Stats Methods

Summarizes the center, spread, and range of a dataset using values such as mean and standard deviation.

Presents key summary measures for variables in a compact table for quick interpretation.

Lists selected statistics in a straightforward report-style format instead of a full table.

Counts how often each category or value occurs in a dataset.

Checks data for missing values, unusual values, coding problems, and assumption issues before analysis.

Creates artificial data from a chosen model to explore how an analysis behaves under known conditions.

Assesses whether a variable follows a roughly normal distribution.

Looks for unusually extreme values that may not fit the rest of the sample.

Estimates an interval that should contain a specified proportion of the population.

Analyzes measurements that wrap around a circle, such as angles or directions.

Estimates or tests a single population proportion.

Compares proportions between two independent groups.

Compares paired yes-or-no outcomes measured on the same subjects or matched units.

Summarizes the relationship between two categorical variables in a cross-tabulation.

Tests whether three or more related binary treatments or conditions have equal response rates.

Combines stratified two-by-two tables to estimate an adjusted association.

Models counts in multiway contingency tables to study associations among categorical variables.

Uses exact probability calculations for binary outcomes, especially with small samples.

Tests whether the sample mean differs from a known or target value.

Compares the mean difference between paired measurements on the same subjects.

Compares means between two independent groups.

Tests whether two means are close enough to be considered practically equivalent.

Tests whether a new treatment is not worse than a standard by more than an acceptable margin.

Tests whether a new treatment exceeds a control by at least a clinically meaningful margin.

Analyzes paired crossover studies with two treatments and two periods.

Estimates a plausible range for the true population mean.

Models how one continuous predictor relates to one continuous outcome.

Models a continuous outcome using several predictors at the same time.

Models the probability of a binary outcome using one or more predictors.

Handles matched or stratified binary outcome data where comparisons happen within sets.

Models how predictors affect the hazard, or instantaneous risk, of a time-to-event outcome.

Models count outcomes, especially when the outcome is the number of events in a time or exposure window.

Models count outcomes when variability is larger than a Poisson model can handle.

Models count data with many zeros by combining a zero process with a Poisson count process.

Handles overdispersed count data with excess zeros by mixing a zero model and a negative binomial model.

Models counts or waiting-type outcomes under a geometric distribution framework.

Shrinks regression coefficients to reduce instability when predictors are highly correlated.

Fits a regression line that is less sensitive to outliers or influential observations.

Reduces correlated predictors into components before using them in regression.

Models curved relationships between several inputs and one response, often in optimization studies.

Fits relationships that do not follow a straight-line form.

Models cyclic or seasonal patterns using sine and cosine terms.

Estimates causal-type relationships when a predictor may be endogenous and an instrument is available.

Tests whether part of an effect works through an intermediate variable.

Measures the strength and direction of a linear relationship between two continuous variables.

Measures monotonic association using ranked values rather than raw scores.

Measures rank association based on concordant and discordant pairs.

Displays pairwise correlations across many variables in one table.

Measures association between one continuous variable and one true binary variable.

Estimates association when one variable is artificially dichotomized from an underlying continuum.

Studies association between two sets of variables rather than just one pair.

Measures how well two continuous measurements agree, not just how strongly they correlate.

Assesses agreement between two measurement methods by looking at differences against averages.

Fits a method-comparison line when both measurement methods have error.

A robust nonparametric method-comparison regression less sensitive to outliers and distribution assumptions.

Calculates sensitivity, specificity, predictive values, and related accuracy measures for a diagnostic test.

Uses one ROC curve to assess discrimination and choose a threshold for a continuous marker.

Tests whether one diagnostic model or marker has better discrimination than another.

Shows the tradeoff between sensitivity and false-positive rate across all possible thresholds.

Searches for the threshold that best balances diagnostic goals such as sensitivity and specificity.

Estimates survival probability over time when follow-up lengths differ across subjects.

Summarizes survival experience in grouped time intervals rather than exact event times.

Estimates the proportion of subjects who experience an event over time in the presence of competing risks or follow-up structure.

Fits a parametric survival model when event times follow a Weibull-type pattern.

Models how predictors affect the hazard, or instantaneous risk, of a time-to-event outcome.

Tests whether a new treatment's survival profile is not worse than standard by more than a margin.

Tests whether one survival curve is better than another by a clinically meaningful amount.

Assesses whether two survival experiences are practically similar within prespecified bounds.

Supports interim monitoring of time-to-event studies while controlling error across repeated looks.

Pools event rates or prevalences from several studies into an overall estimate.

Pools paired proportion outcomes across studies where responses are linked within subjects.

Combines mean differences from multiple studies measuring the same continuous outcome.

Combines study effects when outcomes are measured on different scales by standardizing them.

Combines time-to-event effect estimates from multiple survival studies.

Builds a tree of clusters by progressively joining similar observations or variables.

Partitions observations into a chosen number of clusters based on distance to cluster centers.

Allows one observation to belong partly to more than one cluster rather than forcing a hard assignment.

Clusters observations around actual representative cases instead of mathematical centroids.

Clusters observations based on how their regression relationships differ.

Displays a heat map while clustering rows and columns to reveal structure patterns.

Finds hidden latent factors that explain correlations among many observed variables.

Condenses many correlated variables into a smaller set of components that capture most variation.

Builds functions that separate predefined groups based on measured variables.

Compares multivariate mean vectors between groups or against a target profile.

Maps relationships among categories in a contingency table into a low-dimensional display.

Places observations in a low-dimensional space so distances reflect dissimilarity.

Checks whether groups have similar covariance structures across several variables.

Studies association between two sets of variables rather than just one pair.

Compares three or more groups using ranked data when ANOVA assumptions are weak.

Compares two independent groups using ranks rather than raw values.

A rank-based alternative to the two-sample t-test for independent groups.

A rank-based alternative to the paired t-test for matched or repeated data.

Tests paired binary data for a change in response before versus after an intervention.

Tests whether three or more related binary treatments or conditions have equal response rates.

Compares three or more repeated conditions using ranks.

Compares a sample distribution with a reference distribution or compares two distributions directly.

Performs pairwise rank-based comparisons after a significant Kruskal-Wallis result.

Provides nonparametric pairwise multiple comparisons among several groups.

Tests whether paired differences tend to go mostly in one direction without using their size.

Tests hypotheses about medians or other quantiles rather than means.

Assesses whether the order of observations appears random or shows a pattern.

Fits a beta distribution to proportions or rates bounded between zero and one.

Fits a Weibull model to lifetimes or failure times.

Fits a gamma model to positive, right-skewed measurements.

Checks whether data follow a chosen theoretical distribution using a diagnostic plot.

Compares how well different candidate distributions fit the same data.

Creates random treatment assignment schedules for controlled studies.

Assigns treatments efficiently when not every block can receive every treatment.

Studies several factors with fewer runs than a full factorial design.

Controls for two nuisance factors while testing treatments in an efficient square layout.

Designs experiments for estimating curved response surfaces and optimization targets.

Quickly identifies which factors matter most among many possible inputs.

Uses robust design principles to find settings that perform well under noise or variation.

Studies factors at low and high settings to estimate main effects and interactions.

Selects the most informative experimental runs when standard factorial layouts are impractical.

Creates experimental design matrices tailored to the chosen design family and factor structure.

Monitors process mean and within-sample range over time using subgrouped data.

Monitors process mean and within-sample standard deviation over time.

Accumulates small shifts over time to detect gradual process drift earlier than standard charts.

Uses weighted moving averages to detect small process shifts while smoothing noise.

Tracks the average of recent observations to reveal smoother process trends over time.

Monitors one observation at a time when subgroup sampling is not available.

Plots quality-control measurements against control limits, commonly in laboratory monitoring.

Tracks the proportion of defective or positive outcomes over time.

Tracks the count of defective items when subgroup sizes stay constant.

Tracks the count of defects per inspection unit when the area of opportunity is constant.

Tracks defect counts per unit when the size of the inspection unit varies.

Assesses whether a stable process fits within engineering or clinical specification limits.

Ranks problem categories from most common to least common to focus improvement efforts.

Measures how much of observed variability comes from the measurement system itself.

Provides rules for accepting or rejecting a batch based on a sample inspection.

Models time-series data using autoregressive, differencing, and moving-average components.

Automatically searches autoregressive and moving-average models to fit a time series.

Explores or fits autoregressive-moving-average structures under specified assumptions.

Measures how strongly a time series relates to its own past values at different lags.

Measures whether one time series is associated with lagged values of another series.

Studies cyclic patterns in a time series by decomposing variation into frequency components.

Separates trend, seasonality, and residual variation before forecasting forward.

Forecasts future values by weighting recent observations more strongly than older ones.

Models cyclic or seasonal patterns using sine and cosine terms.

Evaluates whether sequences show clustering, alternation, or non-random order.

Estimates the range expected for a healthy or typical population.

Builds different reference ranges for different age groups when the outcome changes with age.

Uses robust regression to estimate reference intervals while limiting the influence of unusual values.

Estimates an interval that should contain a specified proportion of the population.

Evaluates how well questionnaire items discriminate, vary, and contribute to a total score.

Models the probability of a response as a function of a person's latent trait level.

Produces cross-tabulations designed for survey-style data summaries.

Summarizes response counts and percentages for survey questions.

Supports studies where randomization happens at the group or site level rather than by person.

Compares groups when some measurements fall below the laboratory detection limit.

Models relationships involving outcomes that include values below detection limits.

Optimizes a linear objective subject to linear constraints.

Optimizes decisions when some variables must be whole numbers or yes-or-no choices.

Optimizes an objective that includes squared terms under constraints.

Finds the best one-to-one matching between tasks and resources.

Finds the greatest amount that can move through a network without breaking capacity limits.

Moves flow through a network at minimum cost while respecting capacities.

Connects all nodes in a network with the smallest total link cost.

Finds the minimum-distance or minimum-cost path between locations in a network.

Optimizes shipping from several sources to several destinations at lowest overall cost.

Extends transportation models by allowing goods to pass through intermediate nodes.