Test multiple means against a target profile accurately. Review covariance structure, F statistic, and significance. Visualize variable shifts with interactive charts and export data.
Set the dimension, sample size, mean vectors, and covariance matrix.
This example illustrates a three variable test using sample means, hypothesized means, and a covariance structure.
| Variable | Sample Mean | Hypothesized Mean | Variance |
|---|---|---|---|
| Quality Score | 12.4 | 11.8 | 1.80 |
| Speed Score | 9.6 | 10.0 | 1.50 |
| Accuracy Score | 14.1 | 13.5 | 2.10 |
Hotelling T² formula:
T² = n (x̄ − μ₀)' S⁻¹ (x̄ − μ₀)
Where:
F conversion:
F = ((n − p) / (p(n − 1))) × T²
This follows an F distribution with degrees of freedom (p, n − p) for the one sample multivariate mean test.
It tests whether a sample mean vector differs significantly from a hypothesized multivariate mean vector while accounting for covariance among variables.
Use it when variables are correlated. Multiple separate t tests ignore covariance and increase overall false positive risk.
A valid covariance matrix has mirrored covariances because covariance between variable A and B equals covariance between B and A.
The inverse covariance matrix weights the mean differences while adjusting for scale and correlation across variables.
The test cannot be computed correctly because the inverse matrix does not exist. Adjust the covariance inputs or reduce redundancy.
A small p value suggests the observed sample mean vector is unlikely under the hypothesized multivariate mean assumption.
Yes. This calculator supports two to six variables and automatically rebuilds the vector and covariance input fields.
It shows each variable’s mean shift scaled by its variance, helping you see which dimensions contribute most to the multivariate result.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.