# fraction.subtraction.data: Fraction Subtraction Data In CDM: Cognitive Diagnosis Modeling

 fraction.subtraction.data R Documentation

## Fraction Subtraction Data

### Description

Tatsuoka's (1984) fraction subtraction data set is comprised of responses to J=20 fraction subtraction test items from N=536 middle school students.

### Usage

```  data(fraction.subtraction.data)
```

### Format

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.

### Details

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`.

### Source

The Royal Statistical Society Datasets Website, Series C, Applied Statistics, Data analytic methods for latent partially ordered classification models:

### References

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.