# 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****Cluster-Randomized****Conditional Power****Confidence Intervals****Correlation****Design of Experiments****Equivalence****Group-Sequential****Means****Microarray****Non-Inferiority****Nonparametric****Normality****Proportions****Quality Control****Rates and Counts****Regression****ROC****Simulation****Superiority by a Margin****Survival****Tolerance Intervals****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

## Cluster-Randomized

### 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

#### Non-Inferiority

#### Superiority by a Margin

#### Equivalence

### Two Proportions

#### 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

#### 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

### Rates and Counts

- Tests for the Difference Between 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

### 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

## Conditional Power

### Means

- Conditional Power of One-Sample T-Tests
- Conditional Power of Paired T-Tests
- Conditional Power of Two-Sample T-Tests
- Conditional Power of 2×2 Cross-Over Designs

### Proportions

### Survival

## 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 Coefficient Alpha
- Confidence Intervals for Kappa

### Means

- Confidence Intervals for One Mean
- Confidence Intervals for One Mean with Tolerance Probability
- 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

### Percentiles

- Confidence Intervals for a Percentile of a Normal Distribution
- 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 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 Kappa

### Quality Control

### Reference Intervals

### 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

### 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

### 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

### 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

- Equivalence Tests for One Mean
- Equivalence Tests for the Difference Between Two Paired Means
- Equivalence Tests for Paired Means (Simulation)
- Equivalence Tests for the Difference Between Two Means
- Equivalence Tests for Two Means (Simulation)
- Equivalence Tests for the Ratio of Two Means
- 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
- 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
- Equivalence Tests for Two Means in a Cluster-Randomized Design

### Proportions

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

### Rates and Counts

- Equivalence Tests for the Ratio of Two Poisson Rates
- 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

## Group-Sequential

### Means

- Group-Sequential Tests for Two Means
- Group-Sequential Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means Assuming Normality (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation)

### Proportions

- Group-Sequential Tests for One Proportion in a Fleming Design
- Group-Sequential Tests for Two Proportions
- Group-Sequential Tests for Two Proportions (Simulation)
- Group-Sequential Non-Inferiority Tests for the Difference of 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 the Difference of 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)
- Single-Stage Phase II Clinical Trials
- Two-Stage Phase II Clinical Trials
- Three-Stage Phase II Clinical Trials

### Survival

## Means

### One Mean

#### Test (Inequality)

- Tests for One Mean
- Tests for One Mean using Effect Size
- Tests for One Mean (Simulation)
- Tests for One Exponential Mean
- Tests for One Poisson Rate

#### Nonparametric

#### Confidence Interval

- Confidence Intervals for One Mean
- Confidence Intervals for One Mean with Tolerance Probability
- Confidence Intervals for a Percentile of a Normal Distribution

#### Non-Inferiority

#### Superiority by a Margin

#### Equivalence

#### Multiple Tests

#### Conditional Power

### Paired Means

#### Test (Inequality)

- Tests for Paired Means
- Tests for Paired Means using Effect Size
- Tests for Paired Means (Simulation)
- Tests for the Matched-Pair Difference of Two Means in a Cluster-Randomized Design

#### Nonparametric

#### Confidence Interval

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

#### Non-Inferiority

#### Superiority by a Margin

#### Equivalence

- Equivalence Tests for the Difference Between Two Paired Means
- Equivalence Tests for Paired Means (Simulation)

#### Cluster-Randomized

#### Multiple Tests

#### Conditional Power

### 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)
- Mann-Whitney-Wilcoxon Tests (Simulation)
- Tests for the Ratio of Two Means
- Tests for Fold Change of Two Means
- Tests for Two Means in a Cluster-Randomized Design

#### Z-Test (Inequality)

#### Nonparametric

#### Ratio Test

- Tests for the Ratio of Two Means
- Non-Inferiority Tests for the Ratio of Two Means
- 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
- 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
- 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

#### Non-Normal Data

- Tests for Two Means (Simulation)
- Mann-Whitney-Wilcoxon Tests (Simulation)
- 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
- 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

- Non-Inferiority Tests for the Difference Between Two Means
- Non-Inferiority Tests for the Ratio of Two Means
- Non-Inferiority Tests for the Ratio of Two Poisson Rates
- Non-Inferiority Tests for the Ratio of Two Negative Binomial Rates
- Non-Inferiority Tests for Two Means in a Cluster-Randomized Design
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation)

#### Superiority by a Margin

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

#### Equivalence

- Equivalence Tests for the Difference Between Two Means
- Equivalence Tests for the Ratio of Two Means
- Equivalence Tests for Two Means (Simulation)
- 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

#### Multicenter-Randomized

#### Repeated Measures

#### Group-Sequential

- Group-Sequential Tests for Two Means
- Group-Sequential Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means Assuming Normality (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation)

#### Multiple Tests

#### Conditional Power

### Two Means (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

### 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

#### 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

#### 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

#### 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

#### Conditional Power

### 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
- 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

#### 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

#### 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

### One-Way Designs (ANOVA)

#### ANOVA F-Test

- One-Way Analysis of Variance F-Tests
- One-Way Analysis of Variance F-Tests using Effect Size
- One-Way Analysis of Variance F-Tests (Simulation)
- Power Comparison of Tests of Means in One-Way Designs (Simulation)
- One-Way Analysis of Variance Contrasts
- One-Way Repeated Measures
- One-Way Repeated Measures Contrasts
- Confidence Intervals for One-Way Repeated Measures Contrasts
- 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

#### Analysis of Covariance

#### 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)

#### Multiple Comparisons

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

#### 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)

### Multi-Factor Designs (ANOVA)

- Factorial Analysis of Variance
- Factorial Analysis of Variance using Effect Size
- Randomized Block Analysis of Variance
- Repeated Measures Analysis
- Mixed Models (Simulation)

### Multiple Comparisons

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

### Analysis of Covariance

### Repeated Measures

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

### Mixed Models

### Multivariate Means

### Nonparametric

#### One Mean

- Tests for One Mean
- Tests for One Mean (Simulation)
- Non-Inferiority Tests for One Mean
- Superiority by a Margin Tests for One Mean (One-Sample or Paired T-Test)

#### Paired Means

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

#### Two Independent Means

- Mann-Whitney-Wilcoxon Tests (Simulation)
- Tests for Two Means (Simulation)
- Non-Inferiority Tests for the Difference Between Two Means
- Equivalence Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means Assuming Normality (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation)

#### 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)

### Tools

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

## Microarray

- Multiple One-Sample or Paired T-Tests
- Multiple Two-Sample T-Tests
- Tests for Fold Change of Two Means
- Mendelian Randomization with a Binary Outcome

## Non-Inferiority

### Means

- Non-Inferiority Tests for One Mean
- Non-Inferiority Tests for the Difference Between Two Means
- Non-Inferiority Tests for the Ratio of Two Means
- 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
- 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
- Non-Inferiority Tests for Two Means in a Cluster-Randomized Design
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation)

### Proportions

- Non-Inferiority Tests for One Proportion
- Non-Inferiority Tests for the Difference Between Two Correlated Proportions
- Non-Inferiority Tests for the Ratio of Two Correlated 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
- 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
- Group-Sequential Non-Inferiority Tests for the Difference of 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)

### Rates and Counts

- Non-Inferiority Tests for the Ratio of Two Poisson Rates
- Non-Inferiority Tests for 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

## Nonparametric

### One Mean

- Tests for One Mean
- Tests for One Mean (Simulation)
- Non-Inferiority Tests for One Mean
- Superiority by a Margin Tests for One Mean (One-Sample or Paired T-Test)
- Confidence Intervals for a Percentile of a Normal Distribution

### Paired Means

- Tests for Paired Means
- Tests for Paired Means (Simulation)
- Non-Inferiority Tests for One Mean
- Superiority by a Margin Tests for One Mean (One-Sample or Paired T-Test)
- Equivalence Tests for Paired Means (Simulation)

### Two Independent Means

- Mann-Whitney-Wilcoxon Tests (Simulation)
- Tests for Two Means (Simulation)
- Non-Inferiority Tests for the Difference Between Two Means
- Superiority by a Margin Tests for the Difference Between Two Means
- Equivalence Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means Assuming Normality (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation)

### 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)

### Tolerance Intervals

## Normality

## 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

#### Confidence Interval

- Confidence Intervals for One Proportion
- Confidence Intervals for One Proportion from a Finite Population

#### Non-Inferiority

#### Superiority by a Margin

#### Equivalence

#### Group-Sequential

- Group-Sequential Tests for One Proportion in a Fleming Design
- Single-Stage Phase II Clinical Trials
- Two-Stage Phase II Clinical Trials
- Three-Stage Phase II Clinical Trials

#### Rare Events

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

#### Post-Marketing Surveillance

#### Conditional Power

### Two Correlated (Paired) Proportions

#### Test (Inequality)

- Tests for Two Correlated Proportions (McNemar Test)
- Tests for the Matched-Pair Difference of Two Proportions in a Cluster-Randomized Design
- Tests for Two Correlated Proportions in a Matched Case-Control 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

#### 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

### Two Independent Proportions

#### Test (Inequality)

#### 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

#### 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

#### 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

#### 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

#### Stratified

#### Group-Sequential

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

### Two Proportions (Cluster-Randomized)

#### 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

#### 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

### Contingency Table (Chi-Square Tests)

### Repeated Measures

### Multiple Comparisons

### Stratified

### Trend

### Ordered Categorical

### 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 Two Binary X’s (Wald Test)
- Tests for the Interaction Odds Ratio in Logistic Regression with Two Binary X’s (Wald Test)

#### 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

#### Binary and Continuous X’s

#### 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

### 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 Ratio of Two Poisson Rates
- 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 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 Negative Binomial Rates

### Equivalence

- Equivalence Tests for the Ratio of Two Poisson Rates
- Equivalence Tests for the Ratio of Two Negative Binomial Rates

### Cluster-Randomized

- Tests for the Difference Between 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

### Poisson Regression

### Post-Marketing Surveillance

### Poisson Rates

- Tests for One Poisson Rate
- 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
- Tests for the Difference Between 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
- Poisson Regression
- Post-Marketing Surveillance

### 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

## Regression

### Linear Regression

- Linear Regression
- Confidence Intervals for Linear Regression Slope
- Tests for the Difference Between Two Linear Regression Slopes
- Tests for the Difference Between Two Linear Regression Intercepts

### Multiple Regression

### Cox Regression

### Poisson Regression

### 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 Two Binary X’s (Wald Test)
- Tests for the Interaction Odds Ratio in Logistic Regression with Two Binary X’s (Wald Test)

#### 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

#### Binary and Continuous X’s

#### 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

### 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

## 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

#### Two Independent Means

- Tests for Two Means (Simulation)
- Mann-Whitney-Wilcoxon 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)

#### Group-Sequential

- Group-Sequential Tests for Two Means (Simulation)
- Group-Sequential Tests for Two Means Assuming Normality (Simulation)
- Group-Sequential Non-Inferiority Tests for Two Means (Simulation)

### Normality Tests

### Proportions

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

### Quality Control

### Survival

### 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)

## Superiority by a Margin

### Means

- Superiority by a Margin Tests for One Mean (One-Sample or Paired T-Test)
- Superiority by a Margin Tests for the Difference Between Two Means
- Superiority by a Margin Tests for the Ratio of Two Means
- 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
- 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
- Superiority by a Margin Tests for Two Means in a Cluster-Randomized Design

### Proportions

- Superiority by a Margin Tests for One Proportion
- 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
- 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
- Group-Sequential Superiority by a Margin Tests for the Difference of 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)

### 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 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

## Survival

### One Survival Curve

### Two Survival Curves

#### Test (Inequality)

- Logrank Tests
- 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

#### 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

#### 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

#### 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

#### Competing Risks

#### Cluster-Randomized

#### Conditional Power

### Cox Regression

### Exponential Means

### 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

### Probit Analysis

### 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

## Variances

### One 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

### 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 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)

## Tools

- Chi-Square Effect Size Estimator
- Data Simulator
- Kappa Estimator
- Odds Ratio and Proportions Conversion Tool
- Probability Calculator
- Survival Parameter Conversion Tool
- Standard Deviation Estimator
- Standard Deviation of Means Calculator
- Spreadsheets
- Macros