List of Sample Size Procedures

This page contains a list of the tests and confidence intervals for which sample size and power can be calculated by PASS.  For a more in-depth look at the features of PASS, please download the free trial. Click to see some additional details about one or two means, multiple meanscorrelation, normality tests, variances, one proportion, two proportions, chi-square and other proportions tests, survival, or regression in PASS. Jump to category:

Cluster-Randomized Designs

  • Test of Two Means from a Cluster-Randomized Design
  • Test of Two Proportions from a Cluster-Randomized Design
  • Equivalence Test of Two Proportions from a Cluster-Randomized Design
  • Non-Inferiority Test of Two Proportions from a Cluster-Randomized Design
  • Superiority Test of Two Proportions from a Cluster-Randomized Design

Conditional Power

  • Conditional Power of a One-Sample T-Test
  • Conditional Power of a Two-Sample T-Test
  • Conditional Power of a Paired T-Test
  • Conditional Power of 2x2 Cross-Over Designs
  • Conditional Power of Logrank Test
  • Conditional Power of One-Proportion Test
  • Conditional Power of Two-Proportions Test

Confidence Intervals

  • Confidence Interval for a Correlation
  • Confidence Interval of a Mean
  • Confidence Interval of a Mean with Tolerance Probability
  • Confidence Interval of the Difference between Two Independent Means
  • Confidence Interval of the Difference between Two Independent Means with Tolerance Probability
  • Confidence Interval of the Difference between Two Paired Means
  • Confidence Interval of the Difference between Two Paired Means with Tolerance Probability
  • Confidence Interval of a Proportion
  • Confidence Interval of a Proportion from a Finite Population
  • Confidence Interval Comparing Two Proportions
  • Confidence Interval of a Regression Slope
  • Confidence Interval of a Standard Deviation entering a Standard Deviation
  • Confidence Interval of a Standard Deviation entering Relative Error
  • Confidence Interval of a Standard Deviation with Tolerance Probability
  • Confidence Interval of One Variance entering a Variance
  • Confidence Interval of One Variance entering Relative Error
  • Confidence Interval of One Variance with Tolerance Probability
  • Confidence Interval of the Ratio of Two Variances entering Variances
  • Confidence Interval of the Ratio of Two Variances entering Relative Error

Correlation

Click here to see additional details about correlation procedures in PASS.
  • One Correlation
  • Two Correlations
  • Pearson’s Correlation Tests with Simulation
  • Spearman’s Rank Correlation Tests with Simulation
  • Kendall’s Tau-b Correlation Tests with Simulation
  • Point Biserial Correlation Tests
  • Power Comparison of Correlation Tests with Simulation
  • Confidence Interval for One 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
  • Coefficient (or Cronbach's) Alpha
  • Confidence Intervals for Coefficient (or Cronbach's) Alpha
  • Intraclass Correlation
  • Kappa Test for Agreement
  • Confidence Intervals for Kappa
  • Lin's Concordance Correlation

Cross-Over Designs

  • Test of the Mean Difference from a 2x2 Cross-Over Design
  • Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Conditional Power of 2x2 Cross-Over Designs
  • Equivalence Test of the Mean Difference from a 2x2 Cross-Over Design
  • Equivalence Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Equivalence Test of the Mean Difference from a Higher-Order Cross-Over Design
  • Equivalence Test of the Mean Ratio from a Higher-Order Cross-Over Design
  • Non-Inferiority Test of the Mean Difference from a 2x2 Cross-Over Design
  • Non-Inferiority Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Non-Inferiority Test of the Mean Difference from a Higher-Order Cross-Over Design
  • Non-Inferiority Test of the Mean Ratio from a Higher-Order Cross-Over Design
  • Superiority Test of the Mean Difference from a 2x2 Cross-Over Design
  • Superiority Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Superiority Test of the Mean Difference from a Higher-Order Cross-Over Design
  • Superiority Test of the Mean Ratio from a Higher-Order Cross-Over Design

Design of Experiments

  • Experimental Design Tools
  • Randomization Lists

Equivalence

  • Equivalence Test of Two Means using Difference
  • Equivalence Test of Two Means using Ratio
  • Equivalence Test of Two Means by Simulation
  • Equivalence Test for Comparing Paired Means
  • Equivalence Test of the Mean Difference from a 2x2 Cross-Over Design
  • Equivalence Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Equivalence Test of the Mean Difference from a Higher-Order Cross-Over Design
  • Equivalence Test of the Mean Ratio from a Higher-Order Cross-Over Design
  • Equivalence of One Proportion
  • Equivalence of Two Proportions
  • Equivalence Test of Two Proportions from a Cluster-Randomized Design
  • Equivalence of Correlated Proportions using McNemar's Test
  • Equivalence Test for Comparing Survival Curves using Cox Regression
  • Equivalence of Hazard Rates assuming an Exponential Model

Exponential Distribution Parameter 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

Group-Sequential Tests

  • Group-Sequential Test for Two Means
  • Group-Sequential Test for Two Means using Simulation Assuming Normality
  • Group-Sequential Test for Two Means using Simulation General Assumptions
  • Group-Sequential Non-Inferiority Test for Two Means
  • Group-Sequential Test for Two Proportions
  • Group-Sequential Non-Inferiority Test for Two Proportions
  • Group-Sequential Superiority Test for Two Proportions
  • Group-Sequential Logrank Test of Two Survival Curves

Means - One

Click here to see additional details about one mean procedures in PASS.
  • One-Sample T-Test
  • One-Sample T-Test using Simulation
  • Wilcoxon Test
  • Multiple One-Sample T-Tests
  • Non-Inferiority Test of One Mean
  • Superiority by a Margin Test for One Mean
  • Confidence Interval for One Mean
  • Confidence Interval of One Mean with Tolerance Probability
  • Exponential Mean
  • Poisson Mean
  • Conditional Power of One-Sample T-Test

Means - Two Independent

Click here to see additional details about two independent means procedures in PASS.
  • Two-Sample T-Test Assuming Equal Variances
  • Two-Sample T-Test Allowing Unequal Variances
  • Two-Sample T-Test using Simulation
  • Mann-Whitney-Wilcoxon Test
  • Two-Sample Z-Test Assuming Equal Variances
  • Two-Sample Z-Test Allowing Unequal Variances
  • Confidence Interval of Difference in Two Means
  • Confidence Interval of Difference in Two Means with Tolerance Probability
  • Equivalence Test of Two Means using Difference
  • Equivalence Test of Two Means using Ratio
  • Equivalence Test of Two Means by Simulation
  • Non-Inferiority Test of Two Means Based on their Difference
  • Non-Inferiority Test of Two Means Based on their Ratio
  • Superiority by a Margin Test of the Difference in Two Means
  • Superiority by a Margin Test of the Ratio of Two Means
  • Test of Two Means from a Cluster-Randomized Design
  • Conditional Power of Two-Sample T-Tests
  • Group-Sequential Test for Two Means
  • Group-Sequential Test for Two Means using Simulation Assuming Normality
  • Group-Sequential Test for Two Means using Simulation General Assumptions
  • Group-Sequential Non-Inferiority Test for Two Means
  • Hotelling's T-Squared
  • Multiple Two-Sample T-Tests
  • Exponential Means
  • Poisson Means
  • Ratio of Two Means
  • Test Comparing Mean Change Scores from a Two Group, Pre-Post Design
  • Time-Averaged Difference of Two Means
  • Two Means from a Repeated Measures Design
  • Tests for Two Means in a Multicenter Randomized Design

Means - Two Correlated or Paired

Click here to see additional details about paired means procedures in PASS.
  • Paired T-Test
  • Paired T-Test using Simulation
  • Wilcoxon Test and Sign Test
  • Equivalence Test for Comparing Paired Means
  • Non-Inferiority Test Comparing Paired Means
  • Superiority by a Margin Test Comparing Paired Means
  • Confidence Interval of the Difference between Two Paired Means
  • Confidence Interval of the Difference between Two Paired Means with Tolerance Probability
  • Multiple Paired T-Tests
  • Conditional Power of Paired T-Test

Means - 2x2 Cross-Over Designs

Click here to see additional details about cross-over designs for two means procedures in PASS.
  • Test of the Mean Difference from a 2x2 Cross-Over Design
  • Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Equivalence Test of the Mean Difference from a 2x2 Cross-Over Design
  • Equivalence Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Non-Inferiority Test of the Mean Difference from a 2x2 Cross-Over Design
  • Non-Inferiority Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Superiority Test of the Mean Difference from a 2x2 Cross-Over Design
  • Superiority Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Conditional Power of 2x2 Cross-Over Designs

Means - Higher-Order Cross-Over Designs

Click here to see additional details about cross-over designs for two means procedures in PASS.
  • Equivalence Test of the Mean Difference from a Higher-Order Cross-Over Design
  • Equivalence Test of the Mean Ratio from a Higher-Order Cross-Over Design
  • Non-Inferiority Test of the Mean Difference from a Higher-Order Cross-Over Design
  • Non-Inferiority Test of the Mean Ratio from a Higher-Order Cross-Over Design
  • Superiority Test of the Mean Difference from a Higher-Order Cross-Over Design
  • Superiority Test of the Mean Ratio from a Higher-Order Cross-Over Design

Means - Many (ANOVA)

Click here to see additional details about multiple means procedures in PASS.
  • One-Way Analysis of Variance
  • One-Way Analysis of Variance with Simulation
  • Kruskal-Wallis Test with Simulation
  • Terry-Hoeffding Normal-Scores Tests of Means with Simulation
  • Van der Waerden Normal Quantiles Tests of Means with Simulation
  • Analysis of Covariance (ANCOVA)
  • Williams Test for the Minimum Effective Dose
  • Factorial Analysis of Variance
  • MANOVA
  • Randomized Block Analysis of Variance
  • Repeated Measures Analysis
  • Mixed Models
  • Multiple Comparisons (Tukey-Kramer, Best, Dunnett)
  • Multiple Comparisons (Pair-Wise: Tukey-Kramer, Kruskal-Wallis)
  • Multiple Comparisons (Treatments vs Control)
  • Multiple Contrasts (Dunn, Bonferroni)

Michaelis-Menten Parameters

  • Confidence Intervals for Michaelis-Menten Parameters

Non-Inferiority

  • Non-Inferiority Test of One Mean
  • Non-Inferiority Test of Two Means Based on their Difference
  • Non-Inferiority Test of Two Means Based on their Ratio
  • Non-Inferiority Test Comparing Paired Means
  • Non-Inferiority Test of the Mean Difference from a 2x2 Cross-Over Design
  • Non-Inferiority Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Non-Inferiority Test of the Mean Difference from a Higher-Order Cross-Over Design
  • Non-Inferiority Test of the Mean Ratio from a Higher-Order Cross-Over Design
  • Group-Sequential Non-Inferiority Test of Two Means
  • Non-Inferiority Test of One Proportion
  • Non-Inferiority Tests of Two Proportions
  • Group-Sequential Non-Inferiority Test of Two Proportions
  • Non-Inferiority Test of Correlated Proportions using McNemar's Test
  • Non-Inferiority Test of Two Proportions from a Cluster-Randomized Design
  • Non-Inferiority Logrank Tests

Normality Tests

Click here to see additional details about normality test procedures in PASS.
  • Normality Tests

Proportions - One

Click here to see additional details about one proportion procedures in PASS.
  • One Proportion Tests
  • Confidence Interval of a Proportion
  • Confidence Interval for One Proportion from a Finite Population
  • Equivalence Test of One Proportion
  • Non-Inferiority Test of One Proportion
  • Superiority Test of One Proportion
  • Single-Stage Phase II Clinical Trial
  • Two-Stage Phase II Clinical Trial (Simon)
  • Three-Stage Phase II Clinical Trial
  • Post-Marketing Surveillance
  • Conditional Power of One-Proportion Test
  • Test for One Sensitivity or Specificity

Proportions - Two Independent

Click here to see additional details about two proportions procedures in PASS.
  • Tests of Two Proportions
  • Fisher's Exact Test of Two Proportions
  • Confidence Interval Comparing Two Proportions
  • Equivalence Tests of Two Proportions
  • Non-Inferiority Tests for Two Proportions
  • Superiority Test of Two Proportions
  • Test for Two Proportions from a Cluster-Randomized Design
  • Equivalence Test of Two Proportions from a Cluster-Randomized Design
  • Non-Inferiority Test of Two Proportions from a Cluster-Randomized Design
  • Superiority Test of Two Proportions from a Cluster-Randomized Design
  • Group-Sequential Tests for Two Proportions
  • Group-Sequential Tests for Two Proportions using Simulation
  • Group-Sequential Non-Inferiority Tests of Two Proportions
  • Group-Sequential Superiority Tests of Two Proportions
  • Cochran/Mantel-Haenzel Test in a Stratified Design
  • Repeated Measures Design Test for Two Proportions
  • Test for Two Independent Sensitivities
  • Time-Averaged Difference of Two Proportions
  • Conditional Power of Two-Proportions Tests

Proportions - Correlated or Paired

Click here to see additional details about correlated proportions procedures in PASS.
  • Test of Two Correlated Proportions using McNemar's Test
  • Equivalence Test of Two Correlated Proportions using McNemar's Test
  • Non-Inferiority Test of Correlated Proportions using McNemar's Test
  • Test of Two Correlated Proportions in a Matched Case-Control Design

Proportions - Sensitivity and Specificity

  • Sensitivity and Specificity for One Group
  • Sensitivity of Paired Groups
  • Sensitivity and Specificity of Two Independent Groups

Proportions - Many

Click here to see additional details about chi-square and other proportions tests procedures in PASS.
  • Chi-Square Contingency Table Test
  • Chi-Square Multinomial Test
  • Cochran-Armitage Test for Trend in Proportions
  • Logistic Regression
  • Two Ordered Categorical Variables

Quality Control

  • Quality Control Charts of Means
  • Quality Control Charts of Variation
  • Confidence Intervals for Cp
  • Confidence Intervals for Cpk

Regression

Click here to see additional details about regression procedures in PASS.
  • Confidence Interval of a Slope
  • Cox Regression
  • Linear Regression
  • Logistic Regression
  • Multiple Regression
  • Poisson Regression
  • Probit Analysis

ROC Curves

  • Test for One ROC Curve
  • Test for Two ROC Curves
  • Confidence Intervals for the Area Under an ROC Curve

Superiority by a Margin Test

  • Superiority Test for One Mean
  • Superiority Test of the Difference in Two Means
  • Superiority by a Margin Test of the Ratio of Two Means
  • Superiority Test Comparing Paired Means
  • Superiority Test of the Mean Difference from a 2x2 Cross-Over Design
  • Superiority Test of the Mean Ratio from a 2x2 Cross-Over Design
  • Superiority Test of the Mean Difference from a Higher-Order Cross-Over Design
  • Superiority Test of the Mean Ratio from a Higher-Order Cross-Over Design
  • Superiority Test of One Proportion
  • Superiority Test of Two Proportions
  • Superiority Test for Two Proportions from a Cluster-Randomized Design
  • Group-Sequential Superiority Test of Two Proportions
  • Superiority Test for Comparing Survival Curve using Cox Regression
  • Superiority Test for Comparing Hazard Rates assuming Exponential Data

Survival Analysis

Click here to see additional details about survival procedures in PASS.
  • Logrank Tests
  • Logrank Tests using Cox Regression
  • Logrank Test assuming Exponential Distribution
  • Logrank Test Accounting for Competing Risks
  • Group-Sequential Logrank Tests
  • Equivalence Test for Comparing Survival Curves using Cox Regression
  • Equivalence of Hazard Rates assuming an Exponential Model
  • Non-Inferiority Logrank Tests
  • Non-Inferiority Test for the Difference of Two Hazard Rates Assuming an Exponential Distribution
  • Non-Inferiority, Logrank Test for Two Survival Curves using Cox Regression
  • Superiority Test for Comparing Survival Curve using Cox Regression
  • Superiority Test for Comparing Hazard Rates assuming Exponential Data
  • Conditional Power of Logrank Tests
  • Cox Regression
  • Exponential Mean (One)
  • Exponential Mean (Two)
  • Probit Analysis

Variances and Standard Deviations

Click here to see additional details about variances and standard deviations in PASS.
  • Test of One Variance
  • Test of Two Variances
  • Bartlett Test of Variances with Simulation
  • Levene Test of Variances with Simulation
  • Brown-Forsythe Test of Variances with Simulation
  • Conover Test of Variances with Simulation
  • Power Comparison of Tests of Variances with Simulation
  • Confidence Interval of a Standard Deviation entering a Standard Deviation
  • Confidence Interval of a Standard Deviation entering Relative Error
  • Confidence Interval of a Standard Deviation with Tolerance Probability
  • Confidence Interval of One Variance entering a Variance
  • Confidence Interval of One Variance entering Relative Error
  • Confidence Interval of One Variance with Tolerance Probability
  • Confidence Interval of the Ratio of Two Variances entering Variances
  • Confidence Interval of the Ratio of Two Variances entering Relative Error
  • Quality Control Charts of Variation

Tools

  • Chi-Square Effect-Size Estimator
  • Multinomial Effect-Size Estimator
  • Odds Ratio to Proportions Converter
  • Probability Calculator (Various Distributions)
  • Standard Deviation Estimator
  • Survival Parameter Conversion Tool
  • Standard Deviation of Means Calculator
  • Data Simulator