Tatsuoka's (1984) fraction subtraction data set is comprised of responses to \(J=20\) fraction subtraction test items from \(N=536\) middle school students.
data(fraction.subtraction.data)The fraction.subtraction.data data frame consists of 536
rows and 20 columns, representing the responses of the \(N=536\)
students to each of the \(J=20\) test items. Each row in the data set
corresponds to the responses of a particular student. Thereby a "1"
denotes that a correct response was recorded, while "0" denotes an
incorrect response. The other way round, each column corresponds
to all responses to a particular item.
The items used for the fraction subtraction test originally appeared
in Tatsuoka (1984) and are published in Tatsuoka (2002). They
can also be found in DeCarlo (2011). All test items are based on 8
attributes (e.g. convert a whole number to a fraction, separate a whole
number from a fraction or simplify before subtracting). The complete
list of skills can be found in fraction.subtraction.qmatrix.
DeCarlo, L. T. (2011). On the analysis of fraction subtraction data: The DINA Model, classification, latent class sizes, and the Q-Matrix. Applied Psychological Measurement, 35, 8--26.
Tatsuoka, C. (2002). Data analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society, Series C, Applied Statistics, 51, 337--350.
Tatsuoka, K. (1984). Analysis of errors in fraction addition and subtraction problems. Final Report for NIE-G-81-0002, University of Illinois, Urbana-Champaign.
fraction.subtraction.qmatrix for the corresponding Q-matrix.