rphbPower - Unified Statistical Power Analysis Framework Package

A comprehensive R framework for a priori statistical power analysis. It provides easy-to-use functions for 11 different statistical methods, all unified by a common effect size metric and a philosophy of conservative study planning.

Framework Overview

This package provides power analysis for a diverse suite of statistical methods unified under a partial correlation framework. All analyses convert common effect sizes (e.g., Cohen’s d, f²) into partial correlations (r_partial), enabling direct and intuitive comparisons of effect magnitude across all included methods.

The framework is built on two core principles:

1. Unified Effect Size: Using r_partial as the common metric simplifies interpretation and promotes a deeper understanding of effect sizes, regardless of the statistical test being used.

2. Conservative Planning: A built-in 0.75 discount factor is automatically applied to all user-provided effect sizes. This encourages prudent and realistic study planning, helping to prevent underpowered research that can result from overly optimistic effect size estimations.

Core Features

• 11 Validated Modules: Covers a wide range of common statistical tests
• Unified Effect Size Metric: All calculations are based on partial correlations (r_partial)
• Parameter Auto-Detection: For any given test, provide any two of (effect size, sample size, power) and the framework will solve for the third
• Built-in Effect Size Conversion: Automatically converts from Cohen’s d, f², R², and η² into r_partial
• Conservative by Default: A 0.75 discount factor is automatically applied to effect size inputs to encourage robust planning

Quick Start

1. Install and Load the Package

The package can be installed directly from the Center For Open Science GitHub repository.

# install.packages("devtools") # Run this if you don't have devtools
devtools::install_github("CenterForOpenScience/rphbPower", build_vignettes = TRUE)

library(rphbPower)

2. Run the Power Analysis

The functions follow a consistent pattern. Provide the parameters you know, and leave the one you want to find as NULL.

# Example 1: Solve for required sample size (N)
result_n <- linear_regression_power(r_partial = 0.25, power = 0.8, n_predictors = 2)
print(result_n$n)

# Example 2: Solve for the power of a planned study
result_power <- linear_regression_power(r_partial = 0.25, n = 121, n_predictors = 2)
print(result_power$power)

3. Use Any Effect Size

The effect_input and effect_type arguments allow you to use effect sizes directly from the literature. The 0.75 discount factor will be applied automatically.

# Use a Cohen's d of 0.5 from a previous study
result <- linear_regression_power(
  effect_input = 0.5,
  effect_type = "d",
  power = 0.8,
  n_predictors = 2
)
print(result)

Available Analysis Methods

Basic and Regression Methods

• Correlation: correlation_power()
• Linear Regression: linear_regression_power()
• Logistic Regression: logistic_regression_power()

Longitudinal Methods

• Cross-Lagged Panel: cross_lagged_panel_power()
• Fixed Effects: fixed_effects_power()
• Repeated Measures: repeated_measures_power()

Mediation Methods

• Mediation (Regression): mediation_regression_power()
• Mediation (SEM): mediation_sem_power()

Advanced Methods

• Multilevel Models: mixed_models_power()
• SEM (Direct Effects): sem_direct_effects_power()
• Wilcoxon Signed-Rank Test: wilcoxon_signed_rank_power()

Method Selection Guide

By Research Design

• Single predictor, continuous outcome → Linear regression
• Multiple predictors, continuous outcome → Linear regression (multiple)
• Binary/categorical outcome → Logistic regression
• Mediation hypotheses → Mediation regression or SEM
• Clustered/nested data → Multilevel models
• Complex structural models with latent vars → SEM direct effects
• Simple bivariate association → Correlation

By Data Characteristics

• Normal, continuous variables → Linear regression methods
• Hierarchical/grouped data → Multilevel models
• Longitudinal/panel data → Cross-lagged, fixed effects, repeated measures
• Latent variable models → SEM approaches

Sample Size Planning Guidelines

A critical reality in study planning is that model complexity significantly impacts sample size requirements. With the corrected engine, the impact of adding covariates is now estimated more accurately.

Example Impact (Effect Size r = 0.20, Target Power = 80%):

• Correlation (1 predictor): ~192 participants
• Regression (5 predictors): ~192 participants (+0% increase)
• Regression (10 predictors): ~197 participants (+3% increase)

This framework helps you account for this complexity directly in your power analysis.

Framework Status

• Current Version: 2.2
• Mathematical Status: All 11 modules have been re-engineered and have passed comprehensive validation tests. The framework is considered complete and robust.
• Validation: 100% pass rate achieved across all modules against external benchmarks or internal consistency checks.

Documentation Structure

For detailed tutorials and guides, refer to the vignettes accessed through browseVignettes("rphbPower"):

• Getting Started: Installation and basic usage
• Effect Size Guidelines: Guidance on choosing an appropriate effect size
• Method Selection Guide: In-depth help for choosing the right analysis
• Quick Reference Guide: A fast lookup for functions and parameters
• Troubleshooting: Solutions for common issues