madp: Mean Absolute Difference for Pairs

In SEAsic: Score Equity Assessment- summary index computation

Description

The mean absolute difference index, MAD, is a summary of the conditional AD(x) index, specifically the mean of absolute differences at each score level x. Formally,

MAD(x)=sum(P|y_j(x) - y_j'(x)|)/s,

where y_j(x) is an equated score based on subpopulation j, y_j'(x) is an equated score based on subpopulation j', P represents a proportion of examinees based on the population distribution specified in argument f, and s is the standard deviation of x scores for the (sub)population of interest. It is considered a pairwise, unconditional invariance method. It was originally presented by Kolen and Brennan (2004). It provides practitioners with a summary of the magnitude of equated score differences between two subpopulations.

Usage

madp(x, g1, g2, f, s)

Arguments

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 madp)

Value

mean absolute difference

Note

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.

Author(s)

Anne Corinne Huggins-Manley

References

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

See Also

adx

Examples

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

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

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

Example output

[1] 0.29631
[1] 5.07474
[1] 1.208271

SEAsic documentation built on May 2, 2019, 2:09 p.m.