Understanding PCA Loadings and Scores

A PCA gives you components, loadings, and scores. Loadings tell you what each component means; scores tell you where each observation sits. Here's how to read both.

Running a PCA is easy; interpreting it is where people get stuck. Two outputs do the work: loadings and scores.

Loadings: what a component means

Each principal component is a weighted blend of your original variables, and the weights are the loadings. A variable with a big positive loading pushes a component up; a big negative one pulls it down; a near-zero loading barely matters. You name a component by reading its strong loadings — if a component loads heavily on height, weight, and shoe size, it's a “body size” axis.

A PCA loadings table in Stratum — Loadings show how each variable contributes to each component.

Scores: where an observation sits

The scores are each observation's coordinates on the new components — plug its values into the weighted blend and you get its score. A high score on the “body size” component means a physically larger individual. Plotting scores on the first two components is how you spot clusters and outliers in reduced space.

Sign is arbitrary. PCA can flip a component's sign without changing anything — what matters is the relative loadings, not whether they're positive or negative. Don't over-read the direction; read which variables group together.

Common mistakes

Forgetting to standardize — then a high-variance variable hijacks the first component.
Interpreting tiny components — if a component explains 3% of the variance, its loadings are mostly noise.
Treating PCA as causal — components describe correlation structure, not cause.

See it end to end in the PCA lesson, or start with How to Run PCA.

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Frequently asked questions

What are PCA loadings?

The weights that say how much each original variable contributes to a principal component. Reading the strong loadings is how you name and interpret a component.

What's the difference between loadings and scores?

Loadings describe the components (how variables combine to form them). Scores describe the observations (each row's coordinates on those components).

Why can the sign of a loading flip?

PCA components are only defined up to a sign, so software may flip a whole component without changing the result. Interpret the relative loadings, not the absolute sign.

How do I name a principal component?

Look at which variables have the largest loadings (positive and negative) and describe the theme they share — e.g. “size,” “price level,” or “intensity.”