The study. Robert Rosenthal (Harvard University) and Lenore
Jacobson (principal of an elementary school in South San Francisco
referred to as "Oak School") set out to test experimentally whether
teacher expectations influence pupil achievement. At the start of the
school year all children were given a standardized test of general
ability, described to teachers as the "Harvard Test of Inflected
Acquisition," a test said to identify children poised for an
intellectual growth spurt. In reality the instrument was Flanagan's
Tests of General Ability (TOGA) and the children identified as likely
"bloomers" were chosen at random, about one in five per
classroom. The only experimental manipulation was the expectation
planted in the teachers' minds. Children were re-tested over the
following year(s), and the question was whether the randomly labeled
bloomers would out-gain their controls in measured IQ. Rosenthal and
Jacobson reported that they did, most strongly in the earliest
grades, and interpreted the difference as evidence that teacher
expectations operate as a self-fulfilling prophecy. The study became
one of the most famous and most debated experiments in the social
sciences; subsequent critiques (e.g., Thorndike, 1968) questioned the
reliability of the TOGA at the extremes of the score range for the
youngest children, which is itself part of why the data are
instructive for teaching careful analysis.
Why it is a benchmark for heterogeneity of regression. A
standard ANCOVA adjusts the group comparison for the pretest
covariate under the assumption that the regression of the outcome on
the covariate has the same slope in every group (homogeneity
of regression). In these data that assumption is questionable: the
within-group regression of iq_8 on iq_pre is steeper
for the bloomers than for the controls, so the estimated treatment
effect depends on the covariate value at which it is evaluated. This
makes the data an ideal teaching example for (a) testing the
homogeneity-of-regression assumption, (b) interpreting a
treatment-by-covariate interaction, and (c) estimating the treatment
effect, and its sampling variance, at chosen covariate values
rather than only at the grand mean.
Reproducible quantities. Fitting the separate-slopes model
lm(iq_8 ~ iq_pre * treatment) gives a within-group slope of
\(0.77799\) for the controls and \(0.96894\) for the bloomers
(reported as \(0.96895\) in MBESS::var.ete, a fifth-decimal
rounding difference). The pooled within-group residual variance is
\(\hat\sigma^2 = 175.3251\) on 306 degrees of freedom, and the
sample variance of the covariate is \(348.91\). These are exactly
the inputs used in the worked example for the variance of the
estimated treatment effect at selected covariate values under
heterogeneity of regression (Li, McLouth, and Delaney; see
MBESS::var.ete).
Relationship to the AMCP package. The same numeric data
ship with the book's data companion, the AMCP package, as
chapter_9_exercise_15 and chapter_9_extension_exercise_3
(with IQGain) and chapter_3_exercise_22 (without it).
The version here renames the columns to DMAR's descriptive
snake_case style and labels the experimental condition as a factor;
no measured value has been altered. See data-raw/pygmalion.R
for the construction script and its verification checks.