This document serves as an operational reference directory for classical statistical tests. These frameworks are utilized within inferential pipelines to isolate structural patterns from ambient random variance and determine whether variations observed across samples hold true within the parent populations.
Statistical routines that operate under the explicit assumption that the underlying parent population metrics follow a specified distribution structure.
Definition: A statistical test used to compare a sample mean to a known population mean when the population standard deviation is fully known and the data tracks normally (or the sample size is sufficiently large via the CLT).
Primary Use Case: Evaluating hypothesis targets regarding population parameters when true parent variances are pre-calculated and constant.
Definition: A statistical test used to compare the means of two distinct groups to isolate whether calculated differences are statistically significant or driven by random sampling variation.
Primary Use Cases:
Definition: An optimized mathematical adaptation of the independent two-sample t-test that adjusts calculated degrees of freedom to account for groups with unequal sample lengths and unequal variances.
Primary Use Case: Comparing means across independent groups when the classic equal variance assumption is explicitly violated.
Definition: An omnibus statistical framework applied to evaluate and compare the sample means of three or more continuous groups simultaneously to confirm whether observed variations stem from true grouping properties or random chance.
Primary Use Case: Evaluating multi-variant treatment arms, tracking multiple product features simultaneously, or assessing multi-class categorical effects on a continuous dependent variable.
Diagnostic verification tests implemented ahead of parametric pipelines to confirm that distributional requirements are completely satisfied.
Definition: A targeted statistical test used to assess if a continuous sample matrix follows a normal distribution pattern.
Primary Use Case: Running sanity validations on residuals or raw values before launching tests like Student's t-tests or classic ANOVA that assume underlying normality.
Definition: A diagnostic test used to verify the homoscedasticity (equality of variances) across distinct population groups or samples.
Primary Use Case: Verifying the equal-variance assumption before kicking off classic pooled independent t-tests or ANOVA routines.
Robust alternative tests used when data scales are ordinal, categorical, or when parametric distribution shapes are completely violated.
Definition: A distribution-free test that calculates the maximum empirical distance between a sample and a target reference cumulative distribution (One-Sample K-S) or between two separate sample cumulative distributions (Two-Sample K-S).
Primary Use Case: Testing if an empirical dataset maps cleanly to a known target function shape, or confirming if two source vectors originate from identical parent structures when normality assumptions fail.
Definition: A non-parametric rank-sum test evaluating whether the distribution scores of two independent groups vary significantly from each other.
Primary Use Case: Serving as a robust distribution-free alternative to the independent two-sample t-test when processing ranked ordinal data or highly skewed, non-normal numeric inputs.
Definition: A non-parametric alternative to one-way ANOVA used to evaluate and compare the overall median rank distributions of three or more independent groups.
Primary Use Case: Comparing multiple groups when data vectors violate normality parameters, variance boundaries, or are bound strictly to ordinal rankings.
Definition: A statistical test analyzing observation counts across an empirical contingency grid to identify if a significant non-random relationship links two discrete categorical features.
Primary Use Case: Testing operational connections between discrete categorical parameters, such as parsing associations between user demographic buckets and feature engagement preferences.
Definition: An exact probability calculator that maps out the true hypergeometric probability distribution of cell counts within small discrete contingency tables, removing approximation steps entirely.
Primary Use Case: Evaluating associations inside categorical matrices when dealing with extremely sparse datasets or small sample counts where Chi-Square frequency cell approximations drop below acceptable safety margins (e.g., cell counts less than 5).