mdp: Mean Difference for Pairs
In SEAsic: Score Equity Assessment- summary index computation

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

The mean difference index (MD) for pairs is the unconditional version of D(x). It is the expectation across x of the arithmetic differences between any y_j(x) and y_j'(x) equated scores. Formally,

MD=sum(P[y_j(x)-y_j'(x)|])/s,

where P is the proportion of examinees scoring at x and s is the standard deviation of x scores in the (sub)population of interest. It is considered a pairwise, unconditional index. It was originally presented by Kolen and Brennan (2004). It provides practitioners with a summary of the magnitude and direction of mean differences between equated scores based on two subpopulations.

1	mdp(x, g1, g2, f, s)

`x`	a column vector of scores on which the rsd is conditioned
`g1`	a column vector of equated scores based on a single subpopulation (aligned with elements in x)
`g2`	a column vector of equated scores based on a different single subpopulation (aligned with elements in x)
`f`	a column vector of relative frequency associated with each raw score (can be based on either overall population or a subpopulation) (aligned with elements in x)
`s`	a scalar representing the standard deviation of x for any (sub)population of interest (e.g., synthetic population) (default is 1, which leads to calculation of the unstandardized mean difference)

mean difference

The equally weighted version of this index (Kolen & Brennan, 2004) can be obtained by inputting an f vector consisting of identical elements that sum to 1. For example, using f=c(rep(.047619,21)) with the example data set, ex.data.

Anne Corinne Huggins-Manley

Kolen, M.J., & Brennan, R.L. (2004). Test equating, scaling, and linking: Methods and practices (2nd ed.). NY: Springer.

dx

#Unstandardized MD for subpopulations 1 and 2 in the example data set, ex.data
mdp(x=ex.data[,1],g1=ex.data[,3],g2=ex.data[,4],f= ex.data[,8])

#Unstandardized MD for subpopulations 4 and 5 in the example data set, ex.data
mdp(x=ex.data[,1],g1=ex.data[,6],g2=ex.data[,7],f= ex.data[,8])

#Standardized MD for subpopulations 4 and 5 in the example data set, ex.data
mdp(x=ex.data[,1],g1=ex.data[,6],g2=ex.data[,7],f= ex.data[,8],s=4.2)