Description Usage Arguments Value Author(s) References See Also Examples
The expected maximum difference index, EMAXD, locates the maximum absolute difference between subpopulation equated scores, y_j(x), and the equated scores based on the overall population, y(x), at each score level x, and then takes the expectation of those maximum scores across score levels. Formally,
EMAXD=sum(P(max[|y_j(x)-y(x)|]))/s,
where P represents a proportion of examinees based on the population distribution specified in argument f, and s is the standard deviation of x scores in the (sub)population of interest. It is considered an omnibus, unconditional index that was originally presented by Dorans and Holland (2000). It provides practitioners with a summary of the maximum differences found between subpopulation and overall equated scores.
1 | emaxd(x, o, g, n, f, s)
|
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 |
column vectors of equated scores based on various subpopulations (aligned with elements in x) |
n |
a scalar indicating the number of groups |
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 emaxd) |
expected maximum difference
Anne Corinne Huggins-Manley
Dorans, N.J., & Holland, P.W. (2000). Population invariance and the equitability of tests: Theory and the linear case. Journal of Educational Measurement, 37, 281-306.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | #Unstandardized EMAXD across subpopulation 1 and subpopulation 2 in the example data set, ex.data
emaxd(x=ex.data[,1],o=ex.data[,2],
g=c(ex.data[,3],ex.data[,4]),
n=2,f=ex.data[,8])
#Unstandardized EMAXD across subpopulations 1 thru 5 in the example data set, ex.data
emaxd(x=ex.data[,1],o=ex.data[,2],
g=c(ex.data[,3],ex.data[,4],ex.data[,5],ex.data[,6],ex.data[,7]),
n=5,f=ex.data[,8])
#Standardized EMAXD across subpopulations 1 thru 5 in the example data set, ex.data
emaxd(x=ex.data[,1],o=ex.data[,2],
g=c(ex.data[,3],ex.data[,4],ex.data[,5],ex.data[,6],ex.data[,7]),
n=5,f=ex.data[,8],s=4.2)
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