2D Density Contour

When two continuous variables are measured across groups with large n (n > 100), a scatter plot overplots —points overlap so densely that the actual distribution is invisible. A 2D kernel density contour plot visualizes the joint distribution of both variables simultaneously, with contour levels showing where data density is highest, grouped by a categorical variable using color.

STEP 1 —When to Use

Use a 2D density contour when: n > 100 per group (overplotting prevents readable scatter); you have two continuous variables and a categorical grouping variable; you want to compare the joint distribution shape and overlap between groups (e.g., flow cytometry data, population surveys, large-scale genomic data).

Do not use when: n < 50 per group (individual points are more informative); groups are so distinct that contours do not overlap (a scatter plot with distinct colors is clearer); the two variables are on incommensurable scales without a meaningful joint distribution.

[Image placeholder: Left —scatter plot with n=500 per group, 2 colors. Massive overplotting, distribution invisible. Right —2D KDE contour of the same data. Two overlapping ellipse-like contour groups clearly visible, overlap region highlighted, density peaks labeled. Same data, radically different readability.]

Scatter overplotting at n=500 (left). 2D KDE contour (right) reveals group distribution shapes and overlap clearly.

STEP 2 —Journal Requirement

Contour levels must be labeled (e.g., "Contour levels at 25th, 50th, 75th, 90th percentile of each group's density").
Bandwidth selection method must be stated (same requirement as for violin plots).
n per group must be stated.
Color palette must be accessible (colorblind-safe distinction between groups).

STEP 3 —Licklider Implementation

Input

Two continuous variables (x and y axes)
Categorical grouping variable (color)
Bandwidth: MISE-optimal (default), user-specified, or diagonal bandwidth matrix
Contour levels: percentile-based (default) or density value-based

Output

Contour lines per group with distinct colors (up to 4 groups with accessible palette)
Filled contours optional (lowest level filled, others outlined)
Marginal density strips on x and y axes (optional)
Individual scatter points plotted semi-transparently beneath contours (optional)
Bandwidth and contour level definition in legend

[Image placeholder: Licklider 2D density contour with 2 groups (n=280 each). Three contour levels (50th, 75th, 90th percentile density) per group in two colorblind-safe colors. Marginal density strips on both axes. Bandwidth in legend. Both groups' density peaks and overlap region clearly visible.]

Licklider 2D density contour: three contour levels per group, marginal density strips, and bandwidth disclosed in legend.

STEP 4 —Draft Output (Draft / Needs review)

Joint distribution of [X variable] and [Y variable] is shown as 2D kernel
density contours for each group (n = 280 per group). Contour lines represent
the 50th, 75th, and 90th percentile density levels for each group.
Bandwidth was selected using the MISE-optimal plug-in estimator.
Marginal density estimates are shown on each axis. Correlation within
each group: Group A: r = 0.42 (p < 0.001); Group B: r = ~.18 (p = 0.003).