PerFit (version 1.2)

G, Gnormed: Number of Guttman errors

Description

van der Flier's statistics based on the number of Guttman errors.

Usage

G(matrix)

Gnormed(matrix)

Arguments

matrix

A data matrix of dichotomous item scores: Persons as rows, items as columns, item scores are either 0 or 1, no missing data.

Value

• An object of class "PerFit", which is a list with elements:
• PFscores
  A vector of length $N$ (number of respondents) with the values of the person-fit statistic.
• PFstatistic
  The name of the person-fit statistic used.

Details

Consider the items' proportion-correct scores, $p_1,p_2,\ldots,p_I$ ($I$ = number of items). A Guttman error consists of an item score pair $(X_i,X_j)=(0,1)$ with $p_i>p_j$. Hence, there is a Guttman error when an easier item is answered incorrectly and a more difficult item is answered correctly. G counts the number of (0,1) pairs given that the items are ordered in decreasing proportion-correct scores order. However, G depends on the total number of items for a given number-correct score. In particular, for a number-correct $S$, G has maximum equal to $S(I-S)$. Gnormed was created to bound G between 0 and 1 by dividing it by its maximum (conditional on the number-correct score). Hence, (potentially) aberrant response behavior is indicated by large values of G/Gnormed (i.e., in the right tail of the sampling distribution). Gnormed is perfectly linearly related to Tatsuoka and Tatsuoka's (1982, 1983) NCI statistic ($NCI = 1-2Gnormed$).

References

Karabatsos, G. (2003) Comparing the Aberrant Response Detection Performance of Thirty-Six Person-Fit Statistics. Applied Measurement In Education, 16(4), 277--298. Meijer, R. R. (1994) The number of Guttman errors as a simple and powerful person-fit statistic. Applied Psychological Measurement, 18(4), 311--314. Meijer, R. R., and Sijtsma, K. (2001) Methodology review: Evaluating person fit. Applied Psychological Measurement, 25(2), 107--135. Tatsuoka, K. K., and Tatsuoka, M. M. (1982) Detection of aberrant response patterns and their effect on dimensionality. Journal of Educational Statistics, 7(3), 215--231. Tatsuoka, K. K., and Tatsuoka, M. M. (1983) Spotting erroneous rules of operation by the individual consistency index. Journal of Educational Measurement, 20(3), 221--230. van der Flier, H. (1977) Environmental factors and deviant response patterns. In Y. H. Poortinga (Ed.), Basic problems in cross-cultural psychology. Amsterdam: The Netherlands.

See Also

NCI

Examples

# Load the inadequacy scale data (dichotomous item scores):
data(InadequacyData);

# Compute the G scores:
G(InadequacyData);

# Compute the Gnormed scores:
Gnormed(InadequacyData);