equate (version 0.1-0)

synthetic: Synthetic Population Values

Description

This function returns the score distribution for a hypothetical synthetic examinee population, as required when equating under the nonequivalent groups design.

Usage

synthetic(x, xv, y, yv, w, method, internal = TRUE, scale, vscale)

Arguments

x

vector of total scores for form X (one per examinee)

xv

vector of scores (one per examinee) for form X examinees on the anchor test

y

vector of total scores for form Y (one per examinee)

yv

vector of scores (one per examinee) for form Y examinees on the anchor test

w

value between 0 and 1 specifying the weight applied to form X scores (and implicitly specifying the form Y weight as 1 - w)

method

string specifying the equating method, where the options are "tucker", levine, and "frequency" (for frequency estimation). For the first two, equating type=linear is assumed, which can only be overridden

internal

logical indicating whether or not the anchor item scores are included in the total scores (default is TRUE). This is only required for the Levine method

scale

the score scale, as a vector (only required for frequency estimation)

vscale

the score scale for the anchor test, as a vector (only required for frequency estimation)

Value

• For the Tucker and Levine methods, a list of length 1 ($synthstats) including the mean and standard deviation for form X, form Y, form XV, form YV, and for the synthetic popultion taking forms X and Y. For the frequency estimation method, a frequency table for the synthetic population taking forms X and Y ($synthtab) is also returned.

Details

The synthetic population score distribution is based on a weighted combination of the form X and Y distributions. The concept of a synthetic population was first described by Braun and Hollan (1982) and Kolen and Brennan (2004) summarize the assumptions made by each equating method.

References

Braun, H. I., & Holland, P. W. (1982). Observed-score test equating: A mathematical analysis of some ETS equating procedures. In P. W. Holland and D. B. Rubin (Eds.), Test Equating (pp. 9-49). New York: Academic. Kolen, M. J., & Brennan, R. L. (2004) Test Equating, Scaling, and Linking. (2nd ed.), New York: Springer.

Examples

x <- KBneat$x[,1]
xv <- KBneat$x[,2]
y <- KBneat$y[,1]
yv <- KBneat$y[,2]
synthetic(x,xv,y,yv,w=1,method="T")
synthetic(x,xv,y,yv,w=1,method="L")
synthetic(x,xv,y,yv,w=1,method="F",scale=0:36,vscale=0:12)