Personality and Individual Differences
Six fictional tasks, a correlation matrix you control, and a first factor that appears whatever structure you put underneath it.
Simulated — fictional tasks, no real intelligence-test data
By the end you should be able to say why a first factor with positive loadings follows arithmetically from the positive manifold, and settles nothing about what produces it.
About 25 minutes. Nothing you do here is saved or sent anywhere.
A factor in this tool is a property of a correlation matrix — a summary of numbers you generated with sliders. It is not a biological entity, a brain structure or a measured quantity.
Across a century of research, scores on almost any pair of cognitive tasks correlate positively. This is called the positive manifold, and factor analysing such a matrix always produces a first factor on which everything loads positively.
Nothing here changes the controls for you, and none of it says what you are going to find.
Three verbal-ish, three spatial-ish. You decide how much of each task's performance is shared with every other task, shared only within its group, or specific and error.
| Task | Group | First-factor loading |
|---|
| Pair | Relationship | Model | Observed in sample |
|---|
Every cognitive task correlates positively with every other, and that pattern is one of the most reliable findings in psychology. What it means is not settled by the pattern. A single shared source produces it; so does a web of overlapping group factors with no general one at all. The first factor is arithmetic performed on the matrix, not evidence about what caused it.