The complete data set from Holzinger and Swineford's (1939) A study in factor analysis: The stability of a bi-factor solution. Scores on 26 ability tests for 301 seventh and eighth grade pupils at two Chicago elementary schools, Pasteur (n = 156) and Grant-White (n = 145). The data have been used over the subsequent decades as one of the most-cited benchmarks in factor analysis, confirmatory factor analysis, structural equation modeling, and reliability research.
holzinger_swinefordA data frame with 301 observations and 34 variables.
idCase identifier as in the original monograph. The numbering is not strictly consecutive; a small number of cases were dropped during data preparation and the original numbering was preserved (hence the visible skips).
sexFactor with levels Female and Male.
gradeGrade in school, 7 or 8.
ageAge in completed years, ignoring months past the most recent birthday.
month_since_birthdayCompleted months since the most recent birthday.
age_monthsAge in completed months, computed as
12 * age + month_since_birthday.
age_yearsAge in fractional years, computed as
age + month_since_birthday / 12.
schoolFactor with levels Grant-White and
Pasteur, naming the two Chicago elementary schools from
which pupils were drawn.
t1_visual_perceptionVisual perception test (spatial).
t2_cubesCubes test (spatial).
t3_paper_form_boardPaper form board test (spatial).
t4_lozengesLozenges test (spatial).
t5_general_informationGeneral information test (verbal).
t6_paragraph_comprehensionParagraph comprehension test (verbal).
t7_sentenceSentence completion test (verbal).
t8_word_classificationWord classification test (verbal).
t9_word_meaningWord meaning test (verbal).
t10_additionAddition test (mental speed).
t11_codeCode test (mental speed).
t12_counting_groups_of_dotsCounting groups of dots test (mental speed).
t13_straight_and_curved_capitalsStraight and curved capitals test (mental speed).
t14_word_recognitionWord recognition test (memory).
t15_number_recognitionNumber recognition test (memory).
t16_figure_recognitionFigure recognition test (memory).
t17_object_numberObject-number test (memory).
t18_number_figureNumber-figure test (memory).
t19_figure_wordFigure-word test (memory).
t20_deductionDeduction test (reasoning).
t21_numerical_puzzlesNumerical puzzles test (reasoning).
t22_problem_reasoningProblem reasoning test (reasoning).
t23_series_completionSeries completion test (reasoning).
t24_woody_mccallWoody-McCall mixed fundamentals, form I (arithmetic).
t25_paper_form_board_rRevised paper form board,
administered only to the Grant-White pupils as an experimental
substitute for t3_paper_form_board. NA for the
156 Pasteur pupils.
t26_flagsFlags test, administered only to the
Grant-White pupils as an experimental substitute for
t4_lozenges. NA for the 156 Pasteur pupils.
Ken Kelley
Karl John Holzinger (1893 to 1954) was a quantitative psychologist at the University of Chicago and one of the central figures in the first generation of factor analysis. He spent the 1922 to 1923 academic year working with Charles Spearman at University College London, absorbing Spearman's two-factor theory of intelligence, and later developed the bi-factor model as an extension of that theory. The bi-factor model posits a single general intelligence factor that runs through all tests, plus several group factors that capture residual correlation among substantively related subgroups of tests. It is widely regarded as a precursor of modern hierarchical and orthogonal-bifactor models in psychometrics. Frances Swineford was Holzinger's research collaborator at the University of Chicago and a coauthor on much of his applied work.
The 1939 monograph reports a study of pupils in seventh and eighth grade classrooms at two Chicago elementary schools, Pasteur and Grant-White. Two schools were used deliberately, so that the stability of a bi-factor solution could be assessed by fitting the same model in each school and comparing the results. The 26 tests were designed to span five hypothesized ability domains:
Spatial: tests 1 to 4 (visual perception, cubes, paper form board, lozenges), with tests 25 (a revised paper form board) and 26 (flags) administered only to the Grant-White sample as experimental substitutes for tests 3 and 4.
Verbal: tests 5 to 9 (general information, paragraph comprehension, sentence completion, word classification, word meaning).
Mental speed: tests 10 to 13 (addition, code, counting groups of dots, straight and curved capitals).
Memory: tests 14 to 19 (word recognition, number recognition, figure recognition, object-number, number-figure, figure-word).
Reasoning and arithmetic: tests 20 to 24 (deduction, numerical puzzles, problem reasoning, series completion, Woody-McCall mixed fundamentals).
Holzinger and Swineford concluded that the bi-factor solution was reasonably stable across the two schools, supporting the substantive interpretation of a general factor together with group factors.
The data have far outlived their original purpose. Jöreskog (1969)
used a 9-test subset drawn from the Grant-White sample
(n = 145) to introduce confirmatory maximum likelihood
factor analysis; that 9-test subset is the version most modern
confirmatory factor analysis tutorials use and is shipped in
per-item-rescaled form as HolzingerSwineford1939 in the
lavaan package. The complete 26-test data shipped here
support a wider range of analyses, including comparisons of the
spatial, verbal, speed, memory, and reasoning ability blocks and
multiple group analyses across the Pasteur and Grant-White
schools.
The values in holzinger_swineford are the corrected
version of the data, identical on all 26 test cells to
MBESS::HS from MBESS version 4.9.3 onward and to
psychTools::holzinger.raw. An older version of the data,
with approximately 53 cell values that were later corrected,
continues to circulate as HS.data in the sem package
and as HS.ability.data in the OpenMx package; both
are byte-identical snapshots taken from MBESS version 4.6.0
prior to the correction. The corrections are concentrated on the
memory and reasoning tests, with the largest cluster on
t20_deduction (15 cells, including a number of sign flips
that reflect a corrected guessing-penalty adjustment).
Holzinger, K. J., and Swineford, F. (1939). A study in factor analysis: The stability of a bi-factor solution (Supplementary Educational Monographs, No. 48). University of Chicago Press.
Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183--202.
Holzinger, K. J. (1944). A simple method of factor analysis. Psychometrika, 9, 257--262.
data(holzinger_swineford)
str(holzinger_swineford)
# School and grade breakdown.
table(holzinger_swineford$school, holzinger_swineford$grade)
# Jöreskog (1969) drew nine tests from the Grant-White sample, and
# that subset became the modern confirmatory factor analysis
# benchmark.
joreskog_subset <- subset(
holzinger_swineford,
school == "Grant-White",
select = c(t1_visual_perception, t2_cubes, t4_lozenges,
t6_paragraph_comprehension, t7_sentence,
t9_word_meaning, t10_addition,
t12_counting_groups_of_dots,
t13_straight_and_curved_capitals)
)
dim(joreskog_subset)
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