adx: Absolute Difference for Pairs - AD(x)

In SEAsic: Score Equity Assessment- summary index computation

Description

The absolute difference index, AD(x), is the absolute value of the simple arithmetic difference between one subpopulation's conditional equated score, y_j(x),and another subpopulation's conditional equated score, y_j'(x). Formally,

AD(x)=|y_j(x) - y_j'(x)|/s,

where x is a score on the original (i.e., not equated) scale, and s is the standard deviation of x scores in the (sub)population of interest. It is considered a pairwise, conditional invariance method. It was adapted by Huggins and Penfield (2012) from the analogous unconditional index, MAD, presented by Kolen and Brennan (2004). It provides practitioners with the magnitude of equated score differences between a pair of subpopulations at each level of the original scale.

Usage

adx(x, g1, g2, d, s, ymax, xlab, color)

Arguments

x	a column vector of scores on which the AD(x) 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)
d	a scalar of the difference that matters
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 adx)
ymax	A maximum value for the y axis of the plot (default = 3 + the maximum AD(x) value)
xlab	A label for the x axis of the plot (default = Score Scale)
color	color of AD(x) line and points on plot (default = red)

Value

A data frame of AD(x) indices, conditioned on the score scale

A plot of the AD(x) indices in reference to the difference that matters

Author(s)

Anne Corinne Huggins-Manley

References

• Huggins, A.C., & Penfield, R.D. (2012). An NCME instructional module on population invariance in linking and equating. Educational Measurement: Issues and Practices, 31, 27-40.

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

See Also

madp

Examples

#Unstandardized AD(x) for subpopulation 1 and subpopulation 2 in the example data set, ex.data
adx(x=ex.data[,1],g1=ex.data[,3],g2=ex.data[,4],d=.5)

#Unstandardized AD(x) for subpopulation 1 and subpopulation 2 in the example data set, ex.data, 
#with adjustments to the maximum y-axis on the plot, a new xlabel, and points/line in blue.
adx(x=ex.data[,1],g1=ex.data[,3],g2=ex.data[,4],d=.5,ymax=2,xlab="AD(x)",color="blue")

#Unstandardized AD(x) for subpopulation 4 and subpopulation 5 in the example data set, ex.data
adx(x=ex.data[,1],g1=ex.data[,6],g2=ex.data[,7],d=.5)

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

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