SEAsic (version 0.1)

rsd: Root Square Difference

Description

The root square difference index ($RSD$) is a conditional index of the absolute differences between a single subpopulation $j$'s equated score, $y_j(x)$, and the equated score based on the overall population, $y(x)$. Formally, $$RSD_j(x)=\frac{\mid y_j(x)-y(x)\mid}{\sigma_x},$$ where $x$ is a score on the original (i.e., unequated) scale, and $s$ is the standard deviation of x scores in the (sub)population of interest. It is considered a group-to-overall, conditional index. It was adapted from Yang's $RESDj$ (2004) by Huggins and Penfield (2012). It provides practitioners with the magnitude of differences between a single subpopulation's equated scores and the equated score based on the overall population, at each score level on the original score scale.

Usage

rsd(x, o, g, d, s, ymax, xlab, color)

Arguments

x

a column vector of scores on which the rsd is conditioned

o

a column vector of equated scores based on the overall population (aligned with elements in x)

g

a column vector of equated scores based on a 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 rsd)

ymax

A maximum value for the y axis of the plot (default = 3 + the maximum RSD value)

xlab

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

color

of RSD line and points on plot (default = red)

Value

A data frame of root square difference indices, conditioned on the score scaleA plot of the RSD 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.
• Yang, W.L. (2004). Sensitivity of linkings between AP multiple-choice scores and composite scores to geographical region: An illustration of checking for population invariance. Journal of Educational Measurement, 41, 33-41.

See Also

resd

Examples

#Unstandardized RSD for subpopulation 1 in the example data set, ex.data
rsd(x=ex.data[,1],o=ex.data[,2],g=ex.data[,3],d=.5)

#Unstandardized RSD for subpopulation 5 in the example data set, ex.data
rsd(x=ex.data[,1],o=ex.data[,2],g=ex.data[,7],d=.5)

#Unstandardized RSD for subpopulation 5 in the example data set, ex.data 
#with adjustments to the maximum y-axis on the plot, a new x label, 
#and points/line in green
rsd(x=ex.data[,1],o=ex.data[,2],g=ex.data[,7],d=.5,ymax=3,xlab="Old Form",color="green")

#Standardized RSD for subpopulation 5 in the example data set, ex.data
rsd(x=ex.data[,1],o=ex.data[,2],g=ex.data[,7],d=.5,s=4.2)