help for delta                                             Jean-Benoit Hardouin


delta varlist [if exp] [in range] [, ci(#) nodots minscore(#) maxscore(#)]


delta computes the generalized delta index of scale discrimination developed by Hankins (2007) based on the original work of Ferguson (1949). This index measures the scale's ability to distinguish between individuals. A value of 1 indicates that the test has maximal discrimination (all possible scores occur with the same frequency) and a value of 0 means that the test has minimal discrimination (all the respondents have the same score). A value of 0.9 results from a set of scores that is normally distributed. A value of 1 is observed if the scores follow a uniform distribution. Individuals with a missing score are omitted.


If varlist is composed of only one variable, the delta module considers that this variable is the score of the individuals.

ci(#) estimates the confidence interval by boostrap. # is the number of replications to be performed. By default, no confidence interval is calculated.

nodots avoids displaying a dot for each replication (only with ci).

minscore(#) defines the minimal value of the score. By default, this value is fixed to 0.

maxscore(#) defines the maximal value of the score. By default, the maximal observed score is used.


r(delta): Observed value of the delta index.


. delta itemA*

. delta itemA*, ci(500) dots

. delta score, scoremax(8)


Ferguson G. A. (1949) On the theory of test discrimination. Psychometrika, 14: 61-68.

Hankins M. (2007) Questionnaire discrimination: (re)- introducting coefficient delta. BMC Medical Research Methodology, 7: 19.


Jean-Benoit Hardouin, PhD, assistant professor Team of Biostatistics, Clinical Research and Subjective Measures in Health Sciences University of Nantes - Faculty of Pharmaceutical Sciences 1, rue Gaston Veil - BP 53508 44035 Nantes Cedex 1 - FRANCE Email: jean-benoit.hardouin@univ-nantes.fr Websites AnaQol and FreeIRT

Also see

Online: help for alpha and loevH if installed.