PCA Biplot

A PCA biplot overlays the sample scores (observations projected onto principal components) and the variable loadings (original variable contributions to each PC) in the same plot. It simultaneously shows the grouping of samples in reduced-dimensional space and which variables drive that grouping. The choice to center and scale the data before PCA fundamentally changes the result —and must be disclosed.

STEP 1 —When to Use

Use a PCA biplot when: you want to show both the sample grouping pattern AND the variables driving that pattern in a single figure; the number of variables is manageable for loading arrow display (typically 竕､ 20 —more than 20 loadings creates visual clutter); you want to identify which variables are most strongly associated with group separation.

Centering and scaling: PCA should always be centered (subtract mean). Scaling (divide by SD, standardizing to unit variance) is appropriate when variables are on different scales or units —it ensures each variable contributes equally to the decomposition. Unscaled PCA will be dominated by high-variance variables regardless of their scientific importance.

[Image placeholder: PCA biplot with n=40 samples (3 groups, color-coded) and 8 variable loading arrows. PC1 (35% variance) on x-axis, PC2 (22% variance) on y-axis. Loading arrows labeled with variable names. Groups separated along PC1. 95% confidence ellipses per group. Axes labeled: "PC1 (35%)" and "PC2 (22%)". Corner annotation: "Centered and scaled to unit variance."]

PCA biplot: sample scores (colored by group) with 95% ellipses, loading arrows for 8 variables, variance explained per PC on axes.

STEP 2 —Journal Requirement

Variance explained by each displayed PC must be shown on the axis label: "PC1 (35.2% variance explained)".
Total variance explained by displayed PCs must be stated in the legend.
Whether data were centered and/or scaled must be stated.
If group labels are shown: n per group must be stated.
Loading arrow interpretation: arrows pointing in the same direction as a cluster indicate that those variables are higher in that group —this must be stated.

STEP 3 —Licklider Implementation

Input

Numeric matrix (samples xvariables)
Centering: yes (default, mandatory)
Scaling: yes (default when variables have different units), no (when all variables are on the same scale)
PCs to display: 1 vs. 2 (default), 1 vs. 3, or other combination
Loading display: all variables (default if 竕､ 20), top N by loading magnitude

Output

Score plot: sample points colored by group with 95% confidence ellipses
Loading arrows: one arrow per variable, scaled to fit within the score plot bounds
Variable names at arrow tips
Scree plot inset (optional): variance explained per PC
Axes labeled with PC number and variance explained
Centering and scaling disclosure in legend

[Image placeholder: Licklider PCA biplot. Scores: 3 groups (n=15 each) colored red/blue/green with 95% ellipses. Loadings: 10 arrows labeled with variable names, variable names at tips. Inset scree plot (top right corner). Axes: "PC1 (38.4%)" and "PC2 (19.7%)". Legend: "Data centered and scaled to unit variance. Ellipses: 95% bivariate confidence regions."]

Licklider PCA biplot: confidence ellipses per group, labeled loading arrows, inset scree plot, centering/scaling disclosed in legend.

STEP 4 —Draft Output (Draft / Needs review)

Principal Component Analysis (PCA) biplot. Data were centered and scaled
to unit variance prior to PCA. PC1 explains 38.4% of total variance;
PC2 explains 19.7%; together they account for 58.1% of variance.
Sample scores are shown colored by group (n = 15 per group); 95% bivariate
confidence ellipses are shown per group. Loading arrows represent the
contribution of each variable to the displayed principal components.
Variables with arrows pointing toward a group cluster are higher in that group.