Canonical correlation
Relate two sets of columns, not just one pair.
When to use it
Use canonical correlation when each side has more than one column. For example: how does the set of study hours and anxiety line up with the set of recall and confidence? Bivariate correlation only looks at one pair at a time. This finds a weighted combination on each side that correlates as strongly as possible, then a second combination, and so on.
Assumptions
The columns are numeric. The first canonical correlation is the one to read. Later functions are leftover association after the first is removed. Tensr does not test multivariate normality.
Running it in Tensr
Options
Prop
Type
Reading the output
One set is exam score and confidence. The other is hours and anxiety. The sets share a moderate link and a lot of leftover variance.
| Function | Wilks' Λ | F | df | p-value |
|---|---|---|---|---|
| Function 1 | 0.739 | 22.171 | 4 | < .001 |
| Function 2 | 0.964 | 3.52 | 1 | .064 |
| Variable | Function 1 | Function 2 |
|---|---|---|
| score | 0.996 | -0.089 |
| confidence | 0.277 | 0.961 |
Canonical correlation: score, confidence ↔ hours, anxiety, n = 96. Function 1 accounts for 23.3% of shared variance between the two variable sets. Canonical correlation: score, confidence ↔ hours, anxiety, n = 96. Function 1 accounts for 23.3% of shared variance between the two variable sets. Metrics: Canonical r1 = 0.483; Canonical r2 = 0.191.
Reporting (APA 7)
Canonical correlation: score, confidence ↔ hours, anxiety, n = 96. Function 1 accounts for 23.3% of shared variance between the two variable sets. Report the estimate in the table. This procedure is not summarised by one p-value.
Coming from SPSS
Analyze → Correlate → Canonical.
SPSS canonical correlation is a macro in many installations rather than a base dialog. Tensr’s menu path is Analyze → Correlate → Canonical.
Related
One pair of columns is bivariate correlation. Grouping people from several scores is discriminant analysis.