Interactive 3D Visualization of p-Value Surfaces • p3d

p3d is an R package for computing and visualizing the three-dimensional p-value surface of a single-sample t-test. The p-value is expressed as a function of both effect size (Cohen’s d) and sample size (n).

Why p3d?

Traditional p-value visualizations are two-dimensional and show the effect of only one parameter at a time. p3d visualizes the p-value simultaneously across effect size and sample size. It addresses questions such as:

How does the same effect size (d = 0.5) produce different significance outcomes at n = 10 versus n = 100?
Why is the p-value a continuous measure of evidence, not a fixed threshold?
How does sample size moderate the p-value?

Installation

# From CRAN (coming soon)
install.packages("p3d")

# Development version from GitHub
# install.packages("remotes")
remotes::install_github("ahmetkutuk1/p3d")

Basic Usage

library(p3d)

# Compute a 3D p-value surface
surface <- p_surface(d = seq(-2, 2, 0.1), n = seq(5, 200, 5))

# Interactive 3D visualization (plotly engine)
plot_p_surface(surface, engine = "plotly")

# Static 3D perspective (base R)
plot_p_static(surface)

# 2D p-value curve (for comparison)
curve_30 <- p_curve_2d(d = seq(-2, 2, 0.1), n = 30)
head(curve_30)

Main Functions

Function	Purpose
`p_surface(d, n, alpha)`	Compute the 3D p-value surface
`p_curve_2d(d, n, alpha)`	Compute a 2D p-value curve (fixed n)
`plot_p_surface(surface, engine)`	Interactive 3D visualization (rgl / plotly)
`plot_p_static(surface)`	Static 3D perspective (base R)

Mathematical Foundation

For a single-sample t-test, the p-value is:

$p(d, n) = 2 \left[ 1 - F_{t(n-1)}(d \sqrt{n}) \right]$

where $F_{t(n-1)}$ is the cumulative distribution function of the t-distribution with $n-1$ degrees of freedom.

The critical effect size at level $\alpha$ is:

$d_{\text{crit}}(n) = \frac{F^{-1}_{t(n-1)}(1 - \alpha/2)}{\sqrt{n}}$

Motivation

The p-value is a continuous measure of evidence, yet in practice it is often reduced to a binary decision: “p < 0.05 is significant, p ≥ 0.05 is not.” This dichotomous thinking contributes to the reproducibility crisis in science.

p3d aims to weaken the visual basis of this dichotomous thinking by visualizing the p-value over a two-dimensional parameter space. The significance boundary is a curve, not a point.

Performance

p_surface() computes a 60,100-cell grid in 0.02 seconds (approximately 3 million p-values per second). Memory usage is under 3 MB.

Contributing

Please use GitHub Issues for bug reports and feature requests.

p3d: Interactive 3D Visualization of p-Value Surfaces