synthetic {equate}R Documentation

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, y, w, method, internal = TRUE)

Arguments

x, y bivariate score distributions of class “freqtab” for forms X, with the anchor, and Y with the anchor. Columns 1 and 2 of each include all score combinations for the total and anchor test score scales, and column 3 contains the number of examinees obtaining each combination (see freqtab for details)
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 via equate and equate.ln. Frequency estimation implies type=equipercentile
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

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.

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.

Author(s)

Anthony Albano tony.d.albano@gmail.com

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

[Package equate version 0.1-1 Index]