pg-multivariate

name	pg-multivariate
description	Run or generate Pingouin code for multivariate comparisons — Hotelling's T-squared test (multivariate_ttest) — plus the multivariate assumption checks box_m (equal covariance) and multivariate_normality, for designs with several dependent variables.

PG Multivariate

Use when several continuous dependent variables are compared together (a mean-vector / profile question), rather than one outcome at a time.

Load

Read:

• ../../references/supervision-gates.md
• ../../references/pingouin-api-quickref.md
• ../../references/apa-output-template.md if writing results.

Decision Rules

• Compare one group's mean vector to a reference (one-sample) -> pg.multivariate_ttest(X).
• Compare mean vectors of two independent groups -> pg.multivariate_ttest(X, Y).
• Paired multivariate comparison (same participants) -> pg.multivariate_ttest(X, Y, paired=True).
• Check equal covariance matrices across groups (assumption) -> pg.box_m(data, dvs, group).
• Check multivariate normality (assumption) -> pg.multivariate_normality(X).

Required Inputs

• Two or more continuous dependent variables (the outcome vector).
• Grouping column for the two-sample test and Box's M.
• Whether the comparison is one-sample, independent, or paired.
• X/Y are arrays or frames of shape (n, k); drop rows with missing DVs first.

Code Patterns

Hotelling's T-squared, two independent groups:

X = df.loc[df["group"].eq("A"), ["v1", "v2", "v3"]].to_numpy()
Y = df.loc[df["group"].eq("B"), ["v1", "v2", "v3"]].to_numpy()
res = pg.multivariate_ttest(X, Y).round(3)
pg.print_table(res)

One-sample (mean vector vs zero; subtract a reference first if needed):

res = pg.multivariate_ttest(df[["v1", "v2", "v3"]].to_numpy()).round(3)
pg.print_table(res)

Assumption checks:

pg.box_m(df, dvs=["v1", "v2", "v3"], group="group")           # equal covariance
pg.multivariate_normality(df[["v1", "v2", "v3"]], alpha=0.05)  # Henze-Zirkler

Output Checks

multivariate_ttest returns index hotelling with T2, F, df1, df2, pval. box_m returns Chi2, df, pval, equal_cov (bool). multivariate_normality returns (hz, pval, normal); normal=False warns against assuming multivariate normality.

Guardrails

• Hotelling's T-squared needs n greater than the number of DVs and roughly multivariate-normal data; check multivariate_normality.
• A significant Box's M (unequal covariance) undermines the pooled test; report it.
• Pingouin covers Hotelling's T-squared, not full factorial MANOVA — for that recommend statsmodels or R.
• Report T2, F, df, p, and which assumption checks were run.
• End result-bearing answers with one compact S0-S5 audit line.