SEAsic (version 0.1)

madp: Mean Absolute Difference for Pairs

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, $$MAD(x)=\frac{\sum_x P_x\mid y_j(x) - y_{j'}(x) \mid}{\sigma_x},$$ 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

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)