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Binary log loss by forecast

Find the average log penalty and detect impossible forecasts for observed outcomes.

Multiclass confusion matrix reader

Identify the weakest class recall and compare macro recall with overall accuracy.

Threshold net benefit comparison

Compare a fixed decision rule with treating everyone or no one at a stated threshold.

AIC model comparison

Rank likelihood fits and inspect their relative support within a candidate set.

Unequal-variance mean contrast

Compute the unpooled standard error and Welch–Satterthwaite degrees of freedom.

Direct rate standardization

Compare crude and directly standardized rates using explicit reference weights.

Observed versus expected events

Apply reference rates to stratum-specific exposure and audit an indirectly standardized ratio.

Stratified common odds ratio

Combine stratum cross-products using Mantel–Haenszel weighting.

Finite lot audit detection probability

Estimate the chance of finding at least one defect in a random audit without replacement.

Zero-event upper probability limit

Bound an event probability after zero events using an exact one-sided binomial limit.

Single-sample lot acceptance planner

Find the probability that a lot passes a maximum-defect acceptance rule.

Nested model partial R squared

Quantify the residual variation explained by adding predictors to a nested linear model.