Principal component analysis
Compress correlated variables into a smaller set of components.
When to use it
Use PCA when you have several correlated scores and want a few components that keep as much of the variance as possible. It is a compression of the variables, not a test that a particular factor model is true. For a stated factor model, use confirmatory factor analysis.
Assumptions
Variables are numeric. Tensr standardizes them first, so the analysis is on the correlation matrix, not the covariance matrix. Rows with any missing value are dropped. There is no KMO or Bartlett test on this request.
Running it in Tensr
Options
Prop
Type
The wizard may send an empty string for the component count. That has to become null before it reaches the API. A blank field means “let the server decide.”
Reading the output
Six items from that same scale. The first component should take a clear share and leave a real second component.
| Component | Eigenvalue | Variance % | Cumulative % |
|---|---|---|---|
| PC1 | 2.286 | 37.782% | 37.782% |
| PC2 | 1.024 | 16.923% | 54.705% |
| Variable | PC1 | PC2 |
|---|---|---|
| item1 | 0.378 | -0.316 |
| item2 | 0.426 | -0.429 |
| item3 | 0.448 | -0.32 |
| item4 | 0.449 | 0.231 |
| item5 | 0.414 | 0.291 |
| item6 | 0.321 | 0.69 |
PCA on 6 variables, n = 120. PCA on 6 variables, n = 120. Metrics: Components = 2; PC1 variance = 37.782%.
Reporting (APA 7)
PCA on 6 variables, n = 120. Report the estimate in the table. This procedure is not summarised by one p-value.
Coming from SPSS
Analyze → Dimension Reduction → Factor, Extraction: Principal components. SPSS can also print KMO and Bartlett’s test. This request does not.