of predictors. Effects are reported as odds ratios.
Multinomial logistic regression predicts an unordered multi-category outcome, fitting one log-odds equation per non-reference category.
The proportional-odds (cumulative-link) model predicts an ordered categorical outcome, fitting one slope per predictor and k − 1 cumulative…
Conditional logistic regression estimates predictor effects within matched sets in a matched case-control study, eliminating confounding be…
Generalized linear model with log link and Poisson family for non-negative integer outcomes (counts).
Negative binomial regression models overdispersed counts, fitting the log-mean and the dispersion parameter θ jointly.
A generalized linear model lets you choose the family and link yourself — Gaussian, binomial, Poisson, Gamma, inverse Gaussian, quasi-binom…
Generalized estimating equations fit population-averaged regressions for clustered or longitudinal binary, count or continuous outcomes.
Multiple imputation by chained equations (MICE) fills missing values repeatedly, analyses each completed dataset, and pools the results by …
Two-stage least squares (instrumental variables) corrects for endogeneity — the standard remedy when a regressor is correlated with the err…
Panel regression fits pooled OLS, fixed effects (within) or random effects to longitudinal data, with a Hausman test to choose between FE a…
Dynamic panel GMM (Arellano-Bond / Blundell-Bond) estimates a model with a lagged dependent variable and entity effects using instrumental-…
Tobit regression estimates a linear model by maximum likelihood when the outcome is censored at a lower and/or upper limit.
Partial least squares regression reduces predictors to a small set of latent components that best predict Y. Useful when predictors outnumb…

Classification (supervised)

Fisher's linear discriminant analysis classifies by finding the min(k − 1, p) linear combinations of predictors that separate the groups mo…
A CART decision tree splits the data recursively on one predictor at a time, detecting automatically whether the outcome calls for regressi…
k-nearest neighbours classifies each observation by majority vote of its k closest standardized neighbours, validated leave-one-out.
A random forest classifies or predicts by averaging an ensemble of decorrelated decision trees, reporting out-of-bag error and variable imp…
A support vector machine separates classes with a maximum-margin boundary, using kernels for nonlinear separation, reported with 10-fold cr…
Gaussian naive Bayes classifies by Bayes' rule while assuming predictors are independent within each class — fast, surprisingly robust, and…
Gradient boosting fits an ensemble of shallow trees sequentially to the residuals, choosing the stopping iteration by 5-fold cross-validati…
A single-hidden-layer neural network with weight decay learns classification or regression, reported with 5-fold cross-validated performanc…
Regularized regression fits lasso, ridge or elastic net with a cross-validated λ, detecting a Gaussian, binomial or multinomial family auto…
Propensity-score matching estimates the average treatment effect on the treated by pairing treated and control units on their logistic prop…

Relate

Correlation

Pearson's product-moment correlation measures the strength of linear association between two continuous variables, running from −1 (perfect…
Spearman's ρ measures rank correlation between two variables, capturing any monotonic association rather than only a linear one — the stand…
Kendall's τ measures rank correlation by counting concordant and discordant pairs — more robust than Spearman when ties are common or n is …
Partial correlation measures the Pearson or Spearman association between X and Y after linearly removing one or more control variables Z — …

Linear regression

Linear regression estimates the conditional mean of a continuous outcome as a linear function of one or more predictors.
Polynomial regression fits y as a polynomial in x of a chosen degree (2–6), useful when the relationship is curved but its parametric form …
Multiple linear regression models a continuous outcome as a linear function of several predictors, with the same diagnostics as simple line…
A covariate-adjusted reference interval regresses the analyte on a covariate and takes percentile bounds from the residual SD, so the limit…
Quantile regression models a chosen conditional quantile (default median) rather than the mean. Robust to outliers and informative under he…
Test whether two independent simple linear regressions share the same slope. ANCOVA-style x × group interaction.

Nonlinear / curve fitting

The four-parameter logistic (4PL) curve fits dose-response data as y = Bottom + (Top − Bottom) / (1 + 10^((LogEC50 − x) · HillSlope)).
The five-parameter logistic adds an asymmetry parameter S to the 4PL curve, y = Bottom + (Top − Bottom) / (1 + 10^((LogEC50 − x) · HillSlop…
The Hill equation fits cooperative binding as y = Vmax · xⁿ / (Kⁿ + xⁿ) — Michaelis-Menten generalised to a variable Hill coefficient.
Michaelis-Menten kinetics fits y = Vmax · x / (Km + x), the standard model for single-site enzyme kinetics.
One-phase exponential decay fits y = (Y0 − Plateau) · exp(−K · x) + Plateau, with half-life ln(2) / K.
Two-phase exponential decay fits y = SpanFast·exp(−KFast·x) + SpanSlow·exp(−KSlow·x) + Plateau, capturing biphasic clearance.
Exponential association to a plateau fits y = Y0 + (Plateau − Y0) · (1 − exp(−K · x)) — the rising mirror of one-phase decay.
Gompertz growth fits y = A · exp(−B · exp(−C · x)), an asymmetric sigmoid alternative to logistic growth.
Generalized logistic growth fits y = K / (1 + exp(−r · (x − x₀))), where K is the carrying capacity, r the growth rate and x₀ the inflectio…
Fit an arbitrary user-typed nls formula. Provide the formula as 'y ~ …' and starting values as 'name=value, name=value, …'.
Compare two nls fits on the same (X, Y) via the extra sum-of-squares F-test (nested models) and AICc-based Akaike weights (any models).
A global 4PL fit shares parameters across several datasets at once: any subset of Bottom, Top, LogEC50 and HillSlope can be held common or …
Fits up to 9 standard curves (Linear, Logarithmic, Inverse, Quadratic, Cubic, Power, Compound, S-curve, Exponential) to a single (X, Y) and…

Mediation / Moderation

Baron-Kenny mediation analysis splits the X → Y relationship into a direct path c′ and an indirect path X → M → Y, with a Sobel test and a …
Moderation analysis tests whether the effect of X on Y depends on W, fitting Y ~ X · W with simple slopes at W = mean ± 1 SD and the Johnso…

Mixed effects

A linear or generalized linear mixed-effects model fits random intercepts per grouping variable — and optionally random slopes — alongside …

Survival

Time-to-event

The Kaplan-Meier estimator reconstructs the survival function from right-censored follow-up data, with an optional log-rank test for differ…
Cox proportional-hazards regression models the hazard ratio of an event as a multiplicative function of predictors, without specifying the …
Cox regression with time-varying covariates models predictors that change during follow-up, supplied in (start, stop, event) counting-proce…
Cox PH regression with a tt() interaction lets a covariate's effect change as a function of time — both a diagnostic for, and a remedy agai…
Restricted mean survival time averages survival over a window [0, τ] and compares groups by difference or ratio, an alternative to the haza…
Fine-Gray subdistribution hazards regression models the cumulative incidence of the event of interest when competing events can preclude it.

Parametric fits

A maximum-likelihood Weibull fit estimates the shape and scale parameters of uncensored event times.
A parametric accelerated-failure-time (AFT) model fits survival times to a chosen distribution — Weibull, exponential, log-normal, log-logi…

Diagnostics

Diagnostic accuracy

An ROC curve shows how well a continuous biomarker separates a binary outcome across every possible cutoff.
DeLong's paired test compares two ROC curves measured on the same patients — the standard way to decide whether one diagnostic test genuine…
Paired comparison of two precision-recall curves measured on the same patients tests the difference with a percentile bootstrap.
Partial AUC measures the area under the ROC curve over a chosen false-positive range, for when only part of the curve is clinically relevan…
A precision-recall curve and its average precision (AUC-PR) describe classifier performance, and are often more informative than ROC when t…
Stratum-specific likelihood ratios report the LR for each bin of a predictor, with a 95% Wald CI on log(LR).
Criterion analysis traces sensitivity, specificity, PPV, NPV, accuracy and Youden's J across every cutoff, marking the J-optimal threshold.
Probit regression fits a dose-response relationship for a binary outcome and reports the effective-dose quantiles (LD50, ED50 and so on) wi…

Method comparison

Passing-Bablok regression compares two measurement methods without assuming either is error-free — non-parametric, and robust to outliers a…
Deming regression compares two measurement methods when both carry measurement error — the parametric counterpart to Passing-Bablok.
Checks whether an assay reads proportionally across its measuring range by fitting polynomials to a dilution series and testing for departu…
Estimates the lowest concentrations an assay can reliably distinguish from a blank (LoB), detect (LoD), and quantify (LoQ), from blank and …
Estimates how repeatable a measurement procedure is by splitting its scatter into named variance components (repeatability, between-run, be…
Tests whether a suspected interferent shifts an assay's result, from paired measurements of test (spiked) versus control samples, against a…
Combines an assay's bias and imprecision into a single total analytical error and compares it against an allowable total-error goal, with a…
Verifies that an assay's observed precision and bias meet the manufacturer's claims, using a one-sided chi-square for imprecision and a bia…
Assesses whether a reference or QC material behaves like a patient sample, by checking if it falls inside the prediction interval of the pa…
Piecewise (segmented / broken-line) regression fits continuous straight-line segments joined at estimated breakpoints where the slope chang…
A Bland-Altman plot assesses agreement between two measurement methods by plotting each pair's difference against its mean, with 95% limits…
Bland-Altman repeatability analysis uses two or more replicate measurements per subject to yield the within-subject SD, the repeatability c…
A mountain plot folds the empirical CDF of paired differences (A − B) at the median — the same information as Bland-Altman, read as a peak.
Multi-method agreement compares three or more continuous methods at once, reporting a two-way ICC alongside every pairwise Pearson r and Li…
Trapezoidal AUC integrates a paired (X, Y) curve, useful for any cumulative-effect curve such as concentration against time or dose against…
Multiple t-tests run a Welch test on every numeric column against a two-class grouping factor, with built-in multiplicity correction and a …

Agreement

Cohen's κ measures agreement between exactly two raters on a categorical variable, with optional linear or quadratic weights for ordinal ca…
Fleiss' κ extends Cohen's κ to three or more raters, all classifying the same items into the same categories.
The intraclass correlation coefficient measures agreement among continuous ratings from two or more raters, reporting all six Shrout-Fleiss…
Lin's concordance correlation coefficient adjusts Pearson r for shifts in location and scale, reaching 1 only when two methods agree exactl…
Cronbach's α measures the internal-consistency reliability of a multi-item scale, reporting α-if-item-deleted so weak items stand out.
McDonald's ω estimates model-based reliability from a single-factor model — the modern replacement for Cronbach's α when tau-equivalence is…

Patterns

Association rules

Association-rule mining finds "customers who bought A also bought B" patterns in basket data, scoring each rule by support, confidence and …

Dimension reduction

Principal component analysis rotates multivariate numeric data into successive orthogonal directions of maximum variance.
Exploratory factor analysis decomposes variance into shared (communalities) + unique components. Latent-variable model; distinct from PCA i…
Moderated nonlinear factor analysis lets a latent factor's item intercepts, loadings and distribution depend on covariates — a unified test…
Structural equation modeling relates latent factors, measured by observed indicators, to one another and to observed variables — covering C…
Confirmatory factor analysis tests a hypothesised item-to-factor structure, reporting fit indices, loadings and factor covariances.
A latent growth curve model decomposes repeated measures over time into a latent intercept (the starting level) and a latent slope (the rat…
PLS-SEM estimates a structural equation model from composites rather than covariances, maximising explained variance with bootstrap inferen…
Correspondence analysis visualises a categorical contingency table in two dimensions by SVD, placing row and column points on shared axes f…
Canonical correlation analysis finds linear combinations of an X-set and a Y-set that maximise their correlation. Multivariate generalisati…
t-SNE (t-distributed stochastic neighbor embedding) reduces dimensions non-linearly while preserving local neighborhoods — the standard too…
UMAP embeds high-dimensional data in two dimensions non-linearly, preserving local neighbourhoods while retaining more global structure tha…
Classical (metric) multi-dimensional scaling embeds rows into a low-dimensional space whose pairwise Euclidean distances best preserve the …
Non-metric (Kruskal) multi-dimensional scaling preserves only the rank order of distances, making it robust to non-linear distance scales.

Network

Psychometric network analysis draws a Gaussian graphical model whose edges are significance-thresholded partial correlations, laid out as a…

Clustering

The elbow plot charts total within-cluster sum of squares for k = 1..10 in k-means; the bend in the curve is a heuristic choice of k.
k-means clustering partitions n observations into k clusters by minimising total within-cluster squared distance to the cluster centroid.
Fuzzy c-means clustering gives every observation a membership degree in every cluster, replacing the hard labels of k-means with soft assig…
DBSCAN finds clusters of arbitrary shape from density alone, using ε (neighbourhood radius) and minPts (minimum density), and flags low-den…
Agglomerative hierarchical clustering builds a dendrogram from a distance matrix. Cut at a chosen height for cluster assignments.
TwoStep-style cluster analysis evaluates 14 Gaussian-mixture covariance structures across k = 1..maxK and picks the (k, family) pair with t…

Time series

Autocorrelation (ACF) and partial autocorrelation (PACF) plots of a time series + Ljung-Box tests at canonical lags. The diagnostic before …
Decomposes a seasonal time series into trend + seasonal + residual components. Classical (moving-average) or STL (Loess-based).
An ARIMA(p, d, q) model — or seasonal SARIMA(P, D, Q)[s] — fits the Box-Jenkins family to a time series, with manual or automatic order sel…
ARIMA forecasting (automatic order selection or a fixed order) fits the model, projects h steps ahead, and returns a prediction interval as…
Structural (state-space) time-series model decomposes a series into unobserved level, slope, and seasonal components with a Kalman filter, …
Decomposable additive forecast splits a series into a piecewise-linear trend with automatically placed rate changepoints plus a Fourier-ser…
Stationarity tests check whether a series has a unit root: augmented Dickey-Fuller (H₀: unit root) alongside KPSS level and trend variants …
The cross-correlation function measures correlation between two series at lags −lagMax..+lagMax, with ±1.96/√n significance bounds.
Spectral analysis estimates an FFT-based periodogram with a 10% cosine taper, with optional detrending and modified-Daniell smoothing spans.
A vector autoregression regresses each of several time series on p lags of all the series, with Granger-causality tests and a stability che…
A structural VAR identified by a recursive (Cholesky) ordering produces orthogonalized impulse-response functions and a forecast-error vari…
Cointegration tests: Phillips-Ouliaris (residual/Engle-Granger family) plus Johansen's trace and maximum-eigenvalue rank tests.
The ARDL bounds test checks for a long-run level relationship using a joint F-test and a t-test on the lagged dependent level, compared aga…
A GARCH(p, q) model lets conditional variance depend on q past squared shocks and p past variances, with an ARCH-LM test for volatility clu…
Vector error-correction model estimates the cointegrating vector(s) β and the adjustment speeds α for cointegrated I(1) series.
Structural-break tests look for a shift in a regression relationship: a Chow test at a known break point, plus supF (Quandt-Andrews) and OL…
Wald-Wolfowitz runs test for randomness tests whether the number of runs of consecutive +/- around a threshold differs from chance.

Meta-analysis

Generic inverse-variance meta-analysis pools any per-study effect size yᵢ with its standard error seᵢ — the right tool when Hedges' g, log …
Continuous-outcome meta-analysis pools per-study means, SDs and group sizes, giving Hedges' g (SMD) by default, with mean difference and lo…
Meta-analysis of 2 × 2 cell counts. Choose risk ratio, odds ratio, or risk difference; log-scaled measures are back-transformed for the for…
Meta-analysis of a single proportion pools prevalence across studies, using the Freeman-Tukey double-arcsine transform to stabilise the var…
Robust Bayesian meta-analysis model-averages over the presence or absence of an effect, of heterogeneity and of publication bias, reporting…

Specialty

Bayesian

A Beta-Binomial conjugate model gives the Bayesian posterior for a single proportion, with a credible interval.
The JZS (Jeffreys-Zellner-Siow) Bayes factor weighs the evidence for and against a difference in means, for one-sample, two-sample or paire…
The model-averaged robust Bayesian t-test reports inclusion Bayes factors for an effect, for unequal variances and for heavy tails, average…
The JZS Bayes factor weighs the evidence for and against a non-zero Pearson correlation.
Bayesian linear regression with the JZS prior reports the Bayes factor of the full model against intercept-only, plus posterior summaries f…
Bayesian one-way ANOVA with the JZS prior weighs the evidence for a difference between group means.
Bayesian repeated-measures ANOVA: Bayes factor for a within-subject effect, with the subject factor treated as random.
Bayesian ANCOVA compares models by Bayes factor to isolate the group effect after adjusting for a continuous covariate.
Informative-hypothesis Bayes factors test competing order and equality constraints on group means — 'A < B < C' against 'A = B = C' — repor…

Resampling

Bootstrap confidence intervals resample the data to bound any one- or two-sample statistic, including those with no analytic standard error.
A permutation test compares two samples by reshuffling the group labels — distribution-free, and exact when randomisation was part of the d…

Complex samples

Complex-samples regression fits a weighted model with Taylor-linearised standard errors that respect a stratified or clustered survey desig…

Audit

Benford's law analysis compares leading-digit frequencies against log₁₀(1 + 1/d), with a chi-square test and Nigrini's MAD conformity bands…
Statistical audit sampling plans the minimum attribute sample for a tolerable misstatement rate, and evaluates attribute samples with an ex…

Quality control

A Gauge R&R study decomposes measurement variation into repeatability (equipment), reproducibility (appraisers) and part-to-part, following…
Acceptance sampling finds the smallest single sampling plan (n, c) satisfying both the producer's and the consumer's risk points, and draws…
Process capability analysis compares the process spread to the specification limits — Cp/Cpk from the within-subgroup σ, Pp/Ppk from the ov…
Statistical process control charts track a process over time — Shewhart variable charts (I-MR, Xbar-R, Xbar-S), attribute charts (p, np, c,…
A tolerance interval covers at least a proportion P of the population with confidence γ, computed by the normal K-factor method and a distr…
2^k factorial DOE analysis estimates main effects and interactions from a two-level designed experiment, ranks them on a Pareto chart of st…
DOE design generator builds the run sheet for a designed experiment — full factorial 2^k, regular fractional factorial 2^(k−p), central com…

Direct marketing

RFM segmentation bins customers by recency, frequency and monetary value — quantile bins, five by default, with recency inverted — giving e…
TURF analysis (total unduplicated reach and frequency) greedily picks the k items from 0/1 columns that together reach the most distinct re…

Tests on summarized data

Two-proportion z-test from typed-in event / total counts (no raw data needed). Same null as Pearson χ² on a 2 × 2 table.
Fisher's z test compares two independent correlations from typed-in r and n values, testing whether ρ₁ = ρ₂.
Compare two paired ROC AUCs from typed-in summary statistics (AUC₁, SE₁, AUC₂, SE₂, correlation between the two scores). Hanley-McNeil's co…
The exact (Garwood) Poisson interval bounds an incidence rate computed as events divided by person-time.
Comparison of two incidence rates from typed-in event counts + person-time per group. Wald log-rate CI for the rate ratio + score-based equ…
The diagnostic calculator turns sensitivity, specificity and pre-test prevalence into PPV, NPV, LR+ and LR−.

Power (hypothesis tests)

A priori or post-hoc power analysis for one- and two-sample t-tests. Solve for any three of {n, Cohen's d, α, power}; the fourth is compute…
Power analysis for one-way ANOVA uses Cohen's f, solving for any one of n per group, k, f, α or power.
Power analysis for a correlation tests against ρ = 0, solving for any one of n, r, α or power.
Power analysis for a χ² goodness-of-fit or independence test uses Cohen's w to solve for sample size or power.
Power analysis for a one- or two-sample proportion test is parameterised by Cohen's h, the arcsine difference.
Log-rank power analysis uses Schoenfeld's formula to solve for the number of events, the detectable hazard ratio or the power, given α and …
Power analysis for McNemar's paired-proportion test uses the Connor (1987) approximation.
Power analysis for a single AUC against 0.5 uses the Hanley-McNeil standard error.
Power analysis for two paired AUCs uses the Hanley-McNeil correlated standard error.

Precision & CI width

Precision-based sizing finds the n that gives a confidence interval on a mean a target half-width — the alternative to sizing from a hypoth…
Precision-based sizing finds the n that gives a confidence interval on a proportion a target half-width, by the Wald formula, which is cons…
Precision-based sizing finds the per-group n that gives a confidence interval on a difference of means a target half-width, assuming equal …
Precision-based sizing finds the per-group n that gives a confidence interval on a difference of proportions a target half-width.
Precision-based sizing finds the number of pairs that gives a confidence interval on the McNemar paired-proportion difference a target half…
Precision-based sizing finds the n needed to estimate a Bland-Altman limit of agreement to a target half-width, using SE(LoA) ≈ 1.71·σ_d / …
Precision-based sizing finds how many paired duplicates are needed to estimate a coefficient of variation to a target relative half-width, …
Precision-based sizing finds the n a regression-based reference limit needs for a target half-width, from Bland's (2015) SE = σ · √(1/n + z…