SEAsic (version 0.1)

dx: Difference for Pairs - D(x)

Description

The difference index, $D(x)$, for pairs is 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, $$D(x)=\frac{y_j(x)-y_{j'}(x)}{\sigma_x},$$ 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, $MD$, presented by Kolen and Brennan (2004). It provides practitioners with the direction and magnitude of equated score differences between a pair of subpopulations at each level of the original scale.

Usage

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

Arguments

x

a column vector of scores on which the D(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 positive difference that matters (negative of d will be applied as the negative 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 D(x))

ymax

A maximum value for the y axis of the plot (default = 3 + the maximum D(x) value)(negative of ymax will be applied to ymin of plot)

xlab

A label for the x axis of the plot (default = Score Scale)

color

color of D(x) line and points on plot (default = red)

Value

A data frame of D(x) indices, conditioned on the score scaleA plot of the D(x) indices in reference to the difference that matters

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

mdp

Examples

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

#Unstandardized D(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.
dx(x=ex.data[,1],g1=ex.data[,3],g2=ex.data[,4],d=.5,ymax=2,xlab="AD(x)",color="blue")

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

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