stdPDIF: Standardization DIF statistic

Description Usage Arguments Details Value Author(s) References See Also Examples


Calculates standardized P-difference statistics for DIF detection.


stdPDIF(data, member, match = "score", anchor = 1:ncol(data), stdWeight = "focal")



numeric: the data matrix (one row per subject, one column per item).


numeric: the vector of group membership with zero and one entries only. See Details.


specifies the type of matching criterion. Can be either "score" (default) to compute the test score, or any continuous or discrete variable with the same length as the number of rows of data. See Details.


a vector of integer values specifying which items (all by default) are currently considered as anchor (DIF free) items. See Details.


character: the type of weights used for the standardized P-DIF statistic. Possible values are "focal" (default), "reference" and "total". See Details.


This command computes the standardized P-DIF statistic in the specific framework of differential item functioning (Dorans and Kulick, 1986). It forms the basic command of difStd and is specifically designed for this call. In addition, the standardized alpha values (Dorans, 1989) are also computed as a basis for effect size calculation.

The standardized P-DIF statistic is a weighted average of the difference in proportions of successes in the reference group and in the focal group. The average is computed across the test score strata. The weights can be of three kinds (Dorans, 1989; Dorans and Kulick, 1986) and are specified through the stdWeight argument: the proportion of focal groups examinees within each stratum (stdWeight="focal"), the proportion of reference group examinees within each stratum (stdWeight="reference"), and the proportion of examinees (from both groups) within each stratum (stdWeight="total"). By default, the weights are built from the focal group.

Similarly to the 'alpha' estimates of the common odds ratio for the Mantel-Haenszel method (see mantelHaenszel), the standardized alpha values can be computed as rough measures of effect sizes, after a transformation to the Delta Scale (Holland, 1985). See Dorans (1989, p.228, Eqn.15) for further details.

The data are passed through the data argument, with one row per subject and one column per item. Missing values are allowed but must be coded as NA values. They are discarded from sum-score computation.

The vector of group membership, specified with member argument, must hold only zeros and ones, a value of zero corresponding to the reference group and a value of one to the focal group.

The matching criterion can be either the test score or any other continuous or discrete variable to be passed in the stdPDIF function. This is specified by the match argument. By default, it takes the value "score" and the test score (i.e. raw score) is computed. The second option is to assign to match a vector of continuous or discrete numeric values, which acts as the matching criterion. Note that for consistency this vector should not belong to the data matrix.

Option anchor sets the items which are considered as anchor items for computing standardized P-DIF statistics. Items other than the anchor items and the tested item are discarded. anchor must hold integer values specifying the column numbers of the corresponding anchor items. It is mainly designed to perform item purification.


A list with three arguments:


the vector of the standardized P-DIF statistics.


the vector of standardized alpha values.


a character string, either "score" or "matching variable" depending on the match argument.


Sebastien Beland
Collectif pour le Developpement et les Applications en Mesure et Evaluation (Cdame)
Universite du Quebec a Montreal,
David Magis
Department of Psychology, University of Liege
Research Group of Quantitative Psychology and Individual Differences, KU Leuven,
Gilles Raiche
Collectif pour le Developpement et les Applications en Mesure et Evaluation (Cdame)
Universite du Quebec a Montreal,


Dorans, N. J. (1989). Two new approaches to assessing differential item functioning. Standardization and the Mantel-Haenszel method. Applied Measurement in Education, 2, 217-233. doi: 10.1207/s15324818ame0203_3

Dorans, N. J. and Kulick, E. (1986). Demonstrating the utility of the standardization approach to assessing unexpected differential item performance on the Scholastic Aptitude Test. Journal of Educational Measurement, 23, 355-368. doi: 10.1111/j.1745-3984.1986.tb00255.x

Holland, P. W. (1985, October). On the study of differential item performance without IRT. Paper presented at the meeting of Military Testing Association, San Diego (CA).

Magis, D., Beland, S., Tuerlinckx, F. and De Boeck, P. (2010). A general framework and an R package for the detection of dichotomous differential item functioning. Behavior Research Methods, 42, 847-862. doi: 10.3758/BRM.42.3.847

See Also

difStd, dichoDif, mantelHaenszel


 ## Not run: 
 # Loading of the verbal data

 # All items as anchor items
 stdPDIF(verbal[,1:24], verbal[,26])

 # All items as anchor items, reference group weights
 stdPDIF(verbal[,1:24], verbal[,26], stdWeight = "reference")

 # All items as anchor items, both groups' weights
 stdPDIF(verbal[,1:24], verbal[,26], stdWeight = "total")

 # Removing item 6 from the set of anchor items
 stdPDIF(verbal[,1:24], verbal[,26], anchor = c(1:5,7:24))
## End(Not run)

difR documentation built on July 2, 2020, 3:34 a.m.