Normality Testing

• Test numeric variables for compatibility with a normal distribution using Shapiro–Wilk, Lilliefors-corrected Kolmogorov–Smirnov, Anderson–Darling, and D’Agostino–Pearson K² testing

• Validated against R with complete decision agreement at α = 0.05

Chi² Testing

• Analyze 2×2 categorical associations using Yates-corrected Pearson χ² testing and two-sided Fisher’s exact test

• Sigma reports cell counts, expected counts, low-count warnings, p-values, and effect measures

• Fisher p-values matched R up to approximately 10⁻¹²

Unpaired T Testing

• Compare continuous outcomes between two independent groups using Welch’s t-test and the pooled-variance Student t-test

• Sigma reports descriptive statistics, mean differences, confidence intervals, p-values, and effect sizes

• Validated against R with excellent numerical agreement (10⁻¹²)

Paired T Testing

• Analyze paired or before-after measurements using the classical paired-samples t-test

• Sigma reports complete pairs, paired differences, confidence intervals, p-values, and standardized effect sizes

• P-values matched R up to approximately 10⁻¹⁵​​​

Univariate Regression

• Screen predictors of a binary outcome using one-predictor logistic regression models

• Sigma reports odds ratios, confidence intervals, Wald tests, p-values, and warning flags for unstable or separated models.

• Stable cases matched R up to approximately 10⁻⁸ for coefficients

Multivariate Regresssion

• Fit adjusted binary logistic regression models with multiple predictors entered simultaneously

• Sigma reports adjusted odds ratios, confidence intervals, p-values, convergence diagnostics, EPV, and instability warnings

• Stable models matched R up to approximately 10⁻⁷ for coefficients

Propensity Score Matching

• Create balanced observational cohorts using logistic-regression-based propensity scores and 1:1 nearest-neighbor matching without replacement

• Sigma reports matching results, overlap diagnostics, and pre/post balance metrics

• Core matched sample counts showed exact agreement with R

Competing Risk Analysis

• Analyze cause-specific absolute risks using cumulative incidence functions, Gray’s test, and Fine & Gray regression

• Sigma supports competing-event structures where standard survival methods may be inappropriate

• CIF estimates matched R up to approximately 10⁻¹⁵, with strong Gray-test agreement

Methodology

• Deep Explanation of the theoretical methodology for every tool.

• Report availabe in PDF for any queries

Validation

• Validation Report  of every tool

• Excellent Results in comparison to R packages

• Validation in different cohort types (good fit to edge cases) and cohorts sizes (n=3 to n=5000)

• Report availabe in PDF for any queries