The Design and the Population | The Cell Means in a Two-by-Two Layout | Viewing the Population | The Effects Worth Planning | Simple Effects of Both Factors | Contrast Weights | Analytic Power for a Single Contrast | The Arithmetic | A Picture of One Power Calculation | The Shared Design | Composite Power: Detecting Every Effect in One Study | Sizing the Study for Composite Power | Analytic Versus Monte Carlo Power | The Moderator as a Covariate | The Moderator as a Three-Way Interaction | Visualizing the Three-Way Interaction | Effect Sizes for the Moderated Model | Confirming the Plan by Simulation | Summary | References

The Workflow | A Simple Model: Mediation Among Observed Variables | The Population | The Analysis Model and the Parameters of Interest | Composite Power at a Candidate Sample Size | The Necessary Sample Size | The Weakest Parameter Governs the Design | Accuracy for the Set: AIPE | A Latent Growth Curve | The Population Growth Process | The Analysis Model | Composite Power for the Growth Questions | Accuracy for the Growth Parameters | Practical Notes | References

The Data | The Homogeneity-of-Regression Assumption | A Tidy ANCOVA With ancova() | The Treatment Effect Depends on the Covariate | One Study and Its Literature | References

Why This Vignette Exists | The Four Building Blocks | 1. Variance Utility → AIPE Planner | Worked Example: Pearson r | 2. Expected-Value Function → Design-Stage Substitution | Worked Example: The Standardized Mean Difference | 3. Effect Size Transforms: smd ↔ cles ↔ proportion_of_superiority ↔ nnt | Walked Example at Three Reference d Values | 4. Ordinal Alternatives: cliff_delta, vargha_delaney_A, probability_of_superiority_paired | 5. Reliability Composition | 6. The Mediation Pipeline | 7. Multivariate and Agreement Utilities | Argument-Name Conventions | Two Consistent Return Shapes | Recommended Workflows | A. Reporting a Standardized Mean Difference | B. Planning a Partial Correlation Study | C. Planning an Omega Squared CI | D. Reporting an Indirect (Mediated) Effect | E. Two-Method Agreement Study | Summary

What Is DMAR? | Why Effect Size Confidence Intervals? | Two Philosophies of Sample Size Planning | When Do You Reach for DMAR? | 1. I Just Ran an ANOVA, t-Test, or Regression. What's the Effect Size and a CI for It? | 2. I'm Planning a Study. How Many Subjects Do I Need? | 3. I Want to Test a Specific Contrast or Set of Pairwise Comparisons. | 4. I Have Within-Subjects (Repeated Measures) Data. | 5. I Want Descriptive Statistics, a Correlation Table, or Distribution-Shape Diagnostics. | What DMAR Is Not | A Note on Argument Naming | Where to Next | References

Purpose | Rubin's Missingness Taxonomy | Scenario 1: Complete Data (the Baseline) | Scenario 2: Missing Outcome Under MCAR | Scenario 3: Missing Predictor Under MAR (the Bias Case) | Scenario 4: Differential Missingness in a Treatment-Versus-Control Design | When Only the Outcome Is Missing | When a Baseline Covariate Is Missing | When Dropout Tracks an Auxiliary Variable | Reading the Three Cases Together | When FIML Cannot Help: MNAR | Multivariate FIML: When Outcomes Are Correlated | Summary | See Also | References

Why a Reimplementation and Expansion | Migration Table: The Renames That Matter | What DMAR Adds Beyond the MBESS Scope | 1. Maximum Likelihood Multiple Regression With FIML (mlmr() / mlmr_mv()) | 2. broom-Style Integration (generics::tidy() and generics::glance()) | 3. AIPE Sensitivity Analysis | 4. ANOVA and ANCOVA Wrappers | 5. Reliability With Proper CIs | Other Additions | A Short Worked Migration | See Also | References

The Negative Exponential: Change That Only Decelerates | The Logistic: Symmetric S-Shaped Change | The Gompertz: S-Shaped Change That Inflects Early | The Richards Family: The Inflection Becomes a Parameter | Individual Differences, One Parameter at a Time | Nonlinear Versus Polynomial: Why the Parameters Matter | From Curves to Data and Back | References

Two Models, One Question | The Four-Group Running Example | The Effect Size as a Proportional Reduction in Error | Power for the Omnibus Test | Planning the Sample Size | The Model Comparison, Made Literal | Estimating the Effect Size With a Confidence Interval | Carrying Uncertainty Into the Next Study | A Second Example: Three Groups | A Planned Contrast as a Model Comparison | Beyond the Reject or Retain Decision | Planning a Contrast for Precision | Why Not base R's power.anova.test() | References

1. The Design and the Population | 2. Power, Three Ways: ANOVA, and ANCOVA at Two Covariate Strengths | 3. Hypothetical Data | 4. Type III Analysis | 5. Plotting the Interactions Well | 6. Focused Follow-up Comparisons | 7. Reading List

One Kind of Result, Everywhere | What You See Is Rounded; What Is Stored Is Exact | Getting a Single Number Out | The "Wide" View and the One-Row Summary | Wide Tables Read the Same Way | p-Values and Information Criteria | In One Paragraph

A Running Example | Alpha Assumes Equal Loadings | The Denominator Choice in Omega | Categorical Omega for Ordered Items | Coefficient H: A Different Composite | Choosing the Interval | Missing Data: FIML and Auxiliary Variables | One Entry Point and the Broom Verbs | Planning the Study | What Reliability Coefficients Cannot Do | See Also | References

The t Table (A.1) | The Studentized Range (A.4) and Maximum Modulus (A.5) | The Dunnett Tables (A.6, A.7) | Bryant-Paulson (A.8): Where Recomputation Caught an Error | References

1. The Worked Example From Bryant & Bruvold (1980) | Fit the ANCOVA | Adjusted Panel Means | Simultaneous Bryant-Paulson Intervals | 2. Simultaneous vs. Per-Comparison Intervals | 3. A One-Way ANCOVA With ancova() | 4. Critical Values on Their Own | References

Why the Question Arises | A Short History in Psychology | A Sum of Squares Is a Model Comparison | Type I, Type II, and Type III | A Worked Unbalanced Factorial | How factorial_anova() Computes the Types | Balanced Data: The Types Coincide | ANCOVA Is Nonorthogonal by Construction | The Multivariate Case: MANOVA and MANCOVA | Recommendations | References

The Data | Are the Studies Significant in Combination? (Table 2) | Why Do the Studies Disagree? The Prior-Contact Contrast | Low- Versus High-Contact Studies (Table 3) | Tester Awareness (the Condition-Level Rows) | A Modern Reanalysis | References

Introduction | Setup | The Data | Descriptive Statistics | Visualizing Distributions: Raincloud Plots | Standardized Mean Difference | Visualizing With plot_smd() | Visual Representation of $d = 0.50$ | ANOVA Effect Sizes | Omega Squared ($\omega^2$) | Visualizing With plot_ci() | Proportion of Variance Explained: $R^2$ | Confidence Interval for the Multiple Correlation $R$ | Combining Multiple Effect Sizes | Turning Off Annotations | Customizing the Plots | A Note on MBESS | References

The Data: Cohen's Table 1 | Unweighted Kappa | Disagreement Scaling and Weighted Kappa | Cohen's Standard Errors and the Modern Interval | Linear and Quadratic Weights for Ordinal Categories | The Validity Example and an Orientation Question | References

The Design and the Population | The Cell Means in a Two-by-Two Layout | Viewing the Population | The Effects Worth Planning | Simple Effects of Both Factors | Contrast Weights | Analytic Power for a Single Contrast | The Arithmetic | A Picture of One Power Calculation | The Shared Design | Composite Power: Detecting Every Effect in One Study | Sizing the Study for Composite Power | Analytic Versus Monte Carlo Power | The Moderator as a Covariate | The Moderator as a Three-Way Interaction | Visualizing the Three-Way Interaction | Effect Sizes for the Moderated Model | Confirming the Plan by Simulation | Summary | References

The Data | The Homogeneity-of-Regression Assumption | A Tidy ANCOVA With ancova() | The Treatment Effect Depends on the Covariate | One Study and Its Literature | References

Why This Vignette Exists | The Four Building Blocks | 1. Variance Utility → AIPE Planner | Worked Example: Pearson r | 2. Expected-Value Function → Design-Stage Substitution | Worked Example: The Standardized Mean Difference | 3. Effect Size Transforms: smd ↔ cles ↔ proportion_of_superiority ↔ nnt | Walked Example at Three Reference d Values | 4. Ordinal Alternatives: cliff_delta, vargha_delaney_A, probability_of_superiority_paired | 5. Reliability Composition | 6. The Mediation Pipeline | 7. Multivariate and Agreement Utilities | Argument-Name Conventions | Two Consistent Return Shapes | Recommended Workflows | A. Reporting a Standardized Mean Difference | B. Planning a Partial Correlation Study | C. Planning an Omega Squared CI | D. Reporting an Indirect (Mediated) Effect | E. Two-Method Agreement Study | Summary

What Is DMAR? | Why Effect Size Confidence Intervals? | Two Philosophies of Sample Size Planning | When Do You Reach for DMAR? | 1. I Just Ran an ANOVA, t-Test, or Regression. What's the Effect Size and a CI for It? | 2. I'm Planning a Study. How Many Subjects Do I Need? | 3. I Want to Test a Specific Contrast or Set of Pairwise Comparisons. | 4. I Have Within-Subjects (Repeated Measures) Data. | 5. I Want Descriptive Statistics, a Correlation Table, or Distribution-Shape Diagnostics. | What DMAR Is Not | A Note on Argument Naming | Where to Next | References

Why a Reimplementation and Expansion | Migration Table: The Renames That Matter | What DMAR Adds Beyond the MBESS Scope | 1. Maximum Likelihood Multiple Regression With FIML (mlmr() / mlmr_mv()) | 2. broom-Style Integration (generics::tidy() and generics::glance()) | 3. AIPE Sensitivity Analysis | 4. ANOVA and ANCOVA Wrappers | 5. Reliability With Proper CIs | Other Additions | A Short Worked Migration | See Also | References

The Negative Exponential: Change That Only Decelerates | The Logistic: Symmetric S-Shaped Change | The Gompertz: S-Shaped Change That Inflects Early | The Richards Family: The Inflection Becomes a Parameter | Individual Differences, One Parameter at a Time | Nonlinear Versus Polynomial: Why the Parameters Matter | From Curves to Data and Back | References

Two Models, One Question | The Four-Group Running Example | The Effect Size as a Proportional Reduction in Error | Power for the Omnibus Test | Planning the Sample Size | The Model Comparison, Made Literal | Estimating the Effect Size With a Confidence Interval | Carrying Uncertainty Into the Next Study | A Second Example: Three Groups | A Planned Contrast as a Model Comparison | Beyond the Reject or Retain Decision | Planning a Contrast for Precision | Why Not base R's power.anova.test() | References

1. The Design and the Population | 2. Power, Three Ways: ANOVA, and ANCOVA at Two Covariate Strengths | 3. Hypothetical Data | 4. Type III Analysis | 5. Plotting the Interactions Well | 6. Focused Follow-up Comparisons | 7. Reading List

One Kind of Result, Everywhere | What You See Is Rounded; What Is Stored Is Exact | Getting a Single Number Out | The "Wide" View and the One-Row Summary | Wide Tables Read the Same Way | p-Values and Information Criteria | In One Paragraph

1. The Worked Example From Bryant & Bruvold (1980) | Fit the ANCOVA | Adjusted Panel Means | Simultaneous Bryant-Paulson Intervals | 2. Simultaneous vs. Per-Comparison Intervals | 3. A One-Way ANCOVA With ancova() | 4. Critical Values on Their Own | References

Why the Question Arises | A Short History in Psychology | A Sum of Squares Is a Model Comparison | Type I, Type II, and Type III | A Worked Unbalanced Factorial | How factorial_anova() Computes the Types | Balanced Data: The Types Coincide | ANCOVA Is Nonorthogonal by Construction | The Multivariate Case: MANOVA and MANCOVA | Recommendations | References

The Data | Are the Studies Significant in Combination? (Table 2) | Why Do the Studies Disagree? The Prior-Contact Contrast | Low- Versus High-Contact Studies (Table 3) | Tester Awareness (the Condition-Level Rows) | A Modern Reanalysis | References

Introduction | Setup | The Data | Descriptive Statistics | Visualizing Distributions: Raincloud Plots | Standardized Mean Difference | Visualizing With plot_smd() | Visual Representation of $d = 0.50$ | ANOVA Effect Sizes | Omega Squared ($\omega^2$) | Visualizing With plot_ci() | Proportion of Variance Explained: $R^2$ | Confidence Interval for the Multiple Correlation $R$ | Combining Multiple Effect Sizes | Turning Off Annotations | Customizing the Plots | A Note on MBESS | References

The Data: Cohen's Table 1 | Unweighted Kappa | Disagreement Scaling and Weighted Kappa | Cohen's Standard Errors and the Modern Interval | Linear and Quadratic Weights for Ordinal Categories | The Validity Example and an Orientation Question | References

The t Table (A.1) | The Studentized Range (A.4) and Maximum Modulus (A.5) | The Dunnett Tables (A.6, A.7) | Bryant-Paulson (A.8): Where Recomputation Caught an Error | References

The Workflow | A Simple Model: Mediation Among Observed Variables | The Population | The Analysis Model and the Parameters of Interest | Composite Power at a Candidate Sample Size | The Necessary Sample Size | The Weakest Parameter Governs the Design | Accuracy for the Set: AIPE | A Latent Growth Curve | The Population Growth Process | The Analysis Model | Composite Power for the Growth Questions | Accuracy for the Growth Parameters | Practical Notes | References

Purpose | Rubin's Missingness Taxonomy | Scenario 1: Complete Data (the Baseline) | Scenario 2: Missing Outcome Under MCAR | Scenario 3: Missing Predictor Under MAR (the Bias Case) | Scenario 4: Differential Missingness in a Treatment-Versus-Control Design | When Only the Outcome Is Missing | When a Baseline Covariate Is Missing | When Dropout Tracks an Auxiliary Variable | Reading the Three Cases Together | When FIML Cannot Help: MNAR | Multivariate FIML: When Outcomes Are Correlated | Summary | See Also | References

A Running Example | Alpha Assumes Equal Loadings | The Denominator Choice in Omega | Categorical Omega for Ordered Items | Coefficient H: A Different Composite | Choosing the Interval | Missing Data: FIML and Auxiliary Variables | One Entry Point and the Broom Verbs | Planning the Study | What Reliability Coefficients Cannot Do | See Also | References

A Correlation Is Not a Regression Slope | Assuming Less Publication Bias | Auditing the Plan by Simulation | When the Prior Result Cannot Support the Request | References

Assurance: Correcting for Uncertainty | When the Correction Cannot Be Made | The Ceiling, Drawn | alpha_prior: Modeling Publication Bias | Seeing the Assurance Claim Exercised | Practical Guidance | References

Independent t Test | Dependent (Paired) t Test | Between-Subjects ANOVA | Within-Subjects ANOVA | Split-Plot (Mixed) ANOVA | Multiple Regression | Correlation | Analysis of Covariance | Multivariate Comparison of Two Groups | Nested Model Comparison | Unequal Variances | References

Why Not Plan From the Observed Effect Size? | What BUCSS Does | A First Example | Reading the Result | The Replication Example | The Function Family | References

A Literature Built From Underpowered Studies | Why Planning at Face Value Underpowers the Replication | The BUCSS Correction | Reading and Using the Result | The Bigger Picture | References

1. Read It as a Printed Summary | 2. Pull a Single Number Out | 3. The Broom Verbs: tidy() and glance() | What Lives Where | References

Why AMCP Codes Grouping Variables as Numbers | The Two-Line Recipe | A Worked Example With Known Labels | With Three or More Groups, the Coding Matters | Finding the Categorical Variables in a Data Set | Summary

Quick start: every workflow, the easy way | The default Notre Dame palette | From one group to ten | The scales in practice | A gallery of plot types | Base R graphics | Statistical and psychometric visualization | Finding a color by name and role | Mixing in a color from outside the palette | Other palettes | Former Notre Dame colors | Colorblind-friendly Notre Dame colors | Brand tints, backgrounds, and sequential ramps | Theming R Markdown reports | Pairing with a light theme | A note on fonts | Related color tools

A complete example app | How the theming works | A brand-colored bslib theme | Brand-colored figures | Reusing the R Markdown stylesheet | All the colors, with details | The default Notre Dame palette ("nd") | The colorblind-friendly ordering ("nd_cvd") | The former Notre Dame colors ("former") | Near-white brand tints and informal backgrounds | The full color catalog