Principal Components Analysis

Verified

Factor Analysis

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

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Reduces many correlated variables into a few uncorrelated components that capture most of the variance.

PCA finds linear combinations (components) ordered by how much variance they explain — useful for dimension reduction, composite indices, or spotting structure. It's descriptive, not a latent-measurement model.

Worked example

Can 12 economic indicators be summarised by a few components?

PCA on 12 standardised indicators (n = 200), using a scree plot to choose the number of components.

Result

Three components (eigenvalue > 1) explained 73% of the variance; the first component alone accounted for 29%.

How you'd report it (APA)

A PCA reduced the 12 indicators to three components explaining 73% of the variance.

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Reducing many correlated variables
    You want a few uncorrelated components that capture most of the variance. e.g. 12 economic indicators into 3 components.
  • Building a composite index
    The first component is a common way to weight indicators into a single index.
  • A quick look at structure
    Scree and loadings hint at how many dimensions the data carry — as description, before any modelling.

When NOT to — use instead

Assumptions (and what to do if they fail)

Variables are correlated enough to reducehigh

Check: Check sampling adequacy (KMO ≥ .6) and Bartlett's test before extracting; near-uncorrelated variables cannot be summarised.

If violated: PCA on essentially independent variables just relabels them — nothing is reduced.

Scale matters — standardizehigh

Check: PCA on the covariance matrix lets large-variance variables dominate; use the correlation matrix (standardized) unless the scales are comparable on purpose.

If violated: One high-variance variable can hijack the first component.

Components are descriptive, not measurementmedium

Check: Do not interpret components as error-free latent traits.

If violated: Treating a component as a latent factor over-claims what PCA delivers.

Linear relationshipslow

Check: PCA captures linear structure; strong non-linearity is missed.

If violated: Curved structure is under-represented in the components.

Ready to run a Principal Components Analysis on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

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