# PASS Documentation

Use the links below to load individual chapters from the PASS statistical software training documentation in PDF format. The chapters correspond to the procedures available in PASS. Each chapter generally has an introduction to the topic, technical details including power and sample size calculation details, explanations for the procedure options, examples, and procedure validation examples. Each of these chapters is also available through the PASS help system when running the software.

Jump to topic:

**Quick Start****Introduction****Bayesian Approaches****Cluster-Randomized****Conditional Power****Confidence Intervals****Correlation****Design of Experiments****Equivalence****GEE****Group-Sequential****Means****Method Comparison****Microarray****Mixed Models****Non-Inferiority****Nonparametric****Normality****Pilot Studies****Post-Marketing Surveillance****Proportions****Quality Control****Rates and Counts****Regression****ROC****Sample Size Reestimation****Simulation****Stratified****Superiority by a Margin****Survival****Tolerance Intervals****Vaccine Efficacy****Variances****Tools****Plots****References**

## Quick Start

## Introduction

- License Agreement
- The PASS Home Window
- The Procedure Window
- The Output Window
- Introduction to Power Analysis
- Power Analysis of Proportions
- Power Analysis of Means

## Bayesian Approaches

- Bayesian Adjustment using the Posterior Error Approach
- Tests for Two Means Assuming Equal Variances using a Bayesian Approach
- Dose-Finding using the Bayesian Continual Reassessment Method (CRM)

## Cluster-Randomized

### One Mean

#### Confidence Interval

- Confidence Intervals for One Mean in a Cluster-Randomized Design
- Confidence Intervals for One Mean in a Stratified Cluster-Randomized Design

### Two Means

#### Test (Inequality)

- Tests for Two Means in a Cluster-Randomized Design
- Tests for Two Means in a Stepped-Wedge Cluster-Randomized Design
- Tests for the Matched-Pair Difference of Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Stratified Cluster-Randomized Design
- GEE Tests for Two Means in a Split-Mouth Design

#### Non-Inferiority

#### Superiority by a Margin

#### Equivalence

#### Mixed Models (2-Level Hierarchical Design)

- Mixed Models Tests for Two Means in a Cluster-Randomized Design
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Means at the End of Follow-Up in a 2-Level Hierarchical Design

#### Mixed Models (3-Level Hierarchical Design)

- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Means at the End of Follow-Up in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Fixed Slopes (Level-3 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Random Slopes (Level-3 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Fixed Slopes (Level-2 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Random Slopes (Level-2 Randomization)

#### GEE

- GEE Tests for Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Stratified Cluster-Randomized Design
- GEE Tests for Two Means in a Split-Mouth Design

### Multiple Means

#### Mixed Models (Interaction in a 2×2 Factorial Design)

- Mixed Models Tests for Interaction in a 2×2 Factorial 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Interaction in a 2×2 Factorial 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Interaction in a 2×2 Factorial 3-Level Hierarchical Design (Level-2 Randomization)

#### Mixed Models (Slope-Interaction in a 2×2 Factorial Design)

- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 2-Level Hierarchical Design with Fixed Slopes (Level-2 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 2-Level Hierarchical Design with Random Slopes (Level-2 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Fixed Slopes (Level-3 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Fixed Slopes (Level-2 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Random Slopes (Level-3 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Random Slopes (Level-2 Randomization)

#### GEE Tests for Multiple Groups

- GEE Tests for Multiple Means in a Cluster-Randomized Design
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Continuous Outcome)

### One Proportion

#### Confidence Interval

- Confidence Intervals for One Proportion in a Cluster-Randomized Design
- Confidence Intervals for One Proportion in a Stratified Cluster-Randomized Design

### Two Proportions

#### Test (Inequality)

- Tests for Two Proportions in a Cluster-Randomized Design
- Tests for Two Proportions in a Stratified Cluster-Randomized Design (Cochran-Mantel-Haenszel Test)
- Tests for Two Proportions in a Stepped-Wedge Cluster-Randomized Design
- Tests for the Matched-Pair Difference of Two Proportions in a Cluster-Randomized Design
- GEE Tests for Two Proportions in a Split-Mouth Design

#### Test (Non-Zero Null)

- Non-Zero Null Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Non-Unity Null Tests for the Ratio of Two Proportions in a Cluster-Randomized Design

#### Non-Inferiority

- Non-Inferiority Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Proportions in a Cluster-Randomized Design
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Proportions in a Cluster-Randomized Design

#### Superiority by a Margin

- Superiority by a Margin Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Ratio of Two Proportions in a Cluster-Randomized Design
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Proportions in a Cluster-Randomized Design

#### Equivalence

- Equivalence Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Equivalence Tests for the Ratio of Two Proportions in a Cluster-Randomized Design

#### Mixed Models (2-Level Hierarchical Design)

- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-1 Randomization)

#### Mixed Models (3-Level Hierarchical Design)

- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-1 Randomization)

#### GEE

- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for Two Proportions in a Split-Mouth Design

#### Vaccine Efficacy

- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Proportions in a Cluster-Randomized Design
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Proportions in a Cluster-Randomized Design

### Multiple Proportions

- GEE Tests for Multiple Proportions in a Cluster-Randomized Design
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Binary Outcome)

### Rates and Counts

- Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design with Adjustment for Varying Cluster Sizes
- Non-Inferiority Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Tests for Two Poisson Rates in a Stepped-Wedge Cluster-Randomized Design
- Tests for the Matched-Pair Difference of Two Event Rates in a Cluster-Randomized Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for Multiple Poisson Rates in a Cluster-Randomized Design

### Survival

### Stepped-Wedge

- Tests for Two Means in a Stepped-Wedge Cluster-Randomized Design
- Tests for Two Proportions in a Stepped-Wedge Cluster-Randomized Design
- Tests for Two Poisson Rates in a Stepped-Wedge Cluster-Randomized Design

### Mixed Models

#### Means

- Mixed Models Tests for Two Means in a Cluster-Randomized Design
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Means at the End of Follow-Up in a 2-Level Hierarchical Design
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Means at the End of Follow-Up in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Interaction in a 2×2 Factorial 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Interaction in a 2×2 Factorial 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Interaction in a 2×2 Factorial 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 2-Level Hierarchical Design with Fixed Slopes (Level-2 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 2-Level Hierarchical Design with Random Slopes (Level-2 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Fixed Slopes (Level-3 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Fixed Slopes (Level-2 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Random Slopes (Level-3 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Random Slopes (Level-2 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Fixed Slopes (Level-3 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Fixed Slopes (Level-2 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Random Slopes (Level-3 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Random Slopes (Level-2 Randomization)

#### Proportions

- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-1 Randomization)

### GEE

#### Means

- GEE Tests for Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Stratified Cluster-Randomized Design
- GEE Tests for Two Means in a Split-Mouth Design
- GEE Tests for Multiple Means in a Cluster-Randomized Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Continuous Outcome)

#### Proportions

- GEE Tests for Multiple Proportions in a Cluster-Randomized Design
- GEE Tests for Two Proportions in a Split-Mouth Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Binary Outcome)

#### Rates and Counts

- GEE Tests for Multiple Poisson Rates in a Cluster-Randomized Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Count Outcome)

### Vaccine Efficacy

- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Proportions in a Cluster-Randomized Design
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Proportions in a Cluster-Randomized Design
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates in a Cluster-Randomized Design

## Conditional Power

### Means

#### Test (Inequality)

- Conditional Power and Sample Size Reestimation of One-Sample T-Tests
- Conditional Power and Sample Size Reestimation of Paired T-Tests
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests
- Conditional Power and Sample Size Reestimation of Tests for Two Means in a 2×2 Cross-Over Design

#### Non-Inferiority

- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for Two Means in a 2×2 Cross-Over Design

#### Superiority by a Margin

- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for Two Means in a 2×2 Cross-Over Design

### Proportions

#### Test (Inequality)

- Conditional Power and Sample Size Reestimation of Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Tests for the Difference Between Two Proportions

#### Non-Inferiority

- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for Two Proportions

#### Superiority by a Margin

- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for Two Proportions

### Survival

#### Test (Inequality)

#### Non-Inferiority

#### Superiority by a Margin

## Confidence Intervals

### Correlation

- Confidence Intervals for Pearson’s Correlation
- Confidence Intervals for Spearman’s Rank Correlation
- Confidence Intervals for Kendall’s Tau-b Correlation
- Confidence Intervals for Point Biserial Correlation
- Confidence Intervals for Intraclass Correlation
- Confidence Intervals for Intraclass Correlation with Assurance Probability (Two-Sided)
- Confidence Intervals for Intraclass Correlation with Assurance Probability (Lower One-Sided)
- Confidence Intervals for Coefficient Alpha
- Confidence Intervals for Kappa

### Means

- Confidence Intervals for One Mean
- Confidence Intervals for One Mean with Tolerance Probability
- Confidence Intervals for One Mean in a Stratified Design
- Confidence Intervals for One Mean in a Cluster-Randomized Design
- Confidence Intervals for One Mean in a Stratified Cluster-Randomized Design
- Confidence Intervals for Paired Means
- Confidence Intervals for Paired Means with Tolerance Probability
- Confidence Intervals for the Difference Between Two Means
- Confidence Intervals for the Difference Between Two Means with Tolerance Probability
- Confidence Intervals for One-Way Repeated Measures Contrasts

### Method Comparison

- Confidence Intervals for the Bland-Altman Range of Agreement using Assurance Probability
- Confidence Intervals for the Bland-Altman Range of Agreement using Expected Half-Width

### Percentiles

- Confidence Intervals for a Percentile of a Normal Distribution
- Confidence Intervals for a Percentile of a Normal Distribution using Assurance Probability
- Confidence Intervals for a Percentile of a Normal Distribution using Expected Width
- Confidence Intervals for Regression-Based Reference Limits using Assurance Probability
- Confidence Intervals for Regression-Based Reference Limits using Expected Relative Precision
- Confidence Intervals for an Exponential Lifetime Percentile

### Proportions

- Confidence Intervals for One Proportion
- Confidence Intervals for One Proportion from a Finite Population
- Confidence Intervals for One Proportion in a Stratified Design
- Confidence Intervals for One Proportion in a Cluster-Randomized Design
- Confidence Intervals for One Proportion in a Stratified Cluster-Randomized Design
- Confidence Intervals for the Difference Between Two Proportions
- Confidence Intervals for the Ratio of Two Proportions
- Confidence Intervals for the Difference Between Two Correlated Proportions
- Confidence Intervals for Vaccine Efficacy using a Cohort Design
- Confidence Intervals for Vaccine Efficacy using an Unmatched Case-Control Design
- Confidence Intervals for the Odds Ratio of Two Proportions using an Unmatched Case-Control Design
- Confidence Intervals for the Odds Ratio of Two Proportions
- Confidence Intervals for Kappa

### Quality Control

### Reference Intervals

- Reference Intervals for Normal Data
- Nonparametric Reference Intervals for Non-Normal Data
- Reference Intervals for Clinical and Lab Medicine
- Confidence Intervals for Regression-Based Reference Limits using Assurance Probability
- Confidence Intervals for Regression-Based Reference Limits using Expected Relative Precision

### Regression

- Confidence Intervals for Linear Regression Slope
- Confidence Intervals for the Odds Ratio in Logistic Regression with One Binary X
- Confidence Intervals for the Odds Ratio in Logistic Regression with Two Binary X’s
- Confidence Intervals for the Interaction Odds Ratio in Logistic Regression with Two Binary X’s
- Confidence Intervals for Michaelis-Menten Parameters
- Reference Intervals for Clinical and Lab Medicine
- Confidence Intervals for Regression-Based Reference Limits using Assurance Probability
- Confidence Intervals for Regression-Based Reference Limits using Expected Relative Precision

### ROC

### Sensitivity and Specificity

- Confidence Intervals for One-Sample Sensitivity
- Confidence Intervals for One-Sample Specificity
- Confidence Intervals for One-Sample Sensitivity and Specificity

### Standard Deviation

- Confidence Intervals for One Standard Deviation using Standard Deviation
- Confidence Intervals for One Standard Deviation using Relative Error
- Confidence Intervals for One Standard Deviation with Tolerance Probability

### Survival

- Confidence Intervals for the Exponential Lifetime Mean
- Confidence Intervals for an Exponential Lifetime Percentile
- Confidence Intervals for Exponential Reliability
- Confidence Intervals for the Exponential Hazard Rate
- Confidence Intervals for the Weibull Shape Parameter

### Variances

- Confidence Intervals for One Variance using Variance
- Confidence Intervals for One Variance using Relative Error
- Confidence Intervals for One Variance with Tolerance Probability
- Confidence Intervals for the Ratio of Two Variances using Variances
- Confidence Intervals for the Ratio of Two Variances using Relative Error

## Correlation

### Correlation

#### Test (Inequality)

- Pearson’s Correlation Tests
- Pearson’s Correlation Tests (Simulation)
- Spearman’s Rank Correlation Tests (Simulation)
- Kendall’s Tau-b Correlation Tests (Simulation)
- Power Comparison of Correlation Tests (Simulation)
- Tests for Two Correlations
- Point Biserial Correlation Tests

#### Confidence Interval

- Confidence Intervals for Pearson’s Correlation
- Confidence Intervals for Spearman’s Rank Correlation
- Confidence Intervals for Kendall’s Tau-b Correlation
- Confidence Intervals for Point Biserial Correlation

### Coefficient (Cronbach’s) Alpha

- Tests for One Coefficient Alpha
- Tests for Two Coefficient Alphas
- Confidence Intervals for Coefficient Alpha

### Intraclass Correlation

- Tests for Intraclass Correlation
- Confidence Intervals for Intraclass Correlation
- Confidence Intervals for Intraclass Correlation with Assurance Probability (Two-Sided)
- Confidence Intervals for Intraclass Correlation with Assurance Probability (Lower One-Sided)

### Kappa Rater Agreement

### Lin’s Concordance Correlation

## Design of Experiments

### Randomization Lists

### Experimental Design

- Balanced Incomplete Block Designs
- D-Optimal Designs
- Design Generator
- Fractional Factorial Designs
- Latin Square Designs
- Response Surface Designs
- Screening Designs
- Taguchi Designs
- Two-Level Designs

## Equivalence

### Means

#### One Mean

#### Paired Means

- Paired Z-Tests for Equivalence
- Paired T-Tests for Equivalence
- Equivalence Tests for Paired Means (Simulation)

#### Two Independent Means

- Two-Sample T-Tests for Equivalence Assuming Equal Variance
- Two-Sample T-Tests for Equivalence Allowing Unequal Variance
- Equivalence Tests for Two Means (Simulation)
- Equivalence Tests for the Ratio of Two Means (Log-Normal Data)
- Equivalence Tests for the Ratio of Two Means (Normal Data)

#### Two Means (Cluster-Randomized)

#### Cross-Over (2×2) Design

- Equivalence Tests for the Difference Between Two Means in a 2×2 Cross-Over Design
- Equivalence Tests for the Ratio of Two Means in a 2×2 Cross-Over Design (Log-Normal Data)
- Equivalence Tests for the Ratio of Two Means in a 2×2 Cross-Over Design (Normal Data)
- Equivalence Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design

#### Cross-Over (Higher-Order) Design

- Equivalence Tests for the Difference of Two Means in a Higher-Order Cross-Over Design
- Equivalence Tests for the Ratio of Two Means in a Higher-Order Cross-Over Design (Log-Normal Data)

#### Cross-Over (Williams) Design

#### Multiple Means

- Equivalence Tests for One-Way Analysis of Variance Assuming Equal Variances
- Equivalence Tests for One-Way Analysis of Variance Allowing Unequal Variances
- Studentized Range Tests for Equivalence
- Equivalence Tests for the Mean Ratio in a Three-Arm Trial (Normal Data) (Simulation)

### Proportions

#### One Proportion

#### Two Correlated (Paired) Proportions

- Equivalence Tests for the Difference Between Two Correlated Proportions
- Equivalence Tests for the Ratio of Two Correlated Proportions

#### Two Independent Proportions

- Equivalence Tests for the Difference Between Two Proportions
- Equivalence Tests for the Ratio of Two Proportions
- Equivalence Tests for the Odds Ratio of Two Proportions

#### Two Proportions (Cluster-Randomized)

- Equivalence Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Equivalence Tests for the Ratio of Two Proportions in a Cluster-Randomized Design

#### Cross-Over (2×2) Design

- Equivalence Tests for the Difference of Two Proportions in a 2×2 Cross-Over Design
- Equivalence Tests for the Odds Ratio of Two Proportions in a 2×2 Cross-Over Design
- Equivalence Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design

#### Cross-Over (Williams) Design

### Rates and Counts

- Equivalence Tests for the Ratio of Two Poisson Rates
- Equivalence Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design
- Equivalence Tests for the Ratio of Two Negative Binomial Rates

### Survival

- Equivalence Tests for Two Survival Curves Using Cox’s Proportional Hazards Model
- Equivalence Tests for the Difference of Two Hazard Rates Assuming an Exponential Model

### Variances

- Equivalence Tests for the Ratio of Two Variances
- Equivalence Tests for the Ratio of Two Within-Subject Variances in a Parallel Design
- Equivalence Tests for the Ratio of Two Within-Subject Variances in a 2×2M Replicated Cross-Over Design
- Equivalence Tests for the Difference of Two Within-Subject CV’s in a Parallel Design

## GEE

### Means

- GEE Tests for Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Stratified Cluster-Randomized Design
- GEE Tests for Two Means in a Split-Mouth Design
- GEE Tests for Multiple Means in a Cluster-Randomized Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Continuous Outcome)

### Proportions

- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for Two Correlated Proportions with Dropout
- GEE Tests for Two Proportions in a Split-Mouth Design
- GEE Tests for Multiple Proportions in a Cluster-Randomized Design

### Rates and Counts

- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for Multiple Poisson Rates in a Cluster-Randomized Design

## Group-Sequential

### One Mean

#### Test (Inequality)

- Group-Sequential Tests for One Mean with Known Variance (Simulation)
- Group-Sequential T-Tests for One Mean (Simulation)

#### Non-Inferiority

- Group-Sequential Non-Inferiority Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Non-Inferiority T-Tests for One Mean (Simulation)

#### Superiority by a Margin

- Group-Sequential Superiority by a Margin Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for One Mean (Simulation)

### Two Means

#### Test (Inequality)

- Group-Sequential Tests for Two Means with Known Variances (Simulation)
- Group-Sequential T-Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means (Legacy)
- Group-Sequential Tests for Two Means (Simulation) (Legacy)
- Group-Sequential Tests for Two Means Assuming Normality (Simulation) (Legacy)

#### Non-Inferiority

- Group-Sequential Non-Inferiority Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Non-Inferiority T-Tests for Two Means (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation) (Legacy)

#### Superiority by a Margin

- Group-Sequential Superiority by a Margin Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for Two Means (Simulation)

### One Proportion

#### Test (Inequality)

- Group-Sequential Tests for One Proportion (Simulation)
- Group-Sequential Tests for One Proportion in a Fleming Design
- Single-Stage Phase II Clinical Trials
- Two-Stage Designs for Tests of One Proportion (Simon)
- Three-Stage Phase II Clinical Trials

#### Non-Inferiority

#### Superiority by a Margin

### Two Proportions

#### Test (Inequality)

- Group-Sequential Tests for Two Proportions (Simulation)
- Group-Sequential Tests for Two Proportions (Legacy)
- Group-Sequential Tests for Two Proportions (Simulation) (Legacy)

#### Non-Inferiority

- Group-Sequential Non-Inferiority Tests for Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Ratio of Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Odds Ratio of Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Difference of Two Proportions (Simulation) (Legacy)

#### Superiority by a Margin

- Group-Sequential Superiority by a Margin Tests for Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for the Ratio of Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for the Odds Ratio of Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for the Difference of Two Proportions (Simulation) (Legacy)

### Survival

#### Test (Inequality)

- Group-Sequential Tests for Two Hazard Rates (Simulation)
- Group-Sequential Logrank Tests (Legacy)
- Group-Sequential Logrank Tests (Simulation) (Legacy)

#### Non-Inferiority

#### Superiority by a Margin

## Means

### One Mean

#### T-Test (Inequality)

- One-Sample T-Tests
- One-Sample T-Tests using Effect Size
- Tests for One Mean (Simulation)
- Wilcoxon Signed-Rank Tests
- Conditional Power and Sample Size Reestimation of One-Sample T-Tests
- Group-Sequential T-Tests for One Mean (Simulation)
- Multiple Testing for One Mean (One-Sample or Paired Data)

#### Z-Test (Inequality)

- One-Sample Z-Tests
- Group-Sequential Tests for One Mean with Known Variance (Simulation)
- Multiple Testing for One Mean (One-Sample or Paired Data)

#### Nonparametric

- Tests for One Mean (Simulation)
- Wilcoxon Signed-Rank Tests
- Wilcoxon Signed-Rank Tests for Non-Inferiority
- Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Multiple Testing for One Mean (One-Sample or Paired Data)
- Confidence Intervals for a Percentile of a Normal Distribution
- Confidence Intervals for a Percentile of a Normal Distribution using Assurance Probability
- Confidence Intervals for a Percentile of a Normal Distribution using Expected Width

#### Non-Normal Data

- Tests for One Mean (Simulation)
- Tests for One Exponential Mean
- Tests for One Poisson Rate
- Wilcoxon Signed-Rank Tests
- Wilcoxon Signed-Rank Tests for Non-Inferiority
- Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Multiple Testing for One Mean (One-Sample or Paired Data)

#### Confidence Interval

- Confidence Intervals for One Mean
- Confidence Intervals for One Mean with Tolerance Probability
- Confidence Intervals for One Mean in a Stratified Design
- Confidence Intervals for One Mean in a Cluster-Randomized Design
- Confidence Intervals for One Mean in a Stratified Cluster-Randomized Design
- Confidence Intervals for a Percentile of a Normal Distribution
- Confidence Intervals for a Percentile of a Normal Distribution using Assurance Probability
- Confidence Intervals for a Percentile of a Normal Distribution using Expected Width
- Confidence Intervals for Regression-Based Reference Limits using Assurance Probability
- Confidence Intervals for Regression-Based Reference Limits using Expected Relative Precision

#### Non-Inferiority

- One-Sample Z-Tests for Non-Inferiority
- One-Sample T-Tests for Non-Inferiority
- Wilcoxon Signed-Rank Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Non-Inferiority
- Group-Sequential Non-Inferiority Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Non-Inferiority T-Tests for One Mean (Simulation)

#### Superiority by a Margin

- One-Sample Z-Tests for Superiority by a Margin
- One-Sample T-Tests for Superiority by a Margin
- Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Superiority by a Margin
- Group-Sequential Superiority by a Margin Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for One Mean (Simulation)

#### Equivalence

#### Stratified

- Confidence Intervals for One Mean in a Stratified Design
- Confidence Intervals for One Mean in a Stratified Cluster-Randomized Design

#### Multiple Testing

#### Group-Sequential

- Group-Sequential Tests for One Mean with Known Variance (Simulation)
- Group-Sequential T-Tests for One Mean (Simulation)
- Group-Sequential Non-Inferiority Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Superiority by a Margin Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Non-Inferiority T-Tests for One Mean (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for One Mean (Simulation)

#### Conditional Power

- Conditional Power and Sample Size Reestimation of One-Sample T-Tests
- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Superiority by a Margin

### Paired Means

#### T-Test (Inequality)

- Paired T-Tests
- Paired T-Tests using Effect Size
- Tests for Paired Means (Simulation)
- Paired Wilcoxon Signed-Rank Tests
- Multiple Testing for One Mean (One-Sample or Paired Data)
- Tests for the Matched-Pair Difference of Two Means in a Cluster-Randomized Design
- Conditional Power and Sample Size Reestimation of Paired T-Tests
- Tests for Paired Means (Simulation) (Legacy)

#### Z-Test (Inequality)

#### Nonparametric

- Tests for Paired Means (Simulation)
- Paired Wilcoxon Signed-Rank Tests
- Paired Wilcoxon Signed-Rank Tests for Non-Inferiority
- Paired Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Equivalence Tests for Paired Means (Simulation)
- Multiple Testing for One Mean (One-Sample or Paired Data)
- Tests for Paired Means (Simulation) (Legacy)

#### Confidence Interval

- Confidence Intervals for Paired Means
- Confidence Intervals for Paired Means with Tolerance Probability

#### Non-Inferiority

- Paired Z-Tests for Non-Inferiority
- Paired T-Tests for Non-Inferiority
- Paired Wilcoxon Signed-Rank Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Non-Inferiority

#### Superiority by a Margin

- Paired Z-Tests for Superiority by a Margin
- Paired T-Tests for Superiority by a Margin
- Paired Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Superiority by a Margin

#### Equivalence

- Paired Z-Tests for Equivalence
- Paired T-Tests for Equivalence
- Equivalence Tests for Paired Means (Simulation)

#### Cluster-Randomized

#### Multiple Testing

#### Conditional Power

- Conditional Power and Sample Size Reestimation of Paired T-Tests
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Superiority by a Margin

### Two Independent Means

#### T-Test (Inequality)

- Two-Sample T-Tests Assuming Equal Variance
- Two-Sample T-Tests Allowing Unequal Variance
- Two-Sample T-Tests using Effect Size
- Tests for Two Means (Simulation)
- Tests for Two Ordered Categorical Variables (Proportional Odds)
- Tests for Two Ordered Categorical Variables (Non-Proportional Odds, Wilcoxon-Mann-Whitney)
- Mann-Whitney U or Wilcoxon Rank-Sum Tests
- Mann-Whitney U or Wilcoxon Rank-Sum Tests (Simulation)
- Tests for Two Means Assuming Equal Variances using a Bayesian Approach
- Tests for Two Groups Assuming a Two-Part Model
- Tests for Two Groups Assuming a Two-Part Model with Detection Limits
- Tests for the Ratio of Two Means (Log-Normal Data)
- Tests for the Ratio of Two Means (Normal Data)
- Tests for Fold Change of Two Means (Log-Normal Data)
- Tests for Two Means in a Cluster-Randomized Design
- Multiple Testing for Two Means
- Mixed Models Tests for Two Means in a Cluster-Randomized Design
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-1 Randomization)
- GEE Tests for Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Stratified Cluster-Randomized Design
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests

#### Z-Test (Inequality)

- Two-Sample Z-Tests Assuming Equal Variance
- Two-Sample Z-Tests Allowing Unequal Variance
- Multiple Testing for Two Means

#### Nonparametric

- Tests for Two Means (Simulation)
- Tests for Two Ordered Categorical Variables (Proportional Odds)
- Tests for Two Ordered Categorical Variables (Non-Proportional Odds, Wilcoxon-Mann-Whitney)
- Mann-Whitney U or Wilcoxon Rank-Sum Tests
- Mann-Whitney U or Wilcoxon Rank-Sum Tests (Simulation)
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Non-Inferiority
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Superiority by a Margin
- Equivalence Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means (Simulation) (Legacy)
- Group-Sequential Tests for Two Means Assuming Normality (Simulation) (Legacy)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation) (Legacy)
- Tests for Two Groups Assuming a Two-Part Model
- Tests for Two Groups Assuming a Two-Part Model with Detection Limits
- Multiple Testing for Two Means

#### Ratio Test

- Tests for the Ratio of Two Means (Log-Normal Data)
- Tests for the Ratio of Two Means (Normal Data)
- Non-Inferiority Tests for the Ratio of Two Means (Log-Normal Data)
- Non-Inferiority Tests for the Ratio of Two Means (Normal Data)
- Non-Inferiority Tests for the Ratio of Two Poisson Rates
- Non-Inferiority Tests for the Ratio of Two Negative Binomial Rates
- Superiority by a Margin Tests for the Ratio of Two Means (Log-Normal Data)
- Superiority by a Margin Tests for the Ratio of Two Means (Normal Data)
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for the Ratio of Two Negative Binomial Rates
- Equivalence Tests for the Ratio of Two Means (Normal Data)
- Equivalence Tests for the Ratio of Two Means (Log-Normal Data)
- Equivalence Tests for the Ratio of Two Means in a 2×2 Cross-Over Design (Normal Data)
- Equivalence Tests for the Ratio of Two Poisson Rates
- Equivalence Tests for the Ratio of Two Negative Binomial Rates
- Tests for Fold Change of Two Means (Log-Normal Data)

#### Non-Normal Data

- Tests for Two Means (Simulation)
- Mann-Whitney U or Wilcoxon Rank-Sum Tests
- Mann-Whitney U or Wilcoxon Rank-Sum Tests (Simulation)
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Non-Inferiority
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Superiority by a Margin
- Multiple Testing for Two Means
- Tests for Two Exponential Means
- Tests for the Difference Between Two Poisson Rates
- Tests for the Ratio of Two Poisson Rates
- Non-Inferiority Tests for the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates
- Equivalence Tests for the Ratio of Two Poisson Rates
- Non-Inferiority Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Tests for the Ratio of Two Negative Binomial Rates
- Non-Inferiority Tests for the Ratio of Two Negative Binomial Rates
- Superiority by a Margin Tests for the Ratio of Two Negative Binomial Rates
- Equivalence Tests for the Ratio of Two Negative Binomial Rates

#### Confidence Interval

- Confidence Intervals for the Difference Between Two Means
- Confidence Intervals for the Difference Between Two Means with Tolerance Probability

#### Non-Inferiority

- Two-Sample T-Tests for Non-Inferiority Assuming Equal Variance
- Two-Sample T-Tests for Non-Inferiority Allowing Unequal Variance
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Non-Inferiority
- Non-Inferiority Tests for the Ratio of Two Means (Log-Normal Data)
- Non-Inferiority Tests for the Ratio of Two Means (Normal Data)
- Non-Inferiority Tests for the Ratio of Two Poisson Rates
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Non-Inferiority Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Negative Binomial Rates
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates
- Non-Inferiority Tests for Two Means in a Cluster-Randomized Design
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Non-Inferiority
- Group-Sequential Non-Inferiority Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Non-Inferiority T-Tests for Two Means (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation) (Legacy)

#### Superiority by a Margin

- Two-Sample T-Tests for Superiority by a Margin Assuming Equal Variance
- Two-Sample T-Tests for Superiority by a Margin Allowing Unequal Variance
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Superiority by a Margin
- Superiority by a Margin Tests for the Ratio of Two Means (Log-Normal Data)
- Superiority by a Margin Tests for the Ratio of Two Means (Normal Data)
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Ratio of Two Negative Binomial Rates
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates
- Superiority by a Margin Tests for Two Means in a Cluster-Randomized Design
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Superiority by a Margin
- Group-Sequential Superiority by a Margin Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for Two Means (Simulation)

#### Equivalence

- Two-Sample T-Tests for Equivalence Assuming Equal Variance
- Two-Sample T-Tests for Equivalence Allowing Unequal Variance
- Equivalence Tests for Two Means (Simulation)
- Equivalence Tests for the Ratio of Two Means (Normal Data)
- Equivalence Tests for the Ratio of Two Means (Log-Normal Data)
- Equivalence Tests for the Ratio of Two Poisson Rates
- Equivalence Tests for the Ratio of Two Negative Binomial Rates
- Equivalence Tests for Two Means in a Cluster-Randomized Design

#### Cluster-Randomized

- Tests for Two Means in a Cluster-Randomized Design
- Tests for Two Means in a Stepped-Wedge Cluster-Randomized Design
- Non-Inferiority Tests for Two Means in a Cluster-Randomized Design
- Superiority by a Margin Tests for Two Means in a Cluster-Randomized Design
- Equivalence Tests for Two Means in a Cluster-Randomized Design
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-1 Randomization)
- GEE Tests for Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Stratified Cluster-Randomized Design
- Non-Inferiority Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design

#### Multicenter-Randomized

- Tests for Two Means in a Multicenter Randomized Design
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-1 Randomization)
- GEE Tests for Two Means in a Stratified Cluster-Randomized Design

#### Stratified

#### Repeated Measures

- Tests for Two Means in a Repeated Measures Design
- Tests for Two Groups of Pre-Post Scores
- GEE Tests for Two Means in a Split-Mouth Design

#### Group-Sequential

- Group-Sequential Tests for Two Means with Known Variances (Simulation)
- Group-Sequential T-Tests for Two Means (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Non-Inferiority T-Tests for Two Means (Simulation)
- Group-Sequential Superiority by a Margin Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means (Legacy)
- Group-Sequential Tests for Two Means (Simulation) (Legacy)
- Group-Sequential Tests for Two Means Assuming Normality (Simulation) (Legacy)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation) (Legacy)

#### Multiple Testing

#### Conditional Power

- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Superiority by a Margin

#### Pilot Studies

- Pilot Study Sample Size Rules of Thumb
- UCL of the Standard Deviation from a Pilot Study
- Sample Size of a Pilot Study using the Upper Confidence Limit of the SD
- Sample Size of a Pilot Study using the Non-Central t to Allow for Uncertainty in the SD
- Required Sample Size to Detect a Problem in a Pilot Study

### Two Means (Cluster-Randomized Designs)

#### Test (Inequality)

- Tests for Two Means in a Cluster-Randomized Design
- Tests for Two Means in a Stepped-Wedge Cluster-Randomized Design
- Tests for the Matched-Pair Difference of Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Cluster-Randomized Design

#### Non-Inferiority

#### Superiority by a Margin

#### Equivalence

#### Mixed Models (2-Level Hierarchical Design)

- Mixed Models Tests for Two Means in a Cluster-Randomized Design
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Means at the End of Follow-Up in a 2-Level Hierarchical Design

#### Mixed Models (3-Level Hierarchical Design)

- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Means at the End of Follow-Up in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Fixed Slopes (Level-3 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Random Slopes (Level-3 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Fixed Slopes (Level-2 Randomization)
- Mixed Models Tests for the Slope Difference in a 3-Level Hierarchical Design with Random Slopes (Level-2 Randomization)

#### GEE

- GEE Tests for Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Stratified Cluster-Randomized Design
- GEE Tests for Two Means in a Split-Mouth Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Continuous Outcome)

#### Stratified

### Multiple Means (Cluster-Randomized Designs)

#### Mixed Models (Interaction in a 2×2 Design)

- Mixed Models Tests for Interaction in a 2×2 Factorial 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Interaction in a 2×2 Factorial 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Interaction in a 2×2 Factorial 3-Level Hierarchical Design (Level-2 Randomization)

#### Mixed Models (Slope-Interaction in a 2×2 Design)

- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 2-Level Hierarchical Design with Fixed Slopes (Level-2 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 2-Level Hierarchical Design with Random Slopes (Level-2 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Fixed Slopes (Level-3 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Fixed Slopes (Level-2 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Random Slopes (Level-3 Randomization)
- Mixed Models Tests for Slope-Interaction in a 2×2 Factorial 3-Level Hierarchical Design with Random Slopes (Level-2 Randomization)

#### GEE Tests for Multiple Groups

- GEE Tests for Multiple Means in a Cluster-Randomized Design
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Continuous Outcome)

### Cross-Over (2×2) Design

#### Test (Inequality)

- Tests for the Difference Between Two Means in a 2×2 Cross-Over Design
- Tests for the Ratio of Two Means in a 2×2 Cross-Over Design (Log-Normal Data)
- Conditional Power and Sample Size Reestimation of Tests for Two Means in a 2×2 Cross-Over Design
- Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design

#### Non-Inferiority

- Non-Inferiority Tests for the Difference Between Two Means in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Ratio of Two Means in a 2×2 Cross-Over Design (Log-Normal Data)
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for Two Means in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design

#### Superiority by a Margin

- Superiority by a Margin Tests for the Difference of Two Means in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Ratio of Two Means in a 2×2 Cross-Over Design (Log-Normal Data)
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for Two Means in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design

#### Equivalence

- Equivalence Tests for the Difference Between Two Means in a 2×2 Cross-Over Design
- Equivalence Tests for the Ratio of Two Means in a 2×2 Cross-Over Design (Log-Normal Data)
- Equivalence Tests for the Ratio of Two Means in a 2×2 Cross-Over Design (Normal Data)
- Equivalence Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design

#### Conditional Power

- Conditional Power and Sample Size Reestimation of Tests for Two Means in a 2×2 Cross-Over Design
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for Two Means in a 2×2 Cross-Over Design
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for Two Means in a 2×2 Cross-Over Design

### Cross-Over (Higher-Order) Design

#### Test (Inequality)

- Tests for the Difference of Two Means in a Higher-Order Cross-Over Design
- Tests for the Ratio of Two Means in a Higher-Order Cross-Over Design (Log-Normal Data)
- MxM Cross-Over Designs
- M-Period Cross-Over Designs using Contrasts

#### Non-Inferiority

- Non-Inferiority Tests for the Difference of Two Means in a Higher-Order Cross-Over Design
- Non-Inferiority Tests for the Ratio of Two Means in a Higher-Order Cross-Over Design (Log-Normal Data)

#### Superiority by a Margin

- Superiority by a Margin Tests for the Difference of Two Means in a Higher-Order Cross-Over Design
- Superiority by a Margin Tests for the Ratio of Two Means in a Higher-Order Cross-Over Design (Log-Normal Data)

#### Equivalence

- Equivalence Tests for the Difference of Two Means in a Higher-Order Cross-Over Design
- Equivalence Tests for the Ratio of Two Means in a Higher-Order Cross-Over Design (Log-Normal Data)

### Cross-Over (Williams) Design

#### Test (Inequality)

#### Non-Inferiority

#### Superiority by a Margin

#### Equivalence

### One-Way Designs

#### ANOVA F-Test

- One-Way Analysis of Variance Assuming Equal Variances (F-Tests)
- One-Way Analysis of Variance F-Tests (Simulation)
- One-Way Analysis of Variance F-Tests using Effect Size
- Power Comparison of Tests of Means in One-Way Designs (Simulation)
- Non-Zero Null Tests for One-Way Analysis of Variance Assuming Equal Variances

#### Welch’s (Unequal Variances) F-Test

- One-Way Analysis of Variance Allowing Unequal Variances
- Equivalence Tests for One-Way Analysis of Variance Allowing Unequal Variances

#### Contrasts

- One-Way Analysis of Variance Contrasts Assuming Equal Variances
- One-Way Analysis of Variance Contrasts Allowing Unequal Variances
- Analysis of Covariance (ANCOVA) Contrasts
- One-Way Repeated Measures Contrasts
- Confidence Intervals for One-Way Repeated Measures Contrasts
- M-Period Cross-Over Designs using Contrasts

#### Multiple Comparisons

- Pair-Wise Multiple Comparisons (Simulation)
- Multiple Comparisons of Treatments vs. a Control (Simulation)
- Multiple Contrasts (Simulation)
- Multiple Comparisons
- Williams’ Test for the Minimum Effective Dose
- One-Way Analysis of Variance Contrasts Assuming Equal Variances
- One-Way Analysis of Variance Contrasts Allowing Unequal Variances
- Analysis of Covariance (ANCOVA) Contrasts
- One-Way Repeated Measures Contrasts
- Confidence Intervals for One-Way Repeated Measures Contrasts

#### Analysis of Covariance (ANCOVA)

- Analysis of Covariance (ANCOVA)
- Analysis of Covariance (ANCOVA) Contrasts
- Analysis of Covariance (ANCOVA) (Legacy)

#### Cross-Over Designs

- M-Period Cross-Over Designs using Contrasts
- Tests for the Difference of Two Means in a Higher-Order Cross-Over Design
- Tests for the Ratio of Two Means in a Higher-Order Cross-Over Design (Log-Normal Data)
- MxM Cross-Over Designs

#### Repeated Measures Designs

- One-Way Repeated Measures
- One-Way Repeated Measures Contrasts
- Confidence Intervals for One-Way Repeated Measures Contrasts
- MxM Cross-Over Designs

#### Three-Arm Designs

#### Equivalence

- Equivalence Tests for One-Way Analysis of Variance Assuming Equal Variances
- Equivalence Tests for One-Way Analysis of Variance Allowing Unequal Variances
- Studentized Range Tests for Equivalence
- Equivalence Tests for the Mean Ratio in a Three-Arm Trial (Normal Data) (Simulation)

#### Non-Zero Null

- Non-Zero Null Tests for One-Way Analysis of Variance Assuming Equal Variances
- Non-Zero Null Studentized Range Tests

#### Non-Normal Data

- One-Way Analysis of Variance F-Tests (Simulation)
- Kruskal-Wallis Tests (Simulation)
- Terry-Hoeffding Normal-Scores Tests of Means (Simulation)
- Van der Waerden Normal Quantiles Tests of Means (Simulation)
- Power Comparison of Tests of Means in One-Way Designs (Simulation)
- Pair-Wise Multiple Comparisons (Simulation)
- Multiple Comparisons of Treatments vs. a Control (Simulation)
- Multiple Contrasts (Simulation)

#### Studentized Range Test

- Studentized Range Tests
- Studentized Range Tests for Equivalence
- Non-Zero Null Studentized Range Tests

#### Nonparametric

- Kruskal-Wallis Tests (Simulation)
- Terry-Hoeffding Normal-Scores Tests of Means (Simulation)
- Van der Waerden Normal Quantiles Tests of Means (Simulation)
- Power Comparison of Tests of Means in One-Way Designs (Simulation)
- Pair-Wise Multiple Comparisons (Simulation)
- Multiple Comparisons of Treatments vs. a Control (Simulation)

#### GEE

- GEE Tests for Multiple Means in a Cluster-Randomized Design
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for Two Means in a Split-Mouth Design

### Multi-Factor Designs (ANOVA)

- Factorial Analysis of Variance
- Factorial Analysis of Variance using Effect Size
- 2×2 Factorial Analysis of Variance Allowing Unequal Variances
- Randomized Block Analysis of Variance
- Repeated Measures Analysis
- Mixed Models (Simulation)

### Multiple Comparisons

- Pair-Wise Multiple Comparisons (Simulation)
- Multiple Comparisons of Treatments vs. a Control (Simulation)
- Multiple Contrasts (Simulation)
- Multiple Comparisons
- Williams’ Test for the Minimum Effective Dose
- One-Way Analysis of Variance Contrasts Assuming Equal Variances
- One-Way Analysis of Variance Contrasts Allowing Unequal Variances
- Analysis of Covariance (ANCOVA) Contrasts
- One-Way Repeated Measures Contrasts
- Confidence Intervals for One-Way Repeated Measures Contrasts

### Analysis of Covariance (ANCOVA)

- Analysis of Covariance (ANCOVA)
- Analysis of Covariance (ANCOVA) Contrasts
- Analysis of Covariance (ANCOVA) (Legacy)

### Repeated Measures

#### Repeated Measures

- Repeated Measures Analysis
- Tests for Two Means in a Repeated Measures Design
- Tests for Two Groups of Pre-Post Scores
- One-Way Repeated Measures
- One-Way Repeated Measures Contrasts
- Confidence Intervals for One-Way Repeated Measures Contrasts

#### Cross-Over Designs

- MxM Cross-Over Designs
- M-Period Cross-Over Designs using Contrasts
- Tests for the Difference of Two Means in a Higher-Order Cross-Over Design
- Tests for the Ratio of Two Means in a Higher-Order Cross-Over Design (Log-Normal Data)

#### Mixed Models

- Mixed Models (Simulation)
- Mixed Models Tests for the Slope Difference in a 2-Level Hierarchical Design with Fixed Slopes
- Mixed Models Tests for the Slope Difference in a 2-Level Hierarchical Design with Random Slopes

#### GEE

- GEE Tests for Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Split-Mouth Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Count Outcome)

### Mixed Models

#### General

#### Two Means (Multicenter Randomized Design)

#### Two Means (2-Level Hierarchical Design)

- Mixed Models Tests for Two Means in a Cluster-Randomized Design
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Means at the End of Follow-Up in a 2-Level Hierarchical Design

#### Two Means (3-Level Hierarchical Design)

- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-1 Randomization)

#### 2×2 Factorial (2-Level Hierarchical Design)

- Mixed Models Tests for Interaction in a 2×2 Factorial 2-Level Hierarchical Design (Level-1 Randomization)

#### 2×2 Factorial (3-Level Hierarchical Design)

- Mixed Models Tests for Interaction in a 2×2 Factorial 3-Level Hierarchical Design (Level-1 Randomization)

#### Slope Difference (2-Level Hierarchical Design)

- Mixed Models Tests for the Slope Difference in a 2-Level Hierarchical Design with Fixed Slopes
- Mixed Models Tests for the Slope Difference in a 2-Level Hierarchical Design with Random Slopes

#### Slope Difference (3-Level Hierarchical Design)

### GEE

- GEE Tests for Two Means in a Cluster-Randomized Design
- GEE Tests for Two Means in a Stratified Cluster-Randomized Design
- GEE Tests for Two Means in a Split-Mouth Design
- GEE Tests for Multiple Means in a Cluster-Randomized Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Continuous Outcome)
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for Multiple Poisson Rates in a Cluster-Randomized Design

### Multivariate Means

### Nonparametric

#### One Mean

- Tests for One Mean (Simulation)
- Wilcoxon Signed-Rank Tests
- Wilcoxon Signed-Rank Tests for Non-Inferiority
- Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Multiple Testing for One Mean (One-Sample or Paired Data)
- Confidence Intervals for a Percentile of a Normal Distribution
- Confidence Intervals for a Percentile of a Normal Distribution using Assurance Probability
- Confidence Intervals for a Percentile of a Normal Distribution using Expected Width
- Confidence Intervals for Regression-Based Reference Limits using Assurance Probability
- Confidence Intervals for Regression-Based Reference Limits using Expected Relative Precision

#### Paired Means

- Tests for Paired Means (Simulation)
- Paired Wilcoxon Signed-Rank Tests
- Paired Wilcoxon Signed-Rank Tests for Non-Inferiority
- Paired Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Equivalence Tests for Paired Means (Simulation)
- Multiple Testing for One Mean (One-Sample or Paired Data)
- Tests for Paired Means (Simulation) (Legacy)

#### Two Independent Means

- Tests for Two Means (Simulation)
- Mann-Whitney U or Wilcoxon Rank-Sum Tests
- Mann-Whitney U or Wilcoxon Rank-Sum Tests (Simulation)
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Non-Inferiority
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Superiority by a Margin
- Equivalence Tests for Two Means (Simulation)
- Tests for Two Groups Assuming a Two-Part Model
- Tests for Two Groups Assuming a Two-Part Model with Detection Limits
- Multiple Testing for Two Means

#### Single-Factor

- Kruskal-Wallis Tests (Simulation)
- Terry-Hoeffding Normal-Scores Tests of Means (Simulation)
- Van der Waerden Normal Quantiles Tests of Means (Simulation)
- Power Comparison of Tests of Means in One-Way Designs (Simulation)

#### Multiple Comparisons

- Pair-Wise Multiple Comparisons (Simulation)
- Multiple Comparisons of Treatments vs. a Control (Simulation)
- Multiple Contrasts (Simulation)

### Tools

- Data Simulator
- Standard Deviation of Means Calculator
- Standard Deviation Estimator
- Probability Calculator

## Method Comparison

- Bland-Altman Method for Assessing Agreement in Method Comparison Studies
- Exact Method for Assessing Agreement in Method Comparison Studies
- Confidence Intervals for the Bland-Altman Range of Agreement using Assurance Probability
- Confidence Intervals for the Bland-Altman Range of Agreement using Expected Half-Width

## Microarray

- Multiple Testing for One Mean (One-Sample or Paired Data)
- Multiple Testing for Two Means
- Tests for Fold Change of Two Means (Log-Normal Data)
- Mendelian Randomization with a Binary Outcome

## Mixed Models

### Means

#### General

#### Two Means (Multicenter Randomized Design)

#### Two Means (2-Level Hierarchical Design)

- Mixed Models Tests for Two Means in a Cluster-Randomized Design
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 2-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Means at the End of Follow-Up in a 2-Level Hierarchical Design

#### Two Means (3-Level Hierarchical Design)

- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Means in a 3-Level Hierarchical Design (Level-1 Randomization)

#### 2×2 Factorial (2-Level Hierarchical Design)

- Mixed Models Tests for Interaction in a 2×2 Factorial 2-Level Hierarchical Design (Level-1 Randomization)

#### 2×2 Factorial (3-Level Hierarchical Design)

- Mixed Models Tests for Interaction in a 2×2 Factorial 3-Level Hierarchical Design (Level-1 Randomization)

#### Slope Difference (2-Level Hierarchical Design)

- Mixed Models Tests for the Slope Difference in a 2-Level Hierarchical Design with Fixed Slopes
- Mixed Models Tests for the Slope Difference in a 2-Level Hierarchical Design with Random Slopes

#### Slope Difference (3-Level Hierarchical Design)

### Proportions

#### Two Proportions (2-Level Hierarchical Design)

- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-1 Randomization)

#### Two Proportions (3-Level Hierarchical Design)

- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-1 Randomization)

## Non-Inferiority

### Means

#### One Mean

- One-Sample Z-Tests for Non-Inferiority
- One-Sample T-Tests for Non-Inferiority
- Wilcoxon Signed-Rank Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Non-Inferiority
- Group-Sequential Non-Inferiority Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Non-Inferiority T-Tests for One Mean (Simulation)

#### Paired Means

- Paired Z-Tests for Non-Inferiority
- Paired T-Tests for Non-Inferiority
- Paired Wilcoxon Signed-Rank Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Non-Inferiority

#### Two Independent Means

- Two-Sample T-Tests for Non-Inferiority Assuming Equal Variance
- Two-Sample T-Tests for Non-Inferiority Allowing Unequal Variance
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Non-Inferiority
- Non-Inferiority Tests for the Ratio of Two Means (Log-Normal Data)
- Non-Inferiority Tests for the Ratio of Two Means (Normal Data)
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Non-Inferiority
- Group-Sequential Non-Inferiority Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Non-Inferiority T-Tests for Two Means (Simulation)

#### Two Means (Cluster-Randomized)

#### Cross-Over (2×2) Design

- Non-Inferiority Tests for the Difference Between Two Means in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Ratio of Two Means in a 2×2 Cross-Over Design (Log-Normal Data)

#### Cross-Over (Higher-Order) Design

- Non-Inferiority Tests for the Difference of Two Means in a Higher-Order Cross-Over Design
- Non-Inferiority Tests for the Ratio of Two Means in a Higher-Order Cross-Over Design (Log-Normal Data)

#### Cross-Over (Williams) Design

#### Group-Sequential

- Group-Sequential Non-Inferiority Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Non-Inferiority T-Tests for Two Means (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation) (Legacy)
- Group-Sequential Non-Inferiority Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Non-Inferiority T-Tests for One Mean (Simulation)

#### Conditional Power

- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Non-Inferiority

### Proportions

#### One Proportion

- Non-Inferiority Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for One Proportion
- Group-Sequential Non-Inferiority Tests for One Proportion (Simulation)
- Group-Sequential Superiority by a Margin Tests for One Proportion (Simulation)

#### Two Correlated (Paired) Proportions

- Non-Inferiority Tests for the Difference Between Two Correlated Proportions
- Non-Inferiority Tests for the Ratio of Two Correlated Proportions

#### Two Independent Proportions

- Non-Inferiority Tests for the Difference Between Two Proportions
- Non-Inferiority Tests for the Ratio of Two Proportions
- Non-Inferiority Tests for the Odds Ratio of Two Proportions
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for Two Proportions
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Non-Inferiority Tests for Vaccine Efficacy with Extremely Low Incidence
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Ratio of Two Means
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Difference of Two Means
- Tests for Vaccine Efficacy with Extremely Low Incidence
- Group-Sequential Non-Inferiority Tests for Two Proportions (Simulation)

#### Two Proportions (Cluster-Randomized)

- Non-Inferiority Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Proportions in a Cluster-Randomized Design

#### Cross-Over (2×2) Design

- Non-Inferiority Tests for the Difference of Two Proportions in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Odds Ratio of Two Proportions in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design

#### Cross-Over (Williams) Design

#### Group-Sequential

- Group-Sequential Non-Inferiority Tests for One Proportion (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Ratio of Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Odds Ratio of Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Difference of Two Proportions (Simulation) (Legacy)

#### Conditional Power

- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for Two Proportions

#### Vaccine Efficacy

- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Non-Inferiority Tests for Vaccine Efficacy with Extremely Low Incidence

### Rates and Counts

- Non-Inferiority Tests for the Ratio of Two Poisson Rates
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Ratio of Two Negative Binomial Rates
- Non-Inferiority Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates

### Survival

- Non-Inferiority Logrank Tests
- Non-Inferiority Tests for Two Survival Curves Using Cox’s Proportional Hazards Model
- Non-Inferiority Tests for the Difference of Two Hazard Rates Assuming an Exponential Model
- Non-Inferiority Tests for Vaccine Efficacy using the Hazard Ratio (Cox’s Proportional Hazards Model)
- Conditional Power and Sample Size Reestimation of Non-Inferiority Logrank Tests
- Group-Sequential Non-Inferiority Tests for Two Hazard Rates (Simulation)

### Variances

- Non-Inferiority Tests for the Ratio of Two Variances
- Non-Inferiority Tests for the Ratio of Two Within-Subject Variances in a Parallel Design
- Non-Inferiority Tests for the Ratio of Two Within-Subject Variances in a 2×2M Replicated Cross-Over Design
- Non-Inferiority Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Non-Inferiority Tests for Two Between Variances in a Replicated Design
- Non-Inferiority Tests for Two Between-Subject Variances in a 2×2M Replicated Cross-Over Design
- Non-Inferiority Tests for Two Total Variances in a Replicated Design
- Non-Inferiority Tests for Two Total Variances in a 2×2 Cross-Over Design
- Non-Inferiority Tests for Two Total Variances in a 2×2M Replicated Cross-Over Design

## Nonparametric

### One Mean

- Tests for One Mean (Simulation)
- Wilcoxon Signed-Rank Tests
- Wilcoxon Signed-Rank Tests for Non-Inferiority
- Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Multiple Testing for One Mean (One-Sample or Paired Data)
- Confidence Intervals for a Percentile of a Normal Distribution
- Confidence Intervals for a Percentile of a Normal Distribution using Assurance Probability
- Confidence Intervals for a Percentile of a Normal Distribution using Expected Width
- Confidence Intervals for Regression-Based Reference Limits using Assurance Probability
- Confidence Intervals for Regression-Based Reference Limits using Expected Relative Precision

### Paired Means

- Tests for Paired Means (Simulation)
- Paired Wilcoxon Signed-Rank Tests
- Paired Wilcoxon Signed-Rank Tests for Non-Inferiority
- Paired Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Equivalence Tests for Paired Means (Simulation)
- Multiple Testing for One Mean (One-Sample or Paired Data)
- Tests for Paired Means (Simulation) (Legacy)

### Two Independent Means

- Tests for Two Means (Simulation)
- Tests for Two Ordered Categorical Variables (Proportional Odds)
- Tests for Two Ordered Categorical Variables (Non-Proportional Odds, Wilcoxon-Mann-Whitney)
- Mann-Whitney U or Wilcoxon Rank-Sum Tests
- Mann-Whitney U or Wilcoxon Rank-Sum Tests (Simulation)
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Non-Inferiority
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Superiority by a Margin
- Equivalence Tests for Two Means (Simulation)
- Tests for Two Groups Assuming a Two-Part Model
- Tests for Two Groups Assuming a Two-Part Model with Detection Limits
- Multiple Testing for Two Means

### Single-Factor

- Kruskal-Wallis Tests (Simulation)
- Terry-Hoeffding Normal-Scores Tests of Means (Simulation)
- Van der Waerden Normal Quantiles Tests of Means (Simulation)
- Power Comparison of Tests of Means in One-Way Designs (Simulation)

### Multiple Comparisons

- Pair-Wise Multiple Comparisons (Simulation)
- Multiple Comparisons of Treatments vs. a Control (Simulation)

### Correlation

- Spearman’s Rank Correlation Tests (Simulation)
- Kendall’s Tau-b Correlation Tests (Simulation)
- Power Comparison of Correlation Tests (Simulation)

### Variances

- Brown-Forsythe Test of Variances (Simulation)
- Conover Test of Variances (Simulation)
- Power Comparison of Tests of Variances (Simulation)

### Reference Intervals

### Tolerance Intervals

## Normality

- Normality Tests (Simulation)
- Confidence Intervals for a Percentile of a Normal Distribution
- Confidence Intervals for a Percentile of a Normal Distribution using Assurance Probability
- Confidence Intervals for a Percentile of a Normal Distribution using Expected Width

## Pilot Studies

- Pilot Study Sample Size Rules of Thumb
- UCL of the Standard Deviation from a Pilot Study
- Sample Size of a Pilot Study using the Upper Confidence Limit of the SD
- Sample Size of a Pilot Study using the Non-Central t to Allow for Uncertainty in the SD
- Required Sample Size to Detect a Problem in a Pilot Study

## Post-Marketing Surveillance

- Tests for One Poisson Rate with No Background Incidence (Post-Marketing Surveillance)
- Tests for One Poisson Rate with Known Background Incidence (Post-Marketing Surveillance)
- Tests for Two Poisson Rates with Background Incidence Estimated by the Control (Post-Marketing Surveillance)
- Tests for Two Poisson Rates in a Matched Case-Control Design (Post-Marketing Surveillance)

## Proportions

### One Proportion

#### Test (Inequality)

- Tests for One Proportion
- Tests for One Proportion using Effect Size
- Acceptance Sampling for Attributes
- Reliability Demonstration Tests of One Proportion
- Reliability Demonstration Tests of One Proportion with Adverse Events
- Conditional Power and Sample Size Reestimation of Tests for One Proportion

#### Confidence Interval

- Confidence Intervals for One Proportion
- Confidence Intervals for One Proportion from a Finite Population
- Confidence Intervals for One Proportion in a Stratified Design
- Confidence Intervals for One Proportion in a Cluster-Randomized Design
- Confidence Intervals for One Proportion in a Stratified Cluster-Randomized Design

#### Non-Inferiority

- Non-Inferiority Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for One Proportion
- Group-Sequential Non-Inferiority Tests for One Proportion (Simulation)

#### Superiority by a Margin

- Superiority by a Margin Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for One Proportion
- Group-Sequential Superiority by a Margin Tests for One Proportion (Simulation)

#### Equivalence

#### Group-Sequential

- Group-Sequential Tests for One Proportion (Simulation)
- Group-Sequential Non-Inferiority Tests for One Proportion (Simulation)
- Group-Sequential Superiority by a Margin Tests for One Proportion (Simulation)
- Group-Sequential Tests for One Proportion in a Fleming Design
- Single-Stage Phase II Clinical Trials
- Two-Stage Designs for Tests of One Proportion (Simon)
- Three-Stage Phase II Clinical Trials

#### Rare Events

- Reliability Demonstration Tests of One Proportion
- Reliability Demonstration Tests of One Proportion with Adverse Events

#### Conditional Power

- Conditional Power and Sample Size Reestimation of Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for One Proportion

### Two Correlated (Paired) Proportions

#### Test (Inequality)

- Tests for Two Correlated Proportions (McNemar Test)
- Tests for Two Correlated Proportions in a Matched Case-Control Design
- Tests for Two Correlated Proportions with Incomplete Observations
- Tests for the Matched-Pair Difference of Two Proportions in a Cluster-Randomized Design
- Tests for the Odds Ratio in a Matched Case-Control Design with a Binary X
- Tests for the Odds Ratio in a Matched Case-Control Design with a Quantitative X
- GEE Tests for Two Correlated Proportions with Dropout

#### Non-Inferiority

- Non-Inferiority Tests for the Difference Between Two Correlated Proportions
- Non-Inferiority Tests for the Ratio of Two Correlated Proportions

#### Equivalence

- Equivalence Tests for the Difference Between Two Correlated Proportions
- Equivalence Tests for the Ratio of Two Correlated Proportions

#### Confidence Interval

### Two Independent Proportions

#### Test (Inequality)

- Tests for Two Proportions
- Tests for Two Proportions using Effect Size
- Fisher’s Exact Test for Two Proportions
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Ratio of Two Means
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Difference of Two Means
- Tests for Vaccine Efficacy with Extremely Low Incidence
- Tests for Two Groups Assuming a Two-Part Model
- Tests for Two Groups Assuming a Two-Part Model with Detection Limits
- Conditional Power and Sample Size Reestimation of Tests for the Difference Between Two Proportions

#### Test (Non-Zero Null)

- Non-Zero Null Tests for the Difference Between Two Proportions
- Non-Unity Null Tests for the Ratio of Two Proportions
- Non-Unity Null Tests for the Odds Ratio of Two Proportions

#### Confidence Interval

- Confidence Intervals for the Difference Between Two Proportions
- Confidence Intervals for the Ratio of Two Proportions
- Confidence Intervals for the Odds Ratio of Two Proportions
- Confidence Intervals for the Odds Ratio of Two Proportions using an Unmatched Case-Control Design
- Confidence Intervals for Vaccine Efficacy using a Cohort Design
- Confidence Intervals for Vaccine Efficacy using an Unmatched Case-Control Design

#### Non-Inferiority

- Non-Inferiority Tests for the Difference Between Two Proportions
- Non-Inferiority Tests for the Ratio of Two Proportions
- Non-Inferiority Tests for the Odds Ratio of Two Proportions
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for Two Proportions
- Group-Sequential Non-Inferiority Tests for Two Proportions (Simulation)
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Non-Inferiority Tests for Vaccine Efficacy with Extremely Low Incidence

#### Superiority by a Margin

- Superiority by a Margin Tests for the Difference Between Two Proportions
- Superiority by a Margin Tests for the Ratio of Two Proportions
- Superiority by a Margin Tests for the Odds Ratio of Two Proportions
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for Two Proportions
- Group-Sequential Superiority by a Margin Tests for Two Proportions (Simulation)
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Superiority by a Margin Tests for Vaccine Efficacy with Extremely Low Incidence

#### Equivalence

- Equivalence Tests for the Difference Between Two Proportions
- Equivalence Tests for the Ratio of Two Proportions
- Equivalence Tests for the Odds Ratio of Two Proportions

#### Repeated Measures

- Tests for Two Proportions in a Repeated Measures Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for Two Proportions in a Split-Mouth Design

#### Stratified (Cochran-Mantel-Haenszel Test)

- Tests for Two Proportions in a Stratified Design (Cochran-Mantel-Haenszel Test)
- Tests for Two Proportions in a Stratified Cluster-Randomized Design (Cochran-Mantel-Haenszel Test)

#### Group-Sequential

- Group-Sequential Tests for Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Ratio of Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Odds Ratio of Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for the Ratio of Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for the Odds Ratio of Two Proportions (Simulation)
- Group-Sequential Tests for Two Proportions (Legacy)
- Group-Sequential Tests for Two Proportions (Simulation) (Legacy)
- Group-Sequential Non-Inferiority Tests for the Difference of Two Proportions (Simulation) (Legacy)
- Group-Sequential Superiority by a Margin Tests for the Difference of Two Proportions (Simulation) (Legacy)

#### Conditional Power

- Conditional Power and Sample Size Reestimation of Tests for the Difference Between Two Proportions
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for Two Proportions
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for Two Proportions

#### Vaccine Efficacy

- Confidence Intervals for Vaccine Efficacy using a Cohort Design
- Confidence Intervals for Vaccine Efficacy using an Unmatched Case-Control Design
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Ratio of Two Means
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Difference of Two Means
- Tests for Vaccine Efficacy with Extremely Low Incidence
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Non-Inferiority Tests for Vaccine Efficacy with Extremely Low Incidence
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Superiority by a Margin Tests for Vaccine Efficacy with Extremely Low Incidence

### Two Proportions (Cluster-Randomized Designs)

#### Test (Inequality)

- Tests for Two Proportions in a Cluster-Randomized Design
- Tests for Two Proportions in a Stepped-Wedge Cluster-Randomized Design
- Tests for the Matched-Pair Difference of Two Proportions in a Cluster-Randomized Design
- GEE Tests for Two Proportions in a Split-Mouth Design

#### Test (Non-Zero Null)

- Non-Zero Null Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Non-Unity Null Tests for the Ratio of Two Proportions in a Cluster-Randomized Design

#### Non-Inferiority

- Non-Inferiority Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Proportions in a Cluster-Randomized Design

#### Superiority by a Margin

- Superiority by a Margin Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Ratio of Two Proportions in a Cluster-Randomized Design

#### Equivalence

- Equivalence Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Equivalence Tests for the Ratio of Two Proportions in a Cluster-Randomized Design

#### Mixed Models (2-Level Hierarchical Design)

- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-1 Randomization)

#### Mixed Models (3-Level Hierarchical Design)

- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-1 Randomization)

#### GEE

- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for Two Proportions in a Split-Mouth Design

#### Vaccine Efficacy

### Multiple Proportions

- Tests for Multiple Proportions in a One-Way Design
- Cochran-Armitage Test for Trend in Proportions
- Multiple Comparisons of Proportions for Treatments vs. a Control
- Tests for Multiple Correlated Proportions (McNemar-Bowker Test of Symmetry)
- Randomized Phase II Selection Designs for Binary Data (Simon)
- Tests for Two Ordered Categorical Variables (Proportional Odds)
- Tests for Two Ordered Categorical Variables (Non-Proportional Odds, Wilcoxon-Mann-Whitney)
- Dose-Finding using the Bayesian Continual Reassessment Method (CRM)

### Multiple Proportions (Cluster-Randomized Designs)

- GEE Tests for Multiple Proportions in a Cluster-Randomized Design
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Binary Outcome)

### Cross-Over (2×2) Design

#### Test (Inequality)

- Tests for the Difference of Two Proportions in a 2×2 Cross-Over Design
- Tests for the Odds Ratio of Two Proportions in a 2×2 Cross-Over Design
- Tests for Two Correlated Proportions (McNemar Test)
- Tests for Two Correlated Proportions with Incomplete Observations
- GEE Tests for Two Correlated Proportions with Dropout
- Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design

#### Non-Inferiority

- Non-Inferiority Tests for the Difference of Two Proportions in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Odds Ratio of Two Proportions in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design

#### Superiority by a Margin

- Superiority by a Margin Tests for the Difference of Two Proportions in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Odds Ratio of Two Proportions in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design

#### Equivalence

- Equivalence Tests for the Difference of Two Proportions in a 2×2 Cross-Over Design
- Equivalence Tests for the Odds Ratio of Two Proportions in a 2×2 Cross-Over Design
- Equivalence Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design

### Cross-Over (Williams) Design

#### Test (Inequality)

#### Non-Inferiority

#### Superiority by a Margin

#### Equivalence

### Contingency Table (Chi-Square Tests)

### Repeated Measures

- Tests for Two Proportions in a Repeated Measures Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for Two Proportions in a Split-Mouth Design
- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-1 Randomization)

### GEE

- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for Two Correlated Proportions with Dropout
- GEE Tests for Two Proportions in a Split-Mouth Design
- GEE Tests for Multiple Proportions in a Cluster-Randomized Design

### Mixed Models

#### Two Proportions (2-Level Hierarchical Design)

- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-1 Randomization)

#### Two Proportions (3-Level Hierarchical Design)

- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-1 Randomization)

### Multiple Comparisons

### Stratified

- Confidence Intervals for One Proportion in a Stratified Design
- Confidence Intervals for One Proportion in a Stratified Cluster-Randomized Design
- Tests for Two Proportions in a Stratified Design (Cochran-Mantel-Haenszel Test)
- Tests for Two Proportions in a Stratified Cluster-Randomized Design (Cochran-Mantel-Haenszel Test)

### Trend

### Vaccine Efficacy

- Confidence Intervals for Vaccine Efficacy using a Cohort Design
- Confidence Intervals for Vaccine Efficacy using an Unmatched Case-Control Design
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Ratio of Two Means
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Difference of Two Means
- Tests for Vaccine Efficacy with Extremely Low Incidence
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Non-Inferiority Tests for Vaccine Efficacy with Extremely Low Incidence
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Superiority by a Margin Tests for Vaccine Efficacy with Extremely Low Incidence

### Ordered Categorical Data

- Tests for Two Ordered Categorical Variables (Proportional Odds)
- Tests for Two Ordered Categorical Variables (Non-Proportional Odds, Wilcoxon-Mann-Whitney)
- Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design
- Equivalence Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design
- Tests for Two Ordered Categorical Variables (Legacy)

### Logistic Regression

#### Binary X (Wald Test)

- Tests for the Odds Ratio in Logistic Regression with One Binary X (Wald Test)
- Tests for the Odds Ratio in Logistic Regression with One Binary X and Other Xs (Wald Test)
- Tests for the Odds Ratio in Logistic Regression with Two Binary X’s (Wald Test)
- Tests for the Interaction Odds Ratio in Logistic Regression with Two Binary X’s (Wald Test)
- Tests for Two Ordered Categorical Variables (Proportional Odds)
- Tests for Two Ordered Categorical Variables (Non-Proportional Odds, Wilcoxon-Mann-Whitney)
- Logistic Regression (Legacy)

#### Binary X (Confidence Interval)

- Confidence Intervals for the Odds Ratio in Logistic Regression with One Binary X
- Confidence Intervals for the Odds Ratio in Logistic Regression with Two Binary X’s
- Confidence Intervals for the Interaction Odds Ratio in Logistic Regression with Two Binary X’s

#### Continuous X’s (Wald Test)

- Tests for the Odds Ratio in Logistic Regression with One Normal X (Wald Test)
- Tests for the Odds Ratio in Logistic Regression with One Normal X and Other Xs (Wald Test)
- Logistic Regression (Legacy)

#### Conditional Logistic Regression

- Tests for the Odds Ratio in a Matched Case-Control Design with a Binary X
- Tests for the Odds Ratio in a Matched Case-Control Design with a Quantitative X

#### GEE Logistic Regression

- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for Two Proportions in a Split-Mouth Design
- GEE Tests for Multiple Proportions in a Cluster-Randomized Design

#### Mixed-Effects Logistic Regression

- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-1 Randomization)

#### Ordinal Logistic Regression

- Tests for Two Ordered Categorical Variables (Proportional Odds)
- Tests for Two Ordered Categorical Variables (Non-Proportional Odds, Wilcoxon-Mann-Whitney)

#### Mediation Analysis

#### Multiple Groups

- Tests for Multiple Proportions in a One-Way Design
- GEE Tests for Multiple Proportions in a Cluster-Randomized Design
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Binary Outcome)

### Kappa Rater Agreement

### Sensitivity and Specificity

- Tests for One-Sample Sensitivity and Specificity
- Tests for Paired Sensitivities
- Tests for Two Independent Sensitivities
- Confidence Intervals for One-Sample Sensitivity
- Confidence Intervals for One-Sample Specificity
- Confidence Intervals for One-Sample Sensitivity and Specificity

### Tools

- Chi-Square Effect Size Estimator
- Odds Ratio and Proportions Conversion Tool
- Kappa Estimator
- Probability Calculator

## Quality Control

- Acceptance Sampling for Attributes
- Operating Characteristic Curves for Acceptance Sampling for Attributes
- Control Charts for Means (Simulation)
- Control Charts for Variability (Simulation)
- Confidence Intervals for Cp
- Confidence Intervals for Cpk

## Rates and Counts

### Test (Inequality)

- Tests for One Poisson Rate
- Tests for the Difference Between Two Poisson Rates
- Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design with Adjustment for Varying Cluster Sizes
- Tests for the Ratio of Two Poisson Rates
- Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design
- Tests for Vaccine Efficacy with Extremely Low Incidence
- Tests for the Ratio of Two Negative Binomial Rates

### Non-Inferiority

- Non-Inferiority Tests for the Ratio of Two Poisson Rates
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Ratio of Two Negative Binomial Rates
- Non-Inferiority Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates

### Superiority by a Margin

- Superiority by a Margin Tests for the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Ratio of Two Negative Binomial Rates
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates

### Equivalence

- Equivalence Tests for the Ratio of Two Poisson Rates
- Equivalence Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design
- Equivalence Tests for the Ratio of Two Negative Binomial Rates

### Cluster-Randomized Designs

- Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design with Adjustment for Varying Cluster Sizes
- Non-Inferiority Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Tests for Two Poisson Rates in a Stepped-Wedge Cluster-Randomized Design
- Tests for the Matched-Pair Difference of Two Event Rates in a Cluster-Randomized Design
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for Multiple Poisson Rates in a Cluster-Randomized Design

### Cross-Over (2×2) Designs

#### Test (Inequality)

#### Non-Inferiority

#### Superiority by a Margin

#### Equivalence

### GEE

- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for Multiple Poisson Rates in a Cluster-Randomized Design

### One-Way Designs

### Poisson Regression

- Poisson Regression
- Tests for Multiple Poisson Rates in a One-Way Design
- Tests of Mediation Effect in Poisson Regression
- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for Multiple Poisson Rates in a Cluster-Randomized Design

### Post-Marketing Surveillance

- Tests for One Poisson Rate with No Background Incidence (Post-Marketing Surveillance)
- Tests for One Poisson Rate with Known Background Incidence (Post-Marketing Surveillance)
- Tests for Two Poisson Rates with Background Incidence Estimated by the Control (Post-Marketing Surveillance)
- Tests for Two Poisson Rates in a Matched Case-Control Design (Post-Marketing Surveillance)

### Poisson Rates

#### One Rate

- Tests for One Poisson Rate
- Tests for One Poisson Rate with No Background Incidence (Post-Marketing Surveillance)
- Tests for One Poisson Rate with Known Background Incidence (Post-Marketing Surveillance)

#### Two Rates

- Tests for the Difference Between Two Poisson Rates
- Tests for the Ratio of Two Poisson Rates
- Tests for Vaccine Efficacy with Extremely Low Incidence
- Non-Inferiority Tests for the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates
- Equivalence Tests for the Ratio of Two Poisson Rates
- Tests for Two Poisson Rates with Background Incidence Estimated by the Control (Post-Marketing Surveillance)
- Tests for Two Poisson Rates in a Matched Case-Control Design (Post-Marketing Surveillance)
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates

#### Two Rates (Cluster-Randomized Design)

- Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for the Difference Between Two Poisson Rates in a Cluster-Randomized Design
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Tests for Two Poisson Rates in a Stepped-Wedge Cluster-Randomized Design
- Tests for the Matched-Pair Difference of Two Event Rates in a Cluster-Randomized Design

#### Two Rates (2×2 Cross-Over Design)

- Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design
- Non-Inferiority Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design
- Equivalence Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design

#### Multiple Rates

#### GEE (Repeated Measures Design)

- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for Multiple Poisson Rates in a Cluster-Randomized Design

#### Poisson Regression

#### Vaccine Efficacy

- Tests for Vaccine Efficacy with Extremely Low Incidence
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates

### Negative Binomal Rates

- Tests for the Ratio of Two Negative Binomial Rates
- Non-Inferiority Tests for the Ratio of Two Negative Binomial Rates
- Superiority by a Margin Tests for the Ratio of Two Negative Binomial Rates
- Equivalence Tests for the Ratio of Two Negative Binomial Rates
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates

### Vaccine Efficacy

- Tests for Vaccine Efficacy with Extremely Low Incidence
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates

## Regression

### Simple Linear Regression

#### Simple Linear Regression

- Simple Linear Regression
- Simple Linear Regression using R²
- Non-Zero Null Tests for Simple Linear Regression
- Non-Zero Null Tests for Simple Linear Regression using ρ²
- Non-Inferiority Tests for Simple Linear Regression
- Superiority by a Margin Tests for Simple Linear Regression
- Equivalence Tests for Simple Linear Regression

#### Difference

- Tests for the Difference Between Two Linear Regression Slopes
- Tests for the Difference Between Two Linear Regression Intercepts

#### Confidence Interval

### Multiple Regression

#### Multiple Regression

#### Effect Size

#### Analysis of Covariance (ANCOVA)

- Analysis of Covariance (ANCOVA)
- Analysis of Covariance (ANCOVA) Contrasts
- Analysis of Covariance (ANCOVA) (Legacy)

#### Mediation Analysis

- Tests of Mediation Effect using the Sobel Test
- Tests of Mediation Effect in Linear Regression
- Joint Tests of Mediation in Linear Regression with Continuous Variables

### Cox Regression

#### Cox Regression

#### Mediation Analysis

### Poisson Regression

#### Poisson Regression

#### GEE Poisson Regression

- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the Slope of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Count Outcome)
- GEE Tests for Multiple Poisson Rates in a Cluster-Randomized Design

#### Mediation Analysis

#### Multiple Groups

### Logistic Regression

#### Binary X (Wald Test)

- Tests for the Odds Ratio in Logistic Regression with One Binary X (Wald Test)
- Tests for the Odds Ratio in Logistic Regression with One Binary X and Other Xs (Wald Test)
- Tests for the Odds Ratio in Logistic Regression with Two Binary X’s (Wald Test)
- Tests for the Interaction Odds Ratio in Logistic Regression with Two Binary X’s (Wald Test)
- Tests for Two Ordered Categorical Variables (Proportional Odds)
- Tests for Two Ordered Categorical Variables (Non-Proportional Odds, Wilcoxon-Mann-Whitney)
- Logistic Regression (Legacy)

#### Binary X (Confidence Interval)

- Confidence Intervals for the Odds Ratio in Logistic Regression with One Binary X
- Confidence Intervals for the Odds Ratio in Logistic Regression with Two Binary X’s
- Confidence Intervals for the Interaction Odds Ratio in Logistic Regression with Two Binary X’s

#### Continuous X’s (Wald Test)

- Tests for the Odds Ratio in Logistic Regression with One Normal X (Wald Test)
- Tests for the Odds Ratio in Logistic Regression with One Normal X and Other Xs (Wald Test)
- Logistic Regression (Legacy)

#### Conditional Logistic Regression

- Tests for the Odds Ratio in a Matched Case-Control Design with a Binary X
- Tests for the Odds Ratio in a Matched Case-Control Design with a Quantitative X

#### GEE Logistic Regression

- GEE Tests for the Slope of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Two Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for the TAD of Multiple Groups in a Repeated Measures Design (Binary Outcome)
- GEE Tests for Multiple Proportions in a Cluster-Randomized Design

#### Mixed-Effects Logistic Regression

- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 2-Level Hierarchical Design (Level-1 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-3 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-2 Randomization)
- Mixed Models Tests for Two Proportions in a 3-Level Hierarchical Design (Level-1 Randomization)

#### Ordinal Logistic Regression

- Tests for Two Ordered Categorical Variables (Proportional Odds)
- Tests for Two Ordered Categorical Variables (Non-Proportional Odds, Wilcoxon-Mann-Whitney)

#### Mediation Analysis

#### Multiple Groups

### Mediation Analysis

- Tests of Mediation Effect using the Sobel Test
- Tests of Mediation Effect in Linear Regression
- Joint Tests of Mediation in Linear Regression with Continuous Variables
- Tests of Mediation Effect in Logistic Regression
- Tests of Mediation Effect in Poisson Regression
- Tests of Mediation Effect in Cox Regression

### Probit Analysis

### Michaelis-Menten Parameters

### Mendelian Randomization

### Reference Intervals

## ROC

- Tests for One ROC Curve
- Tests for Two ROC Curves
- Confidence Intervals for the Area Under an ROC Curve

## Sample Size Reestimation

### Means

#### Test (Inequality)

- Conditional Power and Sample Size Reestimation of One-Sample T-Tests
- Conditional Power and Sample Size Reestimation of Paired T-Tests
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests
- Conditional Power and Sample Size Reestimation of Tests for Two Means in a 2×2 Cross-Over Design

#### Non-Inferiority

- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Non-Inferiority
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Non-Inferiority

#### Superiority by a Margin

- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Superiority by a Margin

### Proportions

#### Test (Inequality)

- Conditional Power and Sample Size Reestimation of Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Tests for the Difference Between Two Proportions

#### Non-Inferiority

- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Non-Inferiority Tests for Two Proportions

#### Superiority by a Margin

- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for Two Proportions

### Survival

#### Test (Inequality)

#### Non-Inferiority

#### Superiority by a Margin

## Simulation

### Data Simulator

### Correlation

- Pearson’s Correlation Tests (Simulation)
- Spearman’s Rank Correlation Tests (Simulation)
- Kendall’s Tau-b Correlation Tests (Simulation)
- Power Comparison of Correlation Tests (Simulation)

### Means

#### One Mean

#### Paired Means

- Tests for Paired Means (Simulation)
- Equivalence Tests for Paired Means (Simulation)
- Tests for Paired Means (Simulation) (Legacy)

#### Two Independent Means

- Tests for Two Means (Simulation)
- Mann-Whitney U or Wilcoxon Rank-Sum Tests (Simulation)
- Equivalence Tests for Two Means (Simulation)

#### Many Means (ANOVA)

- One-Way Analysis of Variance F-Tests (Simulation)
- Kruskal-Wallis Tests (Simulation)
- Terry-Hoeffding Normal-Scores Tests of Means (Simulation)
- Van der Waerden Normal Quantiles Tests of Means (Simulation)
- Power Comparison of Tests of Means in One-Way Designs (Simulation)
- Pair-Wise Multiple Comparisons (Simulation)
- Multiple Comparisons of Treatments vs. a Control (Simulation)
- Multiple Contrasts (Simulation)
- Mixed Models (Simulation)
- Equivalence Tests for the Mean Ratio in a Three-Arm Trial (Normal Data) (Simulation)

#### Group-Sequential

- Group-Sequential Tests for One Mean with Known Variance (Simulation)
- Group-Sequential T-Tests for One Mean (Simulation)
- Group-Sequential Non-Inferiority Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Superiority by a Margin Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Non-Inferiority T-Tests for One Mean (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for One Mean (Simulation)
- Group-Sequential Tests for Two Means with Known Variances (Simulation)
- Group-Sequential T-Tests for Two Means (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Non-Inferiority T-Tests for Two Means (Simulation)
- Group-Sequential Superiority by a Margin Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means (Simulation) (Legacy)
- Group-Sequential Tests for Two Means Assuming Normality (Simulation) (Legacy)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation) (Legacy)

### Normality Tests

### Proportions

- Group-Sequential Tests for One Proportion (Simulation)
- Group-Sequential Non-Inferiority Tests for One Proportion (Simulation)
- Group-Sequential Superiority by a Margin Tests for One Proportion (Simulation)
- Group-Sequential Tests for Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Ratio of Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Odds Ratio of Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for the Ratio of Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for the Odds Ratio of Two Proportions (Simulation)
- Group-Sequential Tests for Two Proportions (Simulation) (Legacy)
- Group-Sequential Non-Inferiority Tests for the Difference of Two Proportions (Simulation) (Legacy)
- Group-Sequential Superiority by a Margin Tests for the Difference of Two Proportions (Simulation) (Legacy)

### Quality Control

### Survival

- Two-Group Survival Comparison Tests (Simulation)
- Group-Sequential Tests for Two Hazard Rates (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Hazard Rates (Simulation)
- Group-Sequential Superiority by a Margin Tests for Two Hazard Rates (Simulation)
- Group-Sequential Logrank Tests (Simulation) (Legacy)

### Variances

- Bartlett Test of Variances (Simulation)
- Levene Test of Variances (Simulation)
- Brown-Forsythe Test of Variances (Simulation)
- Conover Test of Variances (Simulation)
- Power Comparison of Tests of Variances (Simulation)

## Stratified

- Confidence Intervals for One Mean in a Stratified Design
- Confidence Intervals for One Mean in a Stratified Cluster-Randomized Design
- Confidence Intervals for One Proportion in a Stratified Design
- Confidence Intervals for One Proportion in a Stratified Cluster-Randomized Design
- Tests for Two Proportions in a Stratified Design (Cochran-Mantel-Haenszel Test)
- Tests for Two Proportions in a Stratified Cluster-Randomized Design (Cochran-Mantel-Haenszel Test)
- GEE Tests for Two Means in a Stratified Cluster-Randomized Design

## Superiority by a Margin

### Means

#### One Mean

- One-Sample Z-Tests for Superiority by a Margin
- One-Sample T-Tests for Superiority by a Margin
- Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Superiority by a Margin
- Group-Sequential Superiority by a Margin Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for One Mean (Simulation)

#### Paired Means

- Paired Z-Tests for Superiority by a Margin
- Paired T-Tests for Superiority by a Margin
- Paired Wilcoxon Signed-Rank Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Superiority by a Margin

#### Two Independent Means

- Two-Sample T-Tests for Superiority by a Margin Assuming Equal Variance
- Two-Sample T-Tests for Superiority by a Margin Allowing Unequal Variance
- Mann-Whitney U or Wilcoxon Rank-Sum Tests for Superiority by a Margin
- Superiority by a Margin Tests for the Ratio of Two Means (Log-Normal Data)
- Superiority by a Margin Tests for the Ratio of Two Means (Normal Data)
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Superiority by a Margin
- Group-Sequential Superiority by a Margin Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for Two Means (Simulation)

#### Two Means (Cluster-Randomized)

#### Cross-Over (2×2) Design

- Superiority by a Margin Tests for the Difference of Two Means in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Ratio of Two Means in a 2×2 Cross-Over Design (Log-Normal Data)

#### Cross-Over (Higher-Order) Design

- Superiority by a Margin Tests for the Difference of Two Means in a Higher-Order Cross-Over Design
- Superiority by a Margin Tests for the Ratio of Two Means in a Higher-Order Cross-Over Design (Log-Normal Data)

#### Cross-Over (Williams) Design

#### One-Way Design (Studentized Range)

#### Group-Sequential

- Group-Sequential Superiority by a Margin Tests for Two Means with Known Variances (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for Two Means (Simulation)
- Group-Sequential Superiority by a Margin Tests for One Mean with Known Variance (Simulation)
- Group-Sequential Superiority by a Margin T-Tests for One Mean (Simulation)

#### Conditional Power

- Conditional Power and Sample Size Reestimation of One-Sample T-Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of Paired T-Tests for Superiority by a Margin
- Conditional Power and Sample Size Reestimation of Two-Sample T-Tests for Superiority by a Margin

### Proportions

#### One Proportion

- Superiority by a Margin Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for One Proportion
- Group-Sequential Superiority by a Margin Tests for One Proportion (Simulation)

#### Two Independent Proportions

- Superiority by a Margin Tests for the Difference Between Two Proportions
- Superiority by a Margin Tests for the Ratio of Two Proportions
- Superiority by a Margin Tests for the Odds Ratio of Two Proportions
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for Two Proportions
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Superiority by a Margin Tests for Vaccine Efficacy with Extremely Low Incidence

#### Two Proportions (Cluster-Randomized)

- Superiority by a Margin Tests for the Difference of Two Proportions in a Cluster-Randomized Design
- Superiority by a Margin Tests for the Ratio of Two Proportions in a Cluster-Randomized Design

#### Cross-Over (2×2) Design

- Superiority by a Margin Tests for the Difference of Two Proportions in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Odds Ratio of Two Proportions in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Generalized Odds Ratio for Ordinal Data in a 2×2 Cross-Over Design

#### Cross-Over (Williams) Design

#### Group-Sequential

- Group-Sequential Superiority by a Margin Tests for Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for the Ratio of Two Proportions (Simulation)
- Group-Sequential Superiority by a Margin Tests for the Odds Ratio of Two Proportions (Simulation)

#### Conditional Power

- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for One Proportion
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Tests for Two Proportions

#### Vaccine Efficacy

- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Superiority by a Margin Tests for Vaccine Efficacy with Extremely Low Incidence

### Rates and Counts

- Superiority by a Margin Tests for the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for the Ratio of Two Negative Binomial Rates
- Superiority by a Margin Tests for the Ratio of Two Poisson Rates in a Cluster-Randomized Design
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates

### Survival

- Superiority by a Margin Tests for Two Survival Curves Using Cox’s Proportional Hazards Model
- Superiority by a Margin Tests for the Difference of Two Hazard Rates Assuming an Exponential Model
- Superiority by a Margin Tests for Vaccine Efficacy using the Hazard Ratio (Cox’s Proportional Hazards Model)
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Logrank Tests
- Group-Sequential Superiority by a Margin Tests for Two Hazard Rates (Simulation)

### Variances

- Superiority by a Margin Tests for the Ratio of Two Variances
- Superiority by a Margin Tests for the Ratio of Two Within-Subject Variances in a Parallel Design
- Superiority by a Margin Tests for the Ratio of Two Within-Subject Variances in a 2×2M Replicated Cross-Over Design
- Superiority by a Margin Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Superiority by a Margin Tests for Two Between Variances in a Replicated Design
- Superiority by a Margin Tests for Two Between-Subject Variances in a 2×2M Replicated Cross-Over Design
- Superiority by a Margin Tests for Two Total Variances in a Replicated Design
- Superiority by a Margin Tests for Two Total Variances in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for Two Total Variances in a 2×2M Replicated Cross-Over Design

## Survival

### One Survival Curve

- One-Sample Logrank Tests Assuming a Weibull Model (Wu)
- One-Sample Tests of Weibull Hazard Rates
- One-Sample Cure Model Tests
- One-Sample Tests for Exponential Hazard Rate
- Confidence Intervals for the Weibull Shape Parameter

### Two Survival Curves

#### Test (Inequality)

- Logrank Tests
- Logrank Tests (Freedman)
- Logrank Tests (Freedman) (Legacy)
- Logrank Tests (Lachin and Foulkes)
- Two-Group Survival Comparison Tests (Simulation)
- Tests for Two Survival Curves Using Cox’s Proportional Hazards Model
- Tests for the Difference of Two Hazard Rates Assuming an Exponential Model
- Logrank Tests Accounting for Competing Risks
- Logrank Tests in a Cluster-Randomized Design
- Conditional Power and Sample Size Reestimation of Logrank Tests

#### Non-Inferiority

- Non-Inferiority Logrank Tests
- Non-Inferiority Tests for Two Survival Curves Using Cox’s Proportional Hazards Model
- Non-Inferiority Tests for the Difference of Two Hazard Rates Assuming an Exponential Model
- Non-Inferiority Tests for Vaccine Efficacy using the Hazard Ratio (Cox’s Proportional Hazards Model)
- Conditional Power and Sample Size Reestimation of Non-Inferiority Logrank Tests

#### Superiority by a Margin

- Superiority by a Margin Tests for Two Survival Curves Using Cox’s Proportional Hazards Model
- Superiority by a Margin Tests for the Difference of Two Hazard Rates Assuming an Exponential Model
- Superiority by a Margin Tests for Vaccine Efficacy using the Hazard Ratio (Cox’s Proportional Hazards Model)
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Logrank Tests

#### Equivalence

- Equivalence Tests for Two Survival Curves Using Cox’s Proportional Hazards Model
- Equivalence Tests for the Difference of Two Hazard Rates Assuming an Exponential Model

#### Group-Sequential

- Group-Sequential Tests for Two Hazard Rates (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Hazard Rates (Simulation)
- Group-Sequential Superiority by a Margin Tests for Two Hazard Rates (Simulation)
- Group-Sequential Logrank Tests (Legacy)
- Group-Sequential Logrank Tests (Simulation) (Legacy)

#### Competing Risks

#### Cluster-Randomized

#### Conditional Power

- Conditional Power and Sample Size Reestimation of Logrank Tests
- Conditional Power and Sample Size Reestimation of Non-Inferiority Logrank Tests
- Conditional Power and Sample Size Reestimation of Superiority by a Margin Logrank Tests

### Cox Regression

### Exponential Means

- Tests for One Exponential Mean
- Tests for Two Exponential Means
- One-Sample Tests for Exponential Hazard Rate

### Confidence Intervals

- Confidence Intervals for the Exponential Lifetime Mean
- Confidence Intervals for an Exponential Lifetime Percentile
- Confidence Intervals for Exponential Reliability
- Confidence Intervals for the Exponential Hazard Rate
- Confidence Intervals for the Weibull Shape Parameter

### Probit Analysis

### Vaccine Efficacy

- Non-Inferiority Tests for Vaccine Efficacy using the Hazard Ratio (Cox’s Proportional Hazards Model)
- Superiority by a Margin Tests for Vaccine Efficacy using the Hazard Ratio (Cox’s Proportional Hazards Model)

### Legacy Procedures

### Tools

## Tolerance Intervals

- Tolerance Intervals for Normal Data
- Tolerance Intervals for Exponential Data
- Tolerance Intervals for Gamma Data
- Tolerance Intervals for Any Data (Nonparametric)
- Reliability Demonstration Tests of One Proportion
- Reliability Demonstration Tests of One Proportion with Adverse Events

## Vaccine Efficacy

### Composite (Burden-of-Illness)

- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Ratio of Two Means
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Difference of Two Means

### Proportions

- Confidence Intervals for Vaccine Efficacy using a Cohort Design
- Confidence Intervals for Vaccine Efficacy using an Unmatched Case-Control Design
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Ratio of Two Means
- Tests for Vaccine Efficacy with Composite Efficacy Measure using the Difference of Two Means
- Tests for Vaccine Efficacy with Extremely Low Incidence
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Non-Inferiority Tests for Vaccine Efficacy with Extremely Low Incidence
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Proportions
- Superiority by a Margin Tests for Vaccine Efficacy with Extremely Low Incidence

### Rates and Counts

- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Poisson Rates
- Non-Inferiority Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates
- Superiority by a Margin Tests for Vaccine Efficacy using the Ratio of Two Negative Binomial Rates

### Survival

- Non-Inferiority Tests for Vaccine Efficacy using the Hazard Ratio (Cox’s Proportional Hazards Model)

## Variances

### One Standard Deviation

- Tests for One Variance
- Confidence Intervals for One Standard Deviation using Standard Deviation
- Confidence Intervals for One Standard Deviation using Relative Error
- Confidence Intervals for One Standard Deviation with Tolerance Probability

### One Variance

- Tests for One Variance
- Confidence Intervals for One Variance using Variance
- Confidence Intervals for One Variance using Relative Error
- Confidence Intervals for One Variance with Tolerance Probability

### Two Variances

- Tests for the Ratio of Two Variances
- Non-Unity Null Tests for the Ratio of Two Variances
- Non-Inferiority Tests for the Ratio of Two Variances
- Superiority by a Margin Tests for the Ratio of Two Variances
- Equivalence Tests for the Ratio of Two Variances
- Confidence Intervals for the Ratio of Two Variances using Variances
- Confidence Intervals for the Ratio of Two Variances using Relative Error

### Many Variances

- Bartlett Test of Variances (Simulation)
- Levene Test of Variances (Simulation)
- Brown-Forsythe Test of Variances (Simulation)
- Conover Test of Variances (Simulation)
- Power Comparison of Tests of Variances (Simulation)

### Within-Subject Variances

#### Parallel Design (Ratio of Two Variances)

- Tests for the Ratio of Two Within-Subject Variances in a Parallel Design
- Non-Unity Null Tests for the Ratio of Within-Subject Variances in a Parallel Design
- Non-Inferiority Tests for the Ratio of Two Within-Subject Variances in a Parallel Design
- Superiority by a Margin Tests for the Ratio of Two Within-Subject Variances in a Parallel Design
- Equivalence Tests for the Ratio of Two Within-Subject Variances in a Parallel Design

#### Parallel Design (Difference of Coefficients of Variation)

- Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Non-Zero Null Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Non-Inferiority Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Superiority by a Margin Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Equivalence Tests for the Difference of Two Within-Subject CV’s in a Parallel Design

#### 2×2M Replicated Cross-Over Design (Ratio of Two Variances)

- Tests for the Ratio of Two Within-Subject Variances in a 2×2M Replicated Cross-Over Design
- Non-Unity Null Tests for the Ratio of Within-Subject Variances in a 2×2M Replicated Cross-Over Design
- Non-Inferiority Tests for the Ratio of Two Within-Subject Variances in a 2×2M Replicated Cross-Over Design
- Superiority by a Margin Tests for the Ratio of Two Within-Subject Variances in a 2×2M Replicated Cross-Over Design
- Equivalence Tests for the Ratio of Two Within-Subject Variances in a 2×2M Replicated Cross-Over Design

### Between-Subject Variances

#### Parallel Replicated Design

- Tests for Two Between Variances in a Replicated Design
- Non-Unity Null Tests for Two Between Variances in a Replicated Design
- Non-Inferiority Tests for Two Between Variances in a Replicated Design
- Superiority by a Margin Tests for Two Between Variances in a Replicated Design

#### 2×2M Replicated Cross-Over Design

- Tests for Two Between-Subject Variances in a 2×2M Replicated Cross-Over Design
- Non-Unity Null Tests for Two Between-Subject Variances in a 2×2M Replicated Cross-Over Design
- Non-Inferiority Tests for Two Between-Subject Variances in a 2×2M Replicated Cross-Over Design
- Superiority by a Margin Tests for Two Between-Subject Variances in a 2×2M Replicated Cross-Over Design

### Total Variances

#### Parallel Design

- Tests for the Ratio of Two Variances
- Non-Unity Null Tests for the Ratio of Two Variances
- Non-Inferiority Tests for the Ratio of Two Variances
- Superiority by a Margin Tests for the Ratio of Two Variances
- Equivalence Tests for the Ratio of Two Variances

#### Parallel Replicated Design

- Tests for Two Total Variances in a Replicated Design
- Non-Unity Null Tests for Two Total Variances in a Replicated Design
- Non-Inferiority Tests for Two Total Variances in a Replicated Design
- Superiority by a Margin Tests for Two Total Variances in a Replicated Design

#### 2×2 Cross-Over Design

- Tests for Two Total Variances in a 2×2 Cross-Over Design
- Non-Unity Null Tests for Two Total Variances in a 2×2 Cross-Over Design
- Non-Inferiority Tests for Two Total Variances in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for Two Total Variances in a 2×2 Cross-Over Design

#### 2×2M Replicated Cross-Over Design

- Tests for Two Total Variances in a 2×2M Replicated Cross-Over Design
- Non-Unity Null Tests for Two Total Variances in a 2×2M Replicated Cross-Over Design
- Non-Inferiority Tests for Two Total Variances in a 2×2M Replicated Cross-Over Design
- Superiority by a Margin Tests for Two Total Variances in a 2×2M Replicated Cross-Over Design

### Coefficients of Variation

- Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Non-Zero Null Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Non-Inferiority Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Superiority by a Margin Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Equivalence Tests for the Difference of Two Within-Subject CV’s in a Parallel Design

### Non-Inferiority

- Non-Inferiority Tests for the Ratio of Two Variances
- Non-Inferiority Tests for the Ratio of Two Within-Subject Variances in a Parallel Design
- Non-Inferiority Tests for the Ratio of Two Within-Subject Variances in a 2×2M Replicated Cross-Over Design
- Non-Inferiority Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Non-Inferiority Tests for Two Between Variances in a Replicated Design
- Non-Inferiority Tests for Two Between-Subject Variances in a 2×2M Replicated Cross-Over Design
- Non-Inferiority Tests for Two Total Variances in a Replicated Design
- Non-Inferiority Tests for Two Total Variances in a 2×2 Cross-Over Design
- Non-Inferiority Tests for Two Total Variances in a 2×2M Replicated Cross-Over Design

### Superiority by a Margin

- Superiority by a Margin Tests for the Ratio of Two Variances
- Superiority by a Margin Tests for the Ratio of Two Within-Subject Variances in a Parallel Design
- Superiority by a Margin Tests for the Ratio of Two Within-Subject Variances in a 2×2M Replicated Cross-Over Design
- Superiority by a Margin Tests for the Difference of Two Within-Subject CV’s in a Parallel Design
- Superiority by a Margin Tests for Two Between Variances in a Replicated Design
- Superiority by a Margin Tests for Two Between-Subject Variances in a 2×2M Replicated Cross-Over Design
- Superiority by a Margin Tests for Two Total Variances in a Replicated Design
- Superiority by a Margin Tests for Two Total Variances in a 2×2 Cross-Over Design
- Superiority by a Margin Tests for Two Total Variances in a 2×2M Replicated Cross-Over Design

### Equivalence

- Equivalence Tests for the Ratio of Two Variances
- Equivalence Tests for the Ratio of Two Within-Subject Variances in a Parallel Design
- Equivalence Tests for the Ratio of Two Within-Subject Variances in a 2×2M Replicated Cross-Over Design
- Equivalence Tests for the Difference of Two Within-Subject CV’s in a Parallel Design

## Tools

- Probability Calculator
- Standard Deviation Estimator
- Standard Deviation of Means Calculator
- Odds Ratio and Proportions Conversion Tool
- Chi-Square Effect Size Estimator
- Kappa Estimator
- Survival Parameter Conversion Tool
- Randomization Lists
- Data Simulator
- Macro Command Center
- Installation Validation Tool for Installation Qualification (IQ)
- Procedure Validation Tool for Operational Qualification (OQ)
- Spreadsheets
- Macros