Quick Insights for Statistical Tests

A statistical method to analyze SUCCESS/FAILURE data and compare rates using Bayesian inference.​

DATA TYPE: COUNT DATA​

• Successes: How many converted, passed, clicked, responded?​

• Total Trials: How many visitors, units, emails, patients?​

• Result: Success RATE (probability between 0 and 1)​

KEY OUTPUT

• Posterior distribution of each group's success rate (theta).​

• Credible intervals (like confidence intervals, but interpretable!). ​

• Direct probability statements: P(Treatment > Control) = 94%.​

INTUITIVE RESULTS ("There's a 94% probability that the new landing page beats the old one “)​

UNCERTAINTY QUANTIFICATION (Get full distribution of possible success rates)​

WORKS WITH SMALL SAMPLES (Partial pooling borrows strength across groups)​

FLEXIBLE POOLING STRATEGIES​

• Complete: Single rate (benchmark testing)​

• Partial: Related groups (categories, regions)​

• No Pooling: Independent groups (drugs, treatments)​

A statistical method to compare means across groups using Bayesian inference.​

KEY OUTPUT

• Posterior distribution of each group's mean ​

• Credible intervals (like confidence intervals, but interpretable!) ​

• Direct probability statements: P(Group A > Group B) = 92%​

INTUITIVE RESULTS ("There's an 87% probability that Region A outperforms Region B“)​

UNCERTAINTY QUANTIFICATION (Get full distribution, not just point estimate)​

WORKS WITH SMALL SAMPLES (Borrows strength across groups (partial pooling))​

HANDLES REAL-WORLD DATA ​

• Normal: Clean continuous data​

• Robust: Data with outliers​

• Poisson: Count data​

FLEXIBLE POOLING STRATEGIES​

• Partial: Related groups (regions, time periods)​

• No Pooling: Independent groups (different products)​

A statistical method to analyze CATEGORICAL COUNT DATA and compare PROPORTIONS across multiple categories usingBayesian inference.​

DATA TYPE: CATEGORY COUNTS​

• Multiple categories (3 or more typically).​

• Counts in each category (non-negative integers).​

• Result: Proportions that SUM TO 1.​

KEY OUTPUT

• Posterior distribution of each category's proportion (theta).​

• Proportions ALWAYS sum to 1 (Dirichlet distribution).​

INTUITIVE RESULTS ("Mobile traffic is 55% with 95% CI [53%, 57%]" )​

UNCERTAINTY QUANTIFICATION (Get full distribution for each category proportion)​

WORKS WITH SMALL SAMPLES (Bayesian inference handles small counts gracefully)​

HIERARCHICAL MODELING​

• Compare related groups (partial pooling)​

• Compare independent groups (no pooling)​

• Single global estimate (complete pooling)​

MULTIPLE COMPARISON TYPES​

• ONE-SAMPLE: Test if distribution matches expected​

• HOMOGENEITY: Test if groups have same proportions​

• INDEPENDENCE: Test if groups have different proportions​