Let $\Pi_m$ denote the $m$th population with a
$p$-dimensional multivariate normal distribution,
$N_p(\mu_m, \Sigma_m)$ with mean vector $\mu_m$
and covariance matrix $\Sigma_m$. Also, let $e_m$
be the $m$th standard basis vector (i.e., the
$m$th element is 1 and the remaining values are 0).
Then, we define $$\mu_m = \Delta \sum_{j=1}^{p/M}
e_{(p/M)(m-1) + j}.$$ Note that p must be divisible
by M. By default, the first 10 dimensions of
$\mu_1$ are set to delta with all remaining
dimensions set to 0, the second 10 dimensions of
$\mu_2$ are set to delta with all remaining
dimensions set to 0, and so on. Also, we consider intraclass covariance (correlation)
matrices such that $\Sigma_m = \sigma^2 (1 - \rho_m)
J_p + \rho_m I_p$, where $-(p-1)^{-1} < \rho_m < 1$,
$I_p$ is the $p \times p$ identity matrix, and
$J_p$ denotes the $p \times p$ matrix of ones.
By default, we let $M = 5$, $\Delta = 0$, and
$\sigma^2 = 1$. Furthermore, we generate 25
observations from each population by default.
For $\Delta = 0$ and $\rho_m = \rho$, $m = 1,
\ldots, M$, the $M$ populations are equal.