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Category Diversity Summary

Describe categorical distributions with Shannon entropy and effective category counts.

Compute a binary Brier score from groups sharing an identical predicted probability.

Calculate a two-sided 95% t interval from the mean and SD of within-pair differences.

Find integer event counts compatible with a stated percentage and half-up rounding.

Compare continuous and binary baseline covariates with explicit standardization denominators.

Translate four specified logit coefficients into probabilities and contrasts for two binary predictors.

Audit simulation probability precision and plan a conservative number of independent replicates.

Transform a mean, SD, variance and interval endpoints with an explicit linear unit conversion.

Bound group risks and their difference by assigning every unresolved binary outcome in both directions.

Reconcile ordered event, censoring and entry counts and audit product-limit survival steps.

Estimate a binomial proportion and an approximate 95% Wilson score interval, including zero-event samples.

Audit a crude odds ratio and approximate log-Wald interval from four positive independent-group cell counts.