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p3d: Interactive 3D Visualization of p-Value Surfaces

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.

License

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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