SEAsic (version 0.1)

mdp: Mean Difference for Pairs

Description

The mean difference index ($MD$) for pairs is the unconditional version of $D(x)$. It is the expectation across $x$ of the arithmetic differences between any $y_j(x)$ and $y_j'(x)$ equated scores. Formally, $$MD=\frac{\sum_{x}P_x\lbrack y_j(x)-y_{j'}(x)\rbrack}{\sigma_x},$$ where $P$ 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 pairwise, unconditional index. It was originally presented by Kolen and Brennan (2004). It provides practitioners with a summary of the magnitude and direction of mean differences between equated scores based on two subpopulations.

Usage

mdp(x, g1, g2, f, s)

Arguments

x

a column vector of scores on which the rsd 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)

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 mean difference)

Value

mean difference

References

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

See Also

dx

Examples

#Unstandardized MD for subpopulations 1 and 2 in the example data set, ex.data
mdp(x=ex.data[,1],g1=ex.data[,3],g2=ex.data[,4],f= ex.data[,8])

#Unstandardized MD for subpopulations 4 and 5 in the example data set, ex.data
mdp(x=ex.data[,1],g1=ex.data[,6],g2=ex.data[,7],f= ex.data[,8])

#Standardized MD for subpopulations 4 and 5 in the example data set, ex.data
mdp(x=ex.data[,1],g1=ex.data[,6],g2=ex.data[,7],f= ex.data[,8],s=4.2)