pg-multivariatelisted

# 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: ```python 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): ```python res = pg.multivariate_ttest(df[["v1", "v2", "v3"]].to_numpy