Hotelling's T²
Compare two groups on several numeric outcomes at once.
When to use it
Use Hotelling’s T² when you have exactly two groups and several numeric outcomes. It is the multivariate version of the independent-samples t-test. For example: do lecture and workshop students differ on recall and confidence at the same time?
Three or more groups: use MANOVA. One outcome: use the independent-samples t-test.
Assumptions
The outcomes are numeric. The two groups are separate. The outcomes should be roughly multivariate normal, with a similar covariance pattern in each group.
Tensr does not test those assumptions. It does compute η² from the T² statistic and prints it when it is available. You cannot turn that off.
Running it in Tensr
Options
Prop
Type
Reading the output
Two tutorial groups drawn from the same marking scheme, on score and confidence. The groups were not built to differ.
| Variable | A mean | B mean | Difference |
|---|---|---|---|
| score | 68.575 | 68.935 | -0.36 |
| confidence | 48.407 | 51.355 | -2.948 |
Hotelling's T² comparing A vs B on 2 variable(s) (score, confidence). The primary result is not significant (p = .276). This is not large enough to treat the comparison this page is about as a reliable association. The result is non-significant: the data are still compatible with no effect. Metrics: T² = 2.653; F = 1.31; p-value = .276; η² = 0.033.
Reporting (APA 7)
Hotelling's T² comparing A vs B on 2 variable(s) (score, confidence). This result is not significant (p = .276). Report the estimate with that p, and do not describe the pattern as a reliable effect.
Coming from SPSS
The path stored in Tensr is Analyze → Compare Means → Hotelling. The menu you actually open is Analyze → Correlate → Hotelling's T².
SPSS often reaches this test through Multivariate GLM with two groups. Tensr prints T², the converted F, p, η², and the two group means. It does not print a covariance matrix or a univariate t for each outcome.
Related
Three or more groups, or a follow-up ANOVA per outcome: MANOVA. One outcome: independent-samples t-test.