SEAsic (version 0.1)

resd: Root Expected Square Difference

Description

The root expected square difference index ($RESDj$) is a summary index of the weighted differences between a single subpopulation's equated scores, $y_j(x)$, and the equated scores based on the overall population, $y(x)$. Formally, $$RESD_j=\frac{\sqrt{\sum_x P_x \{\lbrack y_j(x)-y(x)\rbrack^2\}}}{\sigma_x,}$$ where $x$ is a score on the original (i.e., unequated) scale, $P$ is the proportion of examinees scoring at $x$ and $s$ is the standard deviation of x scores in the (sub)population of interest. It is considered a group-to-overall, unconditional index. It was originally presented by Yang (2004). It provides practitioners with a summary of the magnitude of differences between a single subpopulation's equated scores and equated scores based on the overall population.

Usage

resd(x, o, g, f, s)

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)

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 resd)

Value

root expected square difference

References

• 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

rsd

Examples

#Unstandardized RESD for subpopulation 1 in the example data set, ex.data
resd(x=ex.data[,1],o=ex.data[,2],g=ex.data[,3],f=ex.data[,8])

#Unstandardized RESD for subpopulation 5 in the example data set, ex.data
resd(x=ex.data[,1],o=ex.data[,2],g=ex.data[,7],f=ex.data[,8])

#Standardized RESD for subpopulation 5 in the example data set, ex.data
resd(x=ex.data[,1],o=ex.data[,2],g=ex.data[,7],f=ex.data[,8],s=4.2)