Six cognitive/achievement test scores for children classified into four
reading-achievement groups (Severe, Mild, Average, Superior),
reconstructed from the group means, standard deviations, and pooled
within-cells correlations reported as a worked "real data example" in
Bray & Maxwell (1985), Table 2.3.
Individual rows are simulated, not the original observations: only
group-level summary statistics were published, with no raw data and no
per-group correlations (a single correlation matrix, pooled across all
four groups, was reported). Each group was drawn from a multivariate
normal with that group's reported means and a covariance matrix built
from that group's reported SDs combined with the pooled correlations,
then forced to match those exact moments via
MASS::mvrnorm(..., empirical = TRUE). Summarizing this data frame by
Group exactly reproduces Bray & Maxwell's Table 2.3 (see
data-raw/ReadingDisability.R).
B&M (p.38) describe the six measures as follows: "The PPVT is a general
verbal measure of IQ, whereas the VF and SIM tests are verbal criteria.
The EF taps higher-order nonverbal abilities, whereas the VMI and RD
are general nonverbal measures."